Batting by F.C. Lane

I mentioned in a previous post that I recently came across a copy of F.C. Lane's (1885-1984) 1925 book Batting: One Thousand Expert Opinions on Every Conceivable Angle of Batting Science. This book was originally published as a supplement to Baseball Magazine at the price of $1 and contains quotes from over 250 players, managers, umpires, and owners on the nature of hitting covering everything from choosing a bat to dealing with umpires to pulling the ball and the merits of "slugging". Lane pulled these quotations from pieces he wrote for Baseball Magazine starting in 1910 or 1911. He continued to write for the magazine through the December 1937 issue and is prominately featured in the book The Numbers Game by Alan Schwarz. The copy I have was published by SABR in 2001 coming in at 218 pages in the original typesetting and contains an index of the quotations.

If you'd like to read something written by Lane see "The Base on Balls: Why Should the Records Ignore This Powerful Factor in Brainy Baseball?" posted by Cyril Morong from 1917.

Here are just a few of the tidbits that caught my attention while perusing the book.

On baseball records:
"The records are the whole thing in baseball. You can't make them too important and you can't be too careful in how you handle them."
- John Heydler, former Secretary of the National League:

"His batting average, then, is the ball player's principal stock in trade and is valuable to him in a personal and business sense. Where the records fail to give him credit due, he has suffered a genuine loss...In 1915, which was not my best year, I made twenty-four homeruns, a modern record. I also made thirty one doubles. I hit for 117 extra bases. The next best man in the League hit for 76. I scored more runs than anybody else on the circuit and drove in more runs. In all the really effective work of the batter I should have led the League by a wide margin." - Cactus Cravath

Lane was a pioneer in pointing out the one-dimensional nature of batting average and used Caravath as a prime example. As documented Schwarz observed in 1916 that batting average was an inadequate way of measuring the contribution individual players by remarking,

"Would a system that placed nickels, dimes, quarters, 50-cent pieces on the same basis be much of a system whereby to compute a man's financial resources? And yet it is precisely such a loose, inaccurate system which obtains in baseball..."

Although slugging percentage was adopted by the National League in 1923 and the American League in 1946 it would take many more years before weighted formulas for run production (Lane produced one himself) would start to take hold.

On slugging versus place hitting:
"My theory is that the bigger the bat, the faster the ball will travel. It's really the weight of the bat that drives the ball. My bat weighs 52 ounces. Most bats weigh 36 to 40 ounces...The harder you grip the bat, the faster the ball will travel...When I swing to meet the baseball I follow it all the way around." - Babe Ruth

"The sluggers have wrecked baseball. They are a thorn in the side of every pitcher. You never know when you have won the game. A homerun dumped into the stands may rob you of a victory any time until the last man is out." - Red Faber

"I do not lay my long hitting to any unusual strength. I believe it is due rather to meeting the ball fair, with a quick snap motion that sends it straight and true out over the diamond...It doesn't follow, however, that a heavy bat is necessary. Some sluggers use heavy bats. Chief Meyers did so and so does Babe Ruth. Most batters will find that an extra heavy bat cuts down the speed of their swing more than enough to offset what the extra weight of the bat can accomplish...I would say that in general the chop hitter would best use a heavy bat and the slugger a light one." - Rogers Hornsby

The debate between using a heavy versus a light bat is one that's had a long life. Over the course of time hitters have tended to move towards smaller bats with thin handles to increase the whip-like motion and therefore the speed of the barrel through the hitting surface. This is backed up by some recent research I wrote about in February. Both Harry Heilmann and Zack Wheat are quoted by Lane as favoring the lighter bat while Ken Williams and Hack Miller favor Ruth's approach. Note also that Robert Adair in his book The Physics of Baseball makes the point that the impact of bat and ball lasts about 1/1000 of a second. Therefore a tight or lose grip makes virtually no difference, nor does releasing the top hand after impact. The impact happens so quickly that the signal does not get processed until long after the ball is gone.

"Ruth is more than a slugger, he is a homerun hitter. Fortunately for him, he began as a pitcher. A pitcher is not expected to hit. Therefore, he can follow his own system without managerial interference. Ruth made the most of this opportunity...I have tried to make myself a batter, which is something quite different. A batter is a man who can bunt, place his hits, beat out infield drives, and slug when the occasion demands it, but he doesn't slug all the time." - Ty Cobb

I thought this was an interesting observation and seems reasonable to me. Had Ruth not been a pitcher a coach along the way might have tried to change his style thereby diminshing his power. It's also interesting to notice that in Lane's book Ruth's ability to hit homeruns and others ability to follow his example is chalked up to adopting a particular style or "speciality" of hitting rather than any influence of different baseballs as is the common perception. To me, the style that Ruth popularized along with the fact that whiter baseballs were kept in play after Ray Chapman's death after being hit with a Carl Mays pitch (Lane has some interesting quotes about beanballs as well including one from Walter Johnson that is especially emotional), and the reluctance of owners to make rules that handicapped Ruth in light of the Black Sox scandal all served to usher in the new slugger's era.

"If I had set out to be a homerun hitter, I am confident in a good season I would have made between twenty and thirty homers...I would naturally have sacrificed place hitting, which, to my way of thinking, is the supreme pinnacle of batting art." - Ty Cobb

This point is emphasized in other quotes Lane records as well. Many of the players, and Lane himself, seem to be of the opinion that while slugging is effective, it isn't pretty and requires less skill. Almost to a man Lane records that everyone thinks Ruth the greatest slugger (and slugging as a specialty) but Cobb the greatest hitter (there are few votes for Honus Wagner as well). Sabermetrics of course, would argue that Cobb should have taken his 30 homeruns. Overall Ty Cobb and George Sisler are most appealed to on the subject of hitting while Ruth and Hornsby are close behind.

There are countless other fascinating little insights as well that any fan of baseball history will enjoy. Highly recommended.

Measuring Baserunning: Setting a Baseline

In the interests of furthering the state of sabermetric knowledge per my previous post I compiled the probabilities of runners advancing in various situations using play-by-play data from the 2003 season. The scenarios I looked at included:

• Runner on 1st, Batter Singles
• Runner on 1st, Batter Doubles
• Runner on 2nd, Batter Singles
• Runner on 2nd, Batter Doubles

For each situation I calculated the odds of advancing a "typical" number of bases (1 for a single, 2 for a double), the odds of going one better, the odds of going 2 better (where applicable), the odds of getting thrown out advancing, and the percentage of the time a runner occupied the base directly in front of the runner. I then create subtotals for each situation by the number of outs and the outfielder who fielded the hit. For example, for a runner on 1st when a batter singles the values are:

Outs To   Typ     +1   +2  OA  Next Base Occ 

All All  70.5% 27.2% 0.9% 1.4% 29.2% 

  0 All  73.4% 25.0% 0.5% 1.2% 21.1% 

      7  84.5% 14.1% 0.6% 0.7% 21.6% 

      8  68.6% 30.1% 0.3% 1.1% 25.0% 

      9  59.7% 38.3% 0.6% 1.4% 16.5% 

  1 All  72.4% 25.5% 0.7% 1.3% 30.6% 

      7  84.7% 13.4% 1.0% 0.9% 31.5% 

      8  70.3% 28.6% 0.4% 0.7% 34.0% 

      9  58.1% 39.0% 0.9% 2.0% 27.9% 

  2 All  66.3% 30.7% 1.4% 1.6% 33.9% 

      7  81.1% 15.8% 1.4% 1.6% 33.8% 

      8  60.0% 35.9% 1.8% 2.3% 33.1% 

      9  48.3% 49.7% 1.0% 1.1% 31.1% 

All   7  83.4% 14.4% 1.0% 1.1% 29.6% 

All   8  65.8% 31.9% 0.9% 1.4% 31.5% 

All   9  55.3% 42.3% 0.8% 1.5% 25.8% 

The value in breaking these numbers down can be illustrated by noticing how runners advance from first to third less than a third of the time (27.2%) overall but almost half the time (49.2%) with two outs when the ball is hit to right field. It's also interesting to notice that runners get thrown out most often in this situation with 2 outs when the ball is hit to center field and that runners only advance to third base 14.4% of the time when the ball is hit to left field.

Because I couldn't format the results as I wanted on this blog I've posted the complete results for all scenarios here.

More on how we can use these numbers to evaluate teams and players next time.

Win Expectancy and Post Season Awards

Nice piece in the NY Times by Alan Schwarz, author of The Numbers Game, on Wins Relative to Average Player (WRAP). This stat was created by Brian Lonergan, a young economist from Yale, and Ben Polak his former dissertation adviser.

Essentially, this technique uses win expectancy tables to calculate the odds of winning before and after each of the 186,000 plate appearances and assigning responsibility to players involved in the play. Each player's contributions are then summed and a total number of wins they are responsible for calculated. The sum of all contributions for all players on the team equal the number of games the team is above .500.

This technique borrows heavily from the Mills Brothers Player Win Averages (PWA) methodology created in the late 1960s as well as Bennett and Flueck's Player Game Percentage (PGP) documented in chapter 10 of Curve Ball. The difference is that this system takes the next step and translates the probabilities into wins ala Bill James' Win Shares system.

Their results for 2004 include:

"A.L. M.V.P. Sheffield, with a 5.60 WRAP, edges out the Angels slugger Vladimir Guerrero (4.45). Ramirez ranks sixth because more of his hits came in game situations that did not have a big effect on the outcome of Boston games.

N.L. M.V.P. Bonds (12.16) tramples the runner-up, Albert Pujols of the Cardinals (6.85), demonstrating that Bonds's walks did indeed help the Giants by setting the table for subsequent, however disappointing, hitters.

A.L. CY YOUNG Despite having a higher E.R.A., Schilling tops Santana, 5.15 to 5.01, because he often performed in hitter-friendly Fenway Park (yes, WRAP accounts for this) and because he thrived in particularly tight situations. But the two were bested by Twins closer Joe Nathan (5.47), whose 1.62 E.R.A. and 44 saves do not truly quantify how many games his late pitching helped decide. (WRAP leans toward relievers because, although they influence fewer at-bats, the at-bats are inherently more crucial.)

N.L. CY YOUNG Once again, closers dominate, with the Dodgers' Eric Gagne (5.69) beating the Astros' Brad Lidge (5.55). San Francisco's Jason Schmidt (5.39) wins among starters, well ahead of the more popular candidates for postseason awards, Randy Johnson of Arizona and Roger Clemens of Houston."

Win Shares of course equate to one-third of a run and so comparing the 2004 Win Shares as calculated on The Hardball Times you get the following for those mentioned in the article (their winners bolded). WS=Win Shares, WSAA=Win Shares Above Average, Wins=WSAA/3 for comparison with WRAP.

          WS WSAA Wins

Sheffield 31 15    5

Guerrero  29 12    4

Ramirez   28 12    4

Santana   27 15    5

Schilling 22  9    3  

Bonds     53 37 12.3

Pujols    40 21    7

Rolen     38 21    7

Beltre    37 19  6.3

Abreu     37 18    6

Gagne     16  8  2.7

Lidge     17  9    3

Schmidt   19  8  2.7

Clemens   20 10  3.3

In evaluating the two systems it seems to me that WRAP overvalues closers because of the highly volatile situations in which they work (the danger of using situation-dependent measures like this) while Win Shares undervalues pitchers (Clemens was the highest rated pitcher in the NL and came in 33rd in total Win Shares behind Miguel Cabrera, Derek Lee, and Luis Castillo). Note, however, that Bonds, Pujols, Sheffield, Guerrero, and Santana were credited with a very similar number of wins in both systems.

You can also note that the ranges of both systems are similar and so generally you can say that MVP-type players may be worth an additional 5 to 8 wins (except for Bonds).

The Argument From Reason

A couple weeks back I attended a lecture by Dr. Ned Keller, a physicist who teaches college in Grand Rapids Michigan. The lecture was entitled "The Nature of Knowledge" and was the first in a series he did discussing "Theories of Origins" at an area church. In it Dr. Keller provided a basic outline of how we know what we know in order to provide a foundation for what he was to talk about the rest of the weekend. Although I didn't get to attend any but the first lecture, I found it interesting that among his preliminary topics for the weekend was:

The preliminary question is whether the universe is best described with a natural or a supernatural worldview. What are miracles? Can they occur and have the occurred?

To answer this question Keller went to chapter 3 of C.S. Lewis’ 1947 book Miracles titled “The Cardinal Difficulty of Naturalism”. In that chapter Lewis makes an argument for God and against Naturalism (that nature is the “whole show”) based on the existence of human reason. Interestingly, after Miracles was first published a debate on Lewis’ argument was held at the Oxford Socratic Club between Lewis and philosopher Elizabeth Anscombe. By all accounts Lewis lost the debate and subsequently rewrote the chapter for subsequent editions of the book.

In his lecture Keller talks both about chapter 3 and about miracles in general.

Lewis’ argument for the existence of the supernatural is known as the “Argument From Reason” or the "Argument From Mind".[1] In short Lewis puts the argument in syllogistic terms like so:

• If supernaturalism is not true, then Nature is all there is and so "every finite thing or event must be (in principal) explicable in terms of the Total System [i.e. Nature]." This is called physicalism by Moreland.
• Therefore if any one thing can be shown to be not explicable in terms of the Total System, then naturalism is not true
• Human reasoning can be shown to be something not explicable in purely physical terms and so naturalism is therefore not true. Man’s "rationality is the little tell-tale rift in Nature which shows that there is something beyond or behind her." [2]

Lewis then defends his conclusion by starting with the premise that all knowledge depends on the validity of our reasoning. If reasoning does not lead us to true conclusions about the world around us, but is rather a product of feelings in our own mind, then all science and all knowledge is worthless. This, says Lewis, points out that strict materialism or physicalism is self-defeating. In other words physicalism may be true, but one cannot argue that it should be believed based on evidence or reasoning.

Lewis then goes on to argue why it is that human reasoning cannot be explained in terms of the “whole show”. He illustrates this through the two different senses of the word "because". In the first sense because can be used to mean a cause and effect relationship ("Grandfather is ill today because he ate lobster yesterday"). In the second sense because is used in a Ground and Consequent relation, for example, "Grandfather must be ill today because he hasn’t got up yet (and we know he is an invariably early riser when he is well"). The first sense indicates a connection between a state of affairs while the second is a logical relation between beliefs that involves an act of knowing or seeing or rational insight. Another example of the second sense of because is the mathematical reasoning if A=B and B=C then A=C.

Lewis then explains that every event in nature, including our very thoughts, must be of the first type if naturalism is true. If this is the case, then when we ask "Why do you think this?", the actual answer must always begin with a Cause-Effect style because. As a result, all of the thoughts that go into answering the question lie in a cause-effect relationship to one another including the final answer. But we know that to be caused is not to proved and so the physicalist, if he is consistent, must admit he has no way to know whether what he thinks is true. He has no way to bridge the gap between the two distinct senses of because. In fact, as Lewis notes, in argumentation people often act as if the two were unrelated so that if a person can find some bit of background about you that might indicate why you believe something (Cause-Effect) they can more easily discount your position. However, in our experience we know that not all of our thoughts are based on wholly on Cause-Effects relationships (we don’t draw all of the inferences possible from each thought). Some of our thoughts can cause other thoughts by being seen to be a ground for them (Ground-Consequent). Therefore, since some of our thoughts can be shown to be true acts of knowing or seeing that cannot be accounted for by naturalism, then naturalism is false. This then explains why all human reasoning and therefore science and knowledge must be thrown out for the physicalist since it depends on Ground-Consequent style thinking including the physicalist’s own conclusion that nature is the whole show. This is why that position is self-refuting. As Lewis conludes:

"But this, as it seems to me, is what Natualism is bound to do. It offers what professes to be a full account of our mental behaviour; but this account, on inspection, leaves no room for the acts of knowing or insight on which the whole value of our thinking, as a means to truth, depends."

He also goes on to address the naturalists claim that our reasoning is the product of natural selection and/or cultural evolution. Against natural selection as the origin he argues that natural selection can only improve man’s physical responses to the world around him and could never in principle develop a relationship between knowledge and truth since there is no connection between the two, no way to bridge the gap. Against cultural evolution or the belief that over time, men were conditioned to make inferences based on experience (where there is smoke there is fire), Lewis argues that inferences are the basis of animal, not human reasoning. The real difference between animal and human reasoning is that human reason need not appeal to experience at all. For example, our belief that A=C as above is not derived from our experience that we’ve never not know A to equal C. Rather, it is based on a real insight that "it must be so". These are the insights that a physicalist cannot explain.

[1] There are several other arguments for God’s existence that can be used including the Ontological Argument, the Cosmological Argument (which has three different forms), and the Argument from Design. The books Scaling the Secular City by J.P. Moreland and Reasonable Faith by William Lane Craig have very readable introductions to these arguments.

[2] Moreland also gives other reasons for thinking that there are entities that cannot be explained naturalistically including moral values, numbers, and universals (concepts such as color)

Neifi the Terrible

So the Cubs signed Neifi Perez to a one-year contract.

With tomorrow being Sunday let us all take a moment to pray that Jim Hendry and Dusty Baker don't actually think that this 32 year-old with a career .301 OBP and .380 slugging percentage (despite playing six of his nine season in Colorado) should be allowed to compete for a starting job.

Despite his 6 for 6 debut with the Cubs and .371 average in 62 at bats he still only managed .255/.296/.336 last season, a shade under replacement level (-.2 runs) based on the VORP numbers from Baseball Prospectus. He also has the distinction of capturing two of the worst nine offensive seasons in baseball history with his normalized OPS (adjusted for park factor) values of 64 in 2002 and 71 in 1999.

At best Perez, with his more than adequate defense, could take the utility infield spot of Jose Macias whose .268/.292/.376 performance was a touch better (+1.9 VORP) than "Neifi the Terrible".

Gruenwald USA Today Athlete of the Week

My sister-in-law's husband Jim Gruenwald was named USA Today athlete of the week. He battled back from a serious injury at the 2003 World Championships to wrestle in Athens for the US Greco-Roman team at 132 pounds. He also wrestled in Sydney in 2000, placing 6th.

The Cubs and OBP

Interesting article about OBP and the Cubs focusing on Mark Bellhorn. It echoes what many of us have been saying for several years, the Cubs just don't get it when it comes to getting guys on base.

"The Cubs finished 11th in the NL in team on-base percentage. Despite a great starting-pitching rotation, they failed down the stretch largely because they didn't score runs, even against the bottom-feeding Mets and Reds. You can blame fatigue, but you also can blame bad approaches at the plate, including too much first-pitch swinging and swinging at bad pitches."

The author also dredges up Dusty's quote on walks "clogging" up the bases that I've referred to several times.

Big League Manager - Desktop Version

Since most folks don't have access to a Pocket PC I created a desktop version of the Big League Pocket Manager simply called Big League Manager. You can download it here. Simply double-click the .msi file to install. This first version has the same functionality as the PPC version but I'm looking for ways to expand it - for example by offering multiple hitter profiles based on lineup position perhaps.

Keep in mind that this is a quick and dirty first version so if you find problems feel free to contact me.

Actuaries and Sabermetrics

I was alerted to an article titled "Stat of the Art: The Actuarial Game of Baseball" published in a journal for actuaries, Contingencies May/June 2004. The article itself is just a recapitulation of Moneyball, Billy Beane, and Bill James with the Red Sox and is old news to anyone who's been following sabermetric developments. Two factual errors I noticed on skimming the article.

1. It says Bill James is from "Lawrenceville" Kansas instead of Lawrence
2. It says Bill James invented On-base percentage. A precursor to OBA was actually developed and then dropped as early as 1879 but OBA became more recognized in the 1950s.

What is more interesting are the eight proposals for "new" statistics from readers of Contingencies that Bill James reviews.

In a nutshell these are:

• The Reliever Effectiveness Ratio by Damian Birnstihl. This is simply a recalculation of ERA by assigning a pitcher a half run for each runner he let on that scores and a half run for each runner he lets in after he comes in as a reliever. This is a simpler version of what Ari Kaplan did a decade ago as I blogged about here.
• Rearranging the Starters by Aryeh Bak. This is a study that concludes that rearranging your starting pitchers based on the opponent's starters could gain a couple extra wins during the season. James points out that this question has been studied before by Dallas Adams and Tom Tippett and that there are so many assumptions you have to make that in practice this doesn't work. To me what is more important is getting your best pitchers on the mound more frequently (hence the four-man rotation), not working matchups.
• A New Wrinkle by Rod Keefer. This is a "new' stat called "Run Production Index" (RPI) that takes runs produced (R+RBI-HR) and divides it by at bats. James points out that runs produced has been around since the 1950s and then goes into its flaws. Keefer also proposes calculating "bases advanced per at bat" (BAAB) or how many bases each offensive event resulted in. To me this makes some sense but is awfully dependent on the other hitters in the lineup.
• The Three-Year-Ago Correlation by Paul Conlin. Conlin said that he found that team winning percentages were more highly correlated with results from three years ago than from any previous year. James responds with a study that refutes it and shows that the average change in wins from one year to the next is around 10 and then steadily increases each prior year.
• Starting Pitchers and Relief Pitchers by Mark Seliber. A spreadsheet with the same stat as RPI as well as new stats for starters and relievers. Nothing new or interesting here.
• The Efficiency Rating by Myron Kraynyk. This is a more interesting attempt that uses the same idea as BAAB but also considers the total possible bases available in each plate appearance. These are summed over all plate appearances and divided to yield an Efficiency Rating. No data is provided however and it suffers from being very context dependent.
• The Base Advancement Percentage by Richard T. Newell Jr. This stat is essentially the same as the Efficiency Rating.
• The Ultimate Baseball Statistic by Spencer M. Gluck. This is essentially another version of Player Win Averages (PWA) developed by the Mills brothers in the late 1960s. James isn't sold on these techniques and says that systems like this that take into account everything end up producing nothing of value since there are too many unknowns that have to be glossed over. Another way of saying it is that a good baseball analyst contributes to the discussion by answering specific questions that are actionable. In summary James says:

"Good analysis never begins with statistics. Good analysis always begins with a specific question, and a question which is of interest to baseball people, whether they are actuaries or artists or aging scouts. Proposing a system which instantly evaluates everything that every player does is analogous to fixing insurance rates for drivers by attaching a box of sensors to the hood of every automobile and keeping track of how often every driver does something dangerous, and calculating exactly how dangerous that was. It’s not the real world. It’s not practical, and it’s not useful. Maybe, in 50 years, it will be practical or it will be useful, but it’s not now. Our general knowledge is limited by our specific knowledge. Our ability to have an impact on the discussion cannot be larger than our ability to find a question which has an actual answer."

What also interested me about these "new" statistics are of course that they're not new and that even in this small sample four of the eight people had an idea that was the same or very similar to one of the others. More to the point, these are the same kinds of ideas that baseball analysts have had going back to F.C. Lane in the 1920s, George Lindsey in the 1950s, Earnshaw Cook, the Mills brothers, Pete Palmer and on and on. Once again this seems to call out for a place where this kind of information is collected.

Measuring Baserunning: A Preliminary Attempt

Another great quote from Rich's post yesterday on the 1984 Baseball Abstract was James' contention that Project Scoresheet was going to definitively answer questions about baserunning.

"Baserunning is perfectly measurable; it can be easily defined and, given properly maintained scoresheets, easily researched. Our lack of knowledge on the subject is attributable entirely to record-keeping decisions that were made a little over a century ago and have never been intelligently or systematically reviewed. We know so much about hitting that we can talk about it forever and measure it with extraordinary precision because a few men, at the beginning of Time, made some very good decisions about how to record and organize information, decisions that are now so natural a part of our thinking about the game that it is difficult even to see that any decision had ever to be made.

For this we applaud them. Their decisions about baserunning and fielding were much less wise. They failed to address many issues, and drew arbitrary lines where they drew them at all, and time has laid waste to their designs."

Rich then goes on to say:

"If this information is known today, it sure isn't widely disseminated. Why don't we know how often (in absolute terms and as a percentage of opportunities) various runners go from first to third on a single, first to home on a double, or second to home on a single? How often does Ichiro Suzuki reach base on an error as opposed to the average batter? Are we limited in recording the data or in distributing the data? Until this information is made available to the public, we will be limited in our ability to fully understand and appreciate all the nuances of the game and its players."

Well, in the interests of picking up the challenge I loaded the 2003 play-by-play data (found on the Yahoo group stats_software) into SQL Server last night and wrote a few quick queries to provide a baseline to answer a couple of Rich's questions and for future work.

Situation
Man on First - Batter Singles
Opportunities: 10430
ToThird: 2841 (27.2%)
Scores: 94 (0.9%)
Out Advancing: 147 (1.4%)

Man on First - Batter Doubles
Opportunities: 2979
Scores: 1315 (44.2%)
Out Advancing: 95 (3.2%)

Man on Second - Batter Singles
Opportunities: 6128
Scores: 3703 (60.4%)
Out Advancing: 217 (3.5%)

I was somewhat surprised how often a runner scores from first on a double (44.2%) and how few times a runner on first is thrown out advancing. Breaking these numbers down by the number of outs (which I plan to do) would also show a difference I assume.

From a team perspective the leaders in these categories were:

Man on First - Batter Singles
ToThird: Colorado and Minnesota (33.3%)
Scores: San Diego (2.0%)
Out Advancing: Houston (3.4%)

Man on First - Batter Doubles
Scores: Montreal (53.8%)
Out Advancing: Cubs (6.4%)

Man on Second - Batter Singles
Scores: Oakland (66.0%)
Out Advancing: Cubs (6.3%)
Cubbs fans should probably not be surprised that former third base coach "Waving" Wendell Kim in 2003 contributed to 20 runners being thrown out on the basepaths, tied for the most in baseball with the Yankees (the Padres had only 6).

These metrics get a bit difficult, however, when you consider the personnel the third base coach has to work with and judging what is and is not an opportunity In these numbers I've looked at all opportunities and not only those where the next base was unoccupied. There is an argument to be made that if the next base is occupied then the runner may be hindered in their attempt to take the extra base. Overall, the next base was unoccupied around 70% of the time so I went ahead and included all opportunities.

Overall, a quick way to measure a team's baserunning skills might be to see how many times they took at least one "extra" base. The percentage leaders are:

Colorado 46.6%
Oakland 46.1%
Minnesota 44.1%
Cleveland 44.0%
Baltimore 43.6%

The Cubs were last at 35.5%.

As far as individual leaders in these categories go:

Man on First - Batter Singles (more than 20 opp)
ToThird: Jose Guillen (59.1% 26/44)
Scores: Luis Matos (12.9% 4/31)
Out Advancing: Matt Lawton (11.1% 3/27)

Man on First - Batter Doubles (more than 10 opp)
Scores: Miguel Tejada (81.3% 13/16)
Out Advancing: Juan Encarnacion (18.2% 2/11)

Man on Second - Batter Singles (more than 20 opp)
Scores: Jose Guillen (90.9% 20/22)
Out Advancing: Tony Womack (14.3% 6/42)

Interestingly Juan Encarnacion was second in getting thrown out when on second with a single 13.6% of the time (3/22). So even from these small samples it appears that perhaps good and bad baserunners can be identified. Jose Guillen looks pretty good here while Juan Encarnacion does not.

My ultimate goal here is to assign weights to the various baserunning plays and come up with a single number that estimates how many runs a player gained or lost for his team on the bases. This methodology has some limitations and doesn't provide a complete picture, e.g. looking only at advancement in this manner does not include advancement on errors, does not measure the impact of holding the runner, doesn't take into account park effects (the Green Monster likely has a negative impact on the times a runner can go from first to third on a single), and as I mentioned there is a strong weighting based on the third base coach that would have to be separated from individual players. Also the sample sizes in a single season for individuals is really very small. I think you'd need 5 to 10 years worth of data to start to get something meaningful.

All of these limitations and more are what make analyzing baserunning difficult.

"THEODORE! with all thy faults — "

Excellent column by George Will that summarizes my reasons for voting for Bush, which in many ways is largely a vote against Kerry.

Baseball from the Outside

Rich Lardner over at Rich's Weekend Baseball BEAT had a great post today about Bill James' 1984 Baseball Abstract. In particular Lardner talks about the essay "Inside-Out Perspective" where James discusses the trend toward "inside stuff" in sportswriting. While that topic seems a bit dated, the most interesting aspect of the essay is his description of what he is doing in the abstracts:

"This is outside baseball. This is a book about what baseball looks like if you step back from it and study it immensely and minutely, but from a distance."

He then goes on to say:

"But perspective can be gained only when details are lost. A sense of the size of everything and the relationships between everything--this can never be put together from details. For the most essential fact of a forest is this: The forest itself is immensely larger than anything inside of it. That is why, of course, you can't see the forest for the trees; each detail, in proportion to its size and your proximity to it, obscures a thousand or a million other details."

I've read that book and essay several times over the years but it wasn't until attending almost three dozen Royals games this season and being immersed in the detail of each play while scoring for MLB.com that the essay brought home to me a new meaning.

I had assumed that viewing the game from that perspective would lead to insights that I hadn't previously been privy to. And indeed I did learn more about pitching patterns and, for example, the importance of establishing the strike zone early in the game. However, overall what I realized from personal experience was that it was very difficult to be immersed in the details of each game and yet maintain perspective on the bigger picture - a picture that looked at season and career trends as well as strategies. By the end of the season I found it quite difficult to separate in my mind events that happened in different games and found that I was thinking about players and had made judgments in terms of just a handful of the plays or situations I remembered clearly. And I only attended less than half the Royals home games.

I think this goes a long way towards explaining why sportswriters and those inside baseball have long resisted sabermetric analysis. They are simply too close to the game. There are too many discrete events in the course of a baseball season and too much randomness thrown in for human minds to sort it all out. Paradoxically, those who have witnessed every inning of every game think they must know more about the game since they've seen more. In actuality, the limitation of our brains makes us susceptible to forming invalid conclusions based on the limited number of events we remember and the emphasis we place on them. In some ways those who are closer actually know less. And so of course, when analysis from an outside perspective calls into question the existing paradigm, there will be fierce resistance. This problem only grows worse when you also consider the personality and relationship issues that are a part of any human endeavor and that go into decision making within a ballclub.

To me this means that a baseball analyst, in order to be effective, must purposefully take a step back from the trees in order to see the forest and work from the proper perspective. The kinds of questions that an analyst can help answer then are by nature big picture questions: Is it generally a good idea to bunt in a particular situation? Is developing a closer useful? Does drafting high-school pitchers pay off? Does guarding the lines help or hurt in the late innings? At what age do players generally start declining in productivity? These are the kinds of conclusions Paul DePodesta talked about with his "Be the House" mantra - general strategies that only pay off over the long haul.

This is precisely the kind of role it appears James now has with the Red Sox. He is not involved in the day to day operations of the team and instead creates studies from an outsider's perspective that GM Theo Epstein and the management team can use in their decision making process.

This also means that if news organizations and other teams want to benefit from that kind of analysis they would do well to hire someone from the outside and then keep that person at arm's length.

Cubs 2005 Hot Stove Heats Up

The final week's collapse by the Cubs as they lost 7 out of 8 games to hand the wildcard to the Astros is behind us. I'm ready to start thinking about 2005. A few observations.

• The Cubs found a new third base coach in Chris Speier after firing "waving" Wendell Kim. Speier played with the Cubs in 85-86. Personally, I though Kim did a much better job this season than last, when it was clear that he used poor judgment on sending runners. Overall, the Cubs definitely need to improve their baserunning. I noticed a marked increase in aggressiveness out of Corey Patterson after Vince Coleman was added as a coach after midseason. From Patterson and Derek Lee that kind of aggressiveness should pay off.
• The Cubs declined their $11.5M option on Moises Alou and their $6M option on Mark Grudzielanek buying both out for $2M and $500K respectively, freeing up $15M. Both had decent years although Grudz was hurt much of the time. It is possible that Alou could be back under a different contract although of course every Cub fan's dream right now is that the money is used to lure Carlos Beltran to Chicago. Beltran's agent Scott Boros is probably looking at $20M although that's certainly more than he's worth. J.D. Drew is also an option.
• That also leaves a hole at second base. Todd Walker is a free agent and has said that he doesn't want a part time job next season although he'd only consider it with the Cubs (November 2004 Vine Line). It seems to me that it's a no brainer to go after Walker and make him the everyday second baseman. That would also get a left-handed bat in the lineup everyday and someone who gets on base.
• The Cubs picked up the option of Ryan Dempster for $2M. In the November issue of Vine Line, GM Jim Hendry said that Dempster has the mentality for the closer role and "has the makeup to do it." Uh oh. Hendry also said, however, that they're leaving Dempster's role up in the air right now and he could be a "rotation guy" or setup man. To me, Dempster clearly has never had enough control to pitch late in the game or come in with runners on base and he didn't show any more control last season. To me, he's a long reliever and spot starter at best.
• Nomar Garciaparra filed for free agency. He says he'll consider staying in Chicago. With his brittleness I don't think a big contract for more than two years and preferably one, makes any sense. Also on the market are Edgar Renteria (728 OPS), Orlando Cabrera (689 OPS), Cristian Guzman (693 OPS), and Jose Valentin (760 OPS). Renteria is probably the best choice both offensively and defensively while Guzman is the youngest. I wouldn't waste any money on the other two since Valentin will be 35 and Cabrera has a .316 lifetime OBP and will command a larger amount because of his improbable postseason performance.
• Other Cubs who are free agents include Matt Clement, Glendon Rusch, Kent Mercker, Ramon Martinez, Tom Goodwin, Paul Bako, and Ben Grieve. I wouldn't mind seeing Rusch, Martinez, and Grieve back in pinstripes. Rusch, as a swingman and lefty spot starter, Martinez who is a good utility man whos offensive production is better than most utlity men despite a poor season (659 OPS), and Grieve as a fourth outfielder and left-handed bat off the bench with some patience. I'm not sure what the status of Todd Hollandsworth is but I'm sure the Cubs have overrated his ability based on his hot start last year.
• Letting Clement go frees up $6M to help in signing free agents.
• There is no way they should re-sign Bako. At $865K he's already way overpriced. If Hall of Famer Greg Maddux can't pitch to Michael Barrett, then there is something seriously wrong. Backup catchers like him can be had for league minimum and almost all of them would be far superior hitters.
• I'd be ok with brining Kent Mercker back He still walks an awful lot of batters but he could be your situational lefty again as long as Dusty finally realizes that Mike Remlinger is not a situational lefty and actually has better stats against right handed batters. Of course, with the option picked up on Dempster that may leave Mercker out.
• Also, in Vine Line Jim Hendry has this to say in regards to Neifi Perez, "We have every interest in trying to re-sign...Neifi Perez more sooner than later-hopefully sometime even before the end of October." I hope he wasn't serious. The only role Perez should play is that of utlity infielder and with his history as an attitude problem, I'm not so sure about that. He is still a good defensive player but if the Cubs think he is suddenly going to perform at the level he did at the end of last season in a full season they're kidding themselves.
• A story in Vine Line hinted that the Mets might want Sammy Sosa because of his connection with Mets GM Omar Minaya. No way. If Sammy is traded he automatically gets his $18M for 2006. I can't imagine that any team in their right mind would trade for the quickly aging Sosa. No, I'm hoping he can bounce back for one more tour with the Cubs in 05 and then they can buy out his contract for $3.5M. On a veteran team like the Cubs his last day shennanigans will likely not have that big of an impact.
• Although the Cubs pitching is relatively young this is still a team built to win now before Aramis Ramirez, Mark Prior and Carlos Zambrano get to be free agents.

Mobility in the .NET DJ

For those who've read Jon's editorial in the latest .NET DJ here is source code for the Big League Pocket Manager and here is the link to the .cab files for installation. Have fun.

.NET UG in Wichita

Yesterday afternoon I was pleased to be able to present at the Wichita .NET User's Group at the invitation of Robert Tesch. I'd like to thank Robert and all the guys there. I had nice time meeting everyone and talking about CF.

The slides for the talk can be found here. The complete code for the MLB Pocket Manager is here and the .cab files for installation on the Pocket PC are here. The code for the network precense component is with the MSDN whitepaper here. The code for the SmartAppUpdater is not yet available since it should be coming out as part of an MSDN whitepaper soon. Stay tuned.

The Corps Of Discovery, October 29, 1804

This fall I started reading the abridged version of the journals of Lewis and Clark by Anthony Brandt and each morning read what Lewis and Clark wrote that day. By October 26, 1804 the Corps of Discovery had made contact with the Mandan tribes in present day North Dakota and on October 29th Clark wrote:

"We collected the chiefs and commenced a council under an awning and our sails stretched around to keep out as much wind as possible. We delivered a long speech, the substance of which was similar to what we had delivered to the nations below [they had already come in contact with the Arikara, Hidasta, Yankton Sioux, Omaha, and Missouri]...After the council we gave presents with much ceremony and put the medals on the chiefs we intended to make, one for each town, to whom we gave coats, hats, flags, and one grant chief for each nation, to whom we gave medals with the President's likeness."

As was their custom they also fired Lewis's air gun that always astonished the Indians. Clark then goes on to talk about a prairie fire that killed a man and a woman and how a young half white boy was saved when his mother threw a buffalo skin over him. The Indians thought he had been saved "by the Great Spirit medicine because he was white".

At this point the Corps was almost ready to setup their winter camp and had scouted for good wood a few days previously but hadn't found much as the land was mostly prairie.

Information at Your Fingertips

Great article here on how the Red Sox use information. Also some insight on this from David Pinto at Baseball Info Solutions.

Stoney Says Goodbye

Derek at The Big Red C reports that Steve Stone is officially gone. Derek also includes his resignation letter. So both sides of the WGN booth are moving on with Chip Caray broadcasting in Atlanta next year with his father.

For my part I think Stoney was among the best color men I've heard. He always did a good job of making his comments concise and to the point and wasn't afraid of anticipating the play rather than simply reacting. He also had a great sense for strategy even though I don't think it was at all refined by numerical analysis. He seemed to be skeptical of Moneyball when it came out but not violently against the ideas as some in the baseball community are.

Little Bingle

As I was thumbing through F.C. Lane's fascinating 1925 book Batting (a topic for another day) I noticed several references to a "bingles", typical of which is the following from the last page where Honus Wagner is quoted:

"It's the hit that counts. You can't score many runs without the old bingle."

Having not heard this term before I Googled it and found several references to bingle as being a synonym for "single" in online dictionaries but no history of the word or thoughts on why it fell out of use.

I posted my query to SABR-L and Merritt Clifton was kind enough to explain that "Bingle" is a contraction of "bunt single." He says that as it was fading from vogue, it came to mean any single, but that was not its original use. In other words a "bingle" was a slap hit as practiced in the deadball era and later by the likes of Maury Wills and Luis Aparacio. Merritt pointed out that for example, a third base coach might shout:

"C'mon, little bingle now, drop one in."

With the idea being to try and coax the third baseman to play in thereby giving the hitter a better chance to slap the ball past him. When I played I recall coaches saying, "C'mon now, little bingo" but not bingle. I asked several fans older than myself if they'd heard the term before and none had stretching back to the mid-fifties so I assume the term died out shortly after the deadball era as more and more hitters turned to "slugging" as Lane would say.

His response made me wonder how many of Ichiro Suzuki's 225 base hits were actually "bingles"?

And the Simulator Says...

With the Cardinals down 3-0 the simulator now says their odds of coming back are about 9.1%. That's not all that bad and the reason they're better than the Red Sox chances in the same situation is that the Cards are a better home and road team than the Red Sox on a percentage basis.

A Brief History of Run Estimation: Estimated Runs Produced

Earlier in this series we looked at Runs Created developed by Bill James in the late 1970s and early 1980s and Batting Runs, a part of the Linear Weights system devised by Pete Palmer in the late 1970s and published in The Hidden Game of Baseball in 1984. Both of these formulas are what Albert and Bennett in Curve Ball call "intuitive" formulas because they attempt to estimate the number of runs created using a model of how baseball is played. However, the former is a non-linear formula since its’ underlying premise is that runs are the product of getting on base and advancing runners, while the latter is a linear formula since it assigns weights to the various offensive events. So now we’re ready to explore Paul Johnson’s Estimated Runs Produced or ERP in the third installment of the series.

History
The story of ERP starts with Bill James 1985 Baseball Abstract. In that book James published an essay by Paul Johnson on ERP after receiving a letter from Johnson explaining his work. Essentially, James published the essay because he found that ERP was simple, on average more accurate than his own Runs Created formula, and because he already knew that his formula overstated runs for teams with both high slugging percentages and on base percentages (something he subsequently fixed as discussed in my previous article).

In a quick study that James did to assess the accuracy of ERP he found that ERP had an average difference of 18.4 runs per team while Runs Created was at 19.3 for 100 teams from 1955 to 1975. On the strength of this James, in a move that should be applauded, felt compelled to provide Johnson with a forum to share his ideas with the baseball analyst community.

In introducing Johnson’s formula James also takes the opportunity to criticize Batting Runs, which he does more fully in the first version of his Historical Baseball Abstract also published in 1985.

"Pete Palmer in The Hidden Game makes a similar claim [for accuracy] for the linear weights method, and Pete is a good friend and an outstanding analyst of the game, but in fact linear weights do meet any acceptable standard of accuracy in assessing an offense."

So what is the formula? In that article Johnson gave as his complete version:

ERP = (2*(TB+BB+HB)+H+SB-(.605*(AB+CS+GIDP-H)))*.16

As you can see the strength of ERP is its simplicity. Only addition, subtraction, and multiplication are required with only eight counting statistics needed. The formula essentially breaks into two sections, the left hand side representing positive offensive accomplishment and right hand side representing negative (we’ll get to the bit about .16 in a minute).

A second strength of ERP is that like Batting Runs it is a linear formula. In other words, when you sum the ERP for all players on a team you get the total ERP calculated for that team. That is not the case with non-linear run estimators like Runs Created and Base Runs, which we’ll look at in our next article in this series. And because ERP is a linear formula Johnson spends the first part of his essay showing how ERP better estimates runs for teams with the combination of high slugging percentages and high on base percentages. He does this not only by looking at teams with the highest number of homeruns and top slugging percentage but also aggregating high scoring World Series games and comparing them with individual players with the same basic profile. For example, he compares the aggregate statistics of 14 World Series games with Babe Ruth’s 1929 season and finds that in those game teams scored 124 runs. His ERP formula estimated 129 runs while Runs Created estimated 148. As mentioned previously, this was a weakness in the Runs Created formula that James explains in his afterword to the essay and has subsequently corrected.

So how did Johnson come up with ERP?

To quote Johnson the formula is “based on charts I made of the number of bases advanced by batters and baserunners on various offensive plays”. From that information Johnson realized that homeruns moved batters and baserunners three times as many bases as did the typical single and that walks advanced the batter and baserunners only two-thirds as many bases as did a single. These insights led to the design of the left-hand side of the formula since:

Home Run = 9 = 2*(4+0+0)+1+0
Single = 3 = 2*(1+0+0)+1+0
Walk = 2 = 2*(0+1+0)+0+0

Values for the other offensive events then follow:

Triple = 7 = 2*(3+0+0)+1+0
Double = 5= 2*(2+0+0)+1+0
Stolen Base = 1 = 2*(0+0+0)+0+1
Hit by Pitch = 2 = 2*(0+0+1)+0+1

As you can seen this formula is indeed intuitive since it attempts to model how runs are scored by looking at the advancement value of each offensive event.

And so the relative weights assigned by Johnson to the events using singles as a baseline were:

Walk = .667
Hit by Pitch = .667
Double = 1.67
Triple = 2.33
Homerun = 3
Stolen Base = .333

If this sounds suspiciously like Batting Runs then you’re on the right track. The weights used in the 1989 version of the formula from Total Baseball were:

Single = .47
Double = .78
Triple = 1.09
Homerun = 1.40
Stolen Base = .30
Walk = .33
Hit by Pitch = .33

Which calculate to weights relative to a single of:

Walk = .702
Hit by Pitch = .702
Double = 1.66
Triple = 2.32
Homerun = 2.98
Stolen Base = .638

As you compare the weights in the two lists you’ll notice that other than the stolen base the relative weights of the offensive events is the same. What Johnson found out with his table was the same information that George Lindsey found from scoring games in the 1950s and that Pete Palmer found when running his simulations in the 1970s. Johnson’s innovation was in expressing these relative weights in an algebraically simpler formula. What Johnson sacrificed for this simplicity was a small amount of precision.

The difference in the relative weight of stolen bases from .333 for Johnson to .638 for Palmer is interesting. As discussed in my previous article, originally Palmer found that the weight for stolen bases actually ranged from .19 to .22 depending on era. He upped the value to .30 on the argument that by and large stolen bases come at strategically more important times and so should be weighted accordingly. While he was no doubt correct in the assessment of the strategic importance of stolen bases it doesn’t make sense to add it to a formula whose goal is to average out the impacts of all sorts of situation-dependant variables. Anyway, eventually Palmer changed his mind and lowered the weight of the stolen base to .22 in the 2004 Baseball Encyclopedia. Using this value the relative weight of the stolen base for Batting Runs is .468, much more inline with what Johnson used.

We now move to the right hand side of the equation.

This side of the formula calculates the negative effect of making outs and therefore represents the context in which the positive weighted events from the left-hand side of the equation occur. This part of the formula counts the number of outs the batter is responsible for by subtracting hits from at bats plus caught stealing and grounded into double plays. The sum of the outs is then multiplied by .605 before being subtracted from the weighted positive offensive events. As a result, the weight of an out relative to a single is -.20 (-.605/3). However, when you look at Batting Runs you notice that the weight of an out is -.25 and so the weight of an out relative to a single is much higher at -.53 (-.25/.47). Why the difference?

The difference here lies in what each formula is attempting to measure. In Batting Runs the end result is the marginal runs or the runs contributed by the batter above what a league average hitter would have supplied whereas ERP, like Runs Created, is attempting to measure the absolute or total number of runs contributed by a batter.

In order for Batting Runs to measure the runs contributed above an average hitter, the formula takes into consideration the value of all outs made and discovers that each out is worth -.25 runs. In the 4.3 runs per game context that Batting Runs was formulated in that means that each out decreases the run potential by .16 runs in terms of shrinking the opportunity for scoring in each inning (4.3 divided by 27 is .16). However, Batting Runs is also taking into consideration the negative value outs have in terms of moving runners along during the inning and this value is then the difference between -.25 and -.16 or -.09. In other words the value of outs can be split into two components; the -.16 that represents the effect an out has on moving closer to the end of an inning, and the -.09 that represents the lack of runner advancement. So the weight of outs relative to singles with respect to advancing runners is -.19 (-.09/.47). This turns out to be the same relative weight Johnson used. If Johnson had used a weight of 1.5 instead of .605 for his outs he would have gotten the same results as Batting Runs and measured instead the marginal runs.

So why does using the smaller relative weight equate to absolute runs? By removing the decreased run potential automatically assigned for each out (-.16) you in essence remove the background noise and judge the hitter or team purely on the basis of the interaction of offensive events and that portion of the outs they make that suppress baserunner advancement. In other words, there is nothing a team can do about those 27 outs they’re going to make each game and so removing their non-discretionary cost results in a measure of the total number of runs scored.

I don’t think Johnson used this kind of logic to come up with his value of .605 and instead simply played around with his formula until he found something that worked. In fact, he says in his essay that,

“The numbers exist only to put proper emphasis on the various events. They are essential to making the equation work, but there’s no need for me to go into how they came to be what they are. I’ll just tell you that it took a hell of a lot of experimenting to settle on the darned things.”

In the final step Johnson take the right side of his equation and subtracts it from the left and then multiples the whole thing by .16. Again, why the .16?

Once you realize that ERP is a simplified version of Batting Runs you can see that the weights assigned by Johnson to offensive events in the left-hand side of his equation multiplied by .16 approximate the weights found by Palmer.

Single = 3*.16 = .48
Double = 5*.16 = .80
Triple = 7*.16 = 1.12
Homerun = 9*.16 = 1.44
Stolen Base = 1*.16 = .16
Walk = 2*.16 = .32
Hit by Pitch = 2*.16 = .32

And as you might have guessed taking the value of outs as -.605 and multiplying it by .16 yields -.097, which not coincidentally is the weight of an out with respect to advancing baserunners in Batting Runs.

However, by using this smaller value for the weight of outs ERP runs into a conceptual problem that Batting Runs does not. It is possible for hitters to accumulate negative ERP values. This doesn’t make sense in a formula that tries to estimate the absolute number of runs contributed by a player. The lower bounds should logically be zero. In fact, the zero-level, the level at which a player has a 0 ERP, is an OPS of between .320 and .330 (depending on the frequency of walks and total bases). What this means is that in practice ERP does not “work” for very restricted run environments. After all, common sense says that a hitter or team with an OPS as low as .320 will still create occasional runs through homeruns and stringing together a few hits. However, the offensive environment this represents is right around a run per game or slightly less. And since a team that scores less than a run per game does not in fact produce any positive offense, you can reasonably assume that a player that contributes at that level would not either.

Johnson went on to give two additional versions of the formula. The first is a simplified version to use when caught stealing, hit batsmen, and double plays grounded into are not available.

ERP2 = (2*(TB+BB)+H+SB-(.615*(AB-H)))*.16

You can see that he simply increased the weight of the out to compensate. The second version Johnson says works better for players with high stolen base totals. I assume he means when caught stealing is not available.

ERP3 = (2*(TB+BB)+H+SB-(.610*(AB+(SB/4) -H)))*.16

This version simply estimate the number of caught stealing by dividing the stolen bases by 4 and adding them to the number of at bats therefore making the outs component larger.

In the end James apparently did not realize that Palmer’s formula he so roundly criticized in The Historical Baseball Abstract was in fact the same formula as ERP in an admittedly simpler guise and with the twist of using a reduced weight for outs. In an ironic comment James says:

“I was originally suspicious of the system when I saw the ‘.16’ at the end of it. Wouldn’t it seem more likely that the most accurate possible system would require multiplication by .15974 or something? My assumption, as I said, was that if better methods were to be developed, they would have to be more complex, more difficult to figure, and that they would grow out of the existing methods.”

In fact, ERP did grow out of an existing method, it’s just that neither Johnson himself nor James realized it at the time.

Because ERP is equivalent to Batting Runs as we’ve shown here most sabermetricians don’t use it and instead rely on the more precise weightings of Batting Runs or Extrapolated Runs (XR) discussed below.

Derivatives
In his original essay Johnson then goes onto offer two extensions to ERP used to calculate the number of runs produced per 162 games. The first is:

ERP/162 = ERP3/(AB+(SB/4)-H)*458

And the second is:

ERP/162 = ERP/(AB+CS+GIDP-H)*474

Apparently, these formulas are an attempt to pro-rate ERP over 162 games and can be used for comparison purposes. These formulas assume a basis of 458 or 474 outs and simply multiply that by the ERP per out. However, I’m not certain where the 458 and 474 came from and Johnson does not say in his essay.

Johnson went on to refine his formula in the STATS 1991 Baseball Scoreboard and christen it “New Estimated Runs Produced” or NERP. The formula presented was:

NERP=(TB/3.15) + ((BB-IBB+HBP-CS-GIDP)/3) + (H/4) + (SB/5) - (AB/11.75)

Or if you prefer:

NERP=TB*.318 + ((BB-IBB+HBP-CS-GIDP)*.333) + (H*.25) + (SB*.2) - (AB*.085)

Once again, this formula is a linear one that can be broken down into left and right hand sides. NERP weights homeruns at 1.52, triples at 1.2, doubles at .89, and singles at .57. It also takes intentional walks out of the equation and weights other single bases gained at .33. Note that stolen bases are now weighted at .2, very similar to Batting Runs. However, the most interesting part is simply subtracting at bats multiplied by .085 from the left hand side of the equation. This seems at first glance to be an arbitrary attempt at estimating the typical number of outs a player makes and to account for the slightly higher weights in the formula. A value of around .065 would be typical be more in line if the weights were lower per the Batting Run formula. However, I don’t want to speculate too much without the original essay in which it was explained.

A few years later Jim Furtado enters the picture. Jim studied ERP and Runs Created and came to the same conclusions about the relationship of ERP and Batting Runs I’ve talked about here. He then went the next step and tried to develop a more accurate linear formula using a combination of regression analysis, comparison to other methods, peer review, and empirical analysis. His result was the Extrapolated Runs (XR) formulas published in the 1999 Big Bad Baseball Annual. He developed three versions as shown here.

XR = (.50 * 1B) + (.72 * 2B) + (1.04 * 3B) + (1.44 * HR) + (.34 * (HP+TBB-IBB)) +(.25 * IBB)+ (.18 * SB) + (-.32 * CS) + (-.090 * (AB - H - K)) + (-.098 * K)+ (-.37 * GIDP) + (.37 * SF) + (.04 * SH)

XRR - Extrapolated Runs Reduced = (.50 * 1B) + (.72 * 2B) + (1.04 * 3B) + (1.44 * HR) + (.33 * (HP+TBB)) + (.18 * SB) + (-.32 * CS) + ((-.098 * (AB - H))

XRB Extrapolated Runs Basic = (.50 * 1B) + (.72 * 2B) + (1.04 * 3B) + (1.44 * HR) + (.34 * (TBB)) + (.18 * SB) + (-.32 * CS) + (-.096 * (AB - H))

As you can see each of these formulas takes the same form as the Batting Runs formula with very similar weights. The difference is that strikeouts are weighted slightly more heavily (-.098) than other outs (-.09) while GIDP and caught stealing are weighted even more heavily. Weighting strikeouts in this way makes logical sense since strikeouts have no opportunity to advance runners.

The outs value here corresponds with the smaller -.09 value discussed previously. It is also interesting that sacrifice flies (SF) and sacrifice bunts (SH) are both included and given positive values. Albert and Bennett in Curve Ball added sacrifice flies to their least squares regression model (p187) and found that it in isolation it correlated strongly with run scoring but its weight was inordinately high and so did not use it in their model. My assumption has always been that sacrifice flies are primarily situation dependent much like RBIs themselves and so generally should not be included in run estimation formulas. Sacrifice bunts as well are typically seen as a net negative drain on offensive production so it is surprising to see them included with even a very small positive coefficient.

Games 3 Notes

A couple of notes on last night's game 3 victory by the Red Sox:

Killer Play
Contrary to Tim McCarver and Joe Buck's comments, the play by Jeff Suppan in the bottom of the third inning was the killer for the Cardinals. With runners on first and third and nobody out Suppan hesitated on the ground ball hit to the second baseman, then went back to third, then started for home again and finally headed back to third only to be thrown out by David Ortiz. Had he scored it would have made the score 2-1 with 1 out and a runner on third with Albert Pujols at the plate. The odds of scoring in that situation are well over 70% (66.2% with an average hitter) which would have tied the game.



Further, it would have stretched Pedro Martinez a bit more and possibly helped him reach the magical 100 pitch mark (he was taken out after 98) an inning sooner, which the Cardinals really needed. No, that was clearly the key play of the game. Larry Walker’s attempted tag on the flyball to Manny Ramirez with one out in the first inning seemed to me gamble worth taking early in the game.

Percentage Play
Later, the Red Sox had runners on first and second and nobody out when a fly ball (a "popup" as Joe Buck says of everything not a homerun) was hit to Jim Edmonds in medium centerfield. The runner on second, Orlando Cabrera, got set to tag and then did not as Edmonds made a pretty strong throw to third baseman Scott Rolen. Tim McCarver quickly opined that having Cabrera tag in that situation would have been a good play since the Red Sox were already up 2-0 and it would have gotten the runner to third.

I don't think McCarver was right. In that situation the run expectancy is 1.573 runs and the probability of scoring any runs is 64.1%. Had the tag been successful and both runners moved up it would have changed the run expectancy to 1.467 and the probability of scoring to 69.5%. However, when you fail the run expectancy drops like a rock to .344 and the probability of scoring to 22.3%. Because the cost of failure in this situation so high and the relative gain so little, when you calculate the break-even percentages on these numbers you quickly find out that it is never the "percentage play" to try and tag if your goal is to maximize the number of runs you’ll score in the inning. It is advisable to tag if you’re trying to score a single run but only if you think your odds of making it are greater than 88.6%. With Edmonds making the throw I don’t think the odds on Cabrera making it were anything like 88%.

A far better strategy in that situation would have been to try and double steal. The break-even percentages on that play are only 52.2% to score a single run and 63.9% to maximize runs. Those break-evens only decrease with 1 outs and so with a fast runner on second it is probably one of the most underutilized plays in baseball.

More on the Double Switch

As often happens a member of SABR added more information to the question of the first double-switch in major league history. Maria Vaccaro noted that she thought it had been accomplished in the 19th century but the first actual citation she could produce was for 8/2/1906 when Highlander manager Clark Griffith put himself in as a relief pitcher in the eighth inning at Detroit and also put catcher Ira Thomas in. Before the switch the catcher's position batted 8th and the pitchers position batted 9th. Griffith inserted himself in the 8th slot and put Thomas 9th.

Is it in the Cards?

With the Cardinals down two games to none I was interested to find out how often they might come back. Using my Series Simulator in 100,000 trials this situation happened 30,401 times. The Cardinals came back to win 8,210 times or 27%. They went on to be swept 4,077 times or around 13% of the time. Here are the complete numbers:

Cards in 7  4788  16%

Cards in 6  3422  11%

Sox in 7    5215  17%

Sox in 6    7470  25%

Sox in 5    5429  18%

Sox Sweep   4077  13%

So as you would guess the likely outcome of the series is that the Red Sox will win, but the most likely outcome is that they'll win it in six games.

The First Double Switch?

Dave Smith at Retrosheet had an interesting post on SABR-L I thought was worth sharing (not that all of his other members posts aren't of course). Anyway, someone asked a question about double-switches and he responded that a few years ago someone did some research on this question and the earliest use of the double-switch came on May 18 and May 21st 1955 and were done by the Orioles and their manager Paul Richards. Note that this simply the first one that can be found and so is not necessarily the final word.

The original poster noted that a double-switch was described in communication by the league office in 1973 but did not describe it as a "double-switch".

NLCS Recap

Here's my quick takes on the NLCS 4-3 series win by the Cardinals over the Astros.

• Julian Tavarez has issues. I kind of knew this when he was with the Cubs but his antics this season leave little room for doubt. Any team that signs him is taking a risk.
• Is there a more complete player in baseball than Carlos Beltran? Having watched him play here in Kansas City I wasn't surprised at what he could do but doing it on the bigger stage made it all the more impressive. It was interesting that when he was traded from the Royals in June one of the local sports radio guys seemed to denigrate the trade by noting that after all, the Royals hadn't won with Beltran. What a ridiculous statement. It'll be interesting to see how much the Yankees (or whoever) pay him next season. He can win games with power (8 homeruns in the post season), speed (his steal of second and tag to third on a medium depth fly ball in game 7 led to a run), and defense (his game saver in game 5) and at 27 he's at or near as good as he'll get. He'd look good in a Cubs uniform.
• Should Carlos Beltran steal more? With his steal of second base off of Jeff Suppan in game seven he had 34 consecutive stolen bases in the National League. During that time he was 16 of 16 stealing third. This question was discussed on SABR-L this week with several arguing that his very high stolen base percentage (highest in history I believe at 89.3% and 192 steals) is an indication that he doesn't steal enough since it is far higher than the break-even percentage required to make it advantageous. That makes sense to me. He could probably steal 50 or 60 bases per season and still keep his percentage well above 70%.
• I thought Phil Garner did the right thing in using Roy Oswalt as his first option in the 7th inning. Too many times a manager will still go with the pitchers he's used during the season in that situation instead of a starter who is almost always a better pitcher (that's why he's a starter).
• It was great to see Suppan execute the squeeze play in game 7 with Tony Womak on third. I've always thought the squeeze was an underutilized strategy. In any situation where you'd settle for a sacrifice fly I would think the odds are better to try the squeeze.
• I don't understand the pitching pattern Roger Clemens used in the 6th and deciding inning of the series. It seemed he fell in love with his fastball, which he didn't locate very well, and only after he gave up the 2-run homer to Scott Rolen did he go back to the splitter when pitching to Jim Edmonds. Was he really trying to throw fastballs past Albert Pujols?
• By the way, does anyone believe Pujols is really 24 years old?
• I also don't understand the Astros approach once they fell behind going into the 7th inning in game 7. They only got 3 hits all day but didn't exhibit any patience in the final three innings. Kiko Calero threw 16 pitches in the 7th, Tavarez threw 10 in the 8th, and Jason Isringhausen threw just 5 in the 9th.
• I've watched alot of games at Enron/Minute Maid and the left field situation there is ridiculous. Left fielders play on the warning track probably because they're used to standing 300 feet from the plate. They need to erect a really big wall there instead of just the scoreboard that's out there now. Left fielders also need to play medium depth there and take away some line drive singles.
• The broadcasting crew for FOX did a good job. Thom Brenneman is always good.
• This is probably the end for the killer B's as far as postseason runs go. Great careers by Craig Biggio and Jeff Bagwell may end without a trip to the World Series. Biggio is a liability in left field with his second baseman's arm and his offensive production is probably not enough for a left fielder. Beltran is gone and I would be a little surprised if Roger Clemens comes back but you never know. As far as I know only Sandy Koufax has retired after a Cy Young award winning season.

Three Questions on Probability and the Playoffs

Cards vs. Red Sox
With the All-Star game now deciding home field advantage in the World Series Cardinal fans particularly are a disgruntled lot. Why not award home field to the team with the best season record? With the advent of interleague play I think that’s a viable solution. If the leagues were still totally separate and if players didn't’t move freely between leagues, the records of the two teams really would have no basis for comparison. Since they do share at least common opponents I say base it on record.

Note: For those who don't remember the genesis for the current system was the Selig driven abomination that was the 2002 All-Star game in Milwaukee where the appropriate solution would simply have been to force the American League to forfeit. There are no ties in baseball.

But the question is, how big an advantage does home cooking give the Red Sox?

Using my Series Simulator I ran 100,000 series with both the Cardinals and Red Sox with home field advantage. With the Red Sox having the advantage the Cardinals won 56% of the time largely on the strength of their major league best .642 winning percentage on the road. When Cardinals had the advantage they won 60% of the time.

Home Field Advantage Generally
But given average major league teams what is the advantage?

The average home field winning percentage in baseball is around .540. So, given two teams that both play .520 ball at home and .480 ball on the road, the winning percentage when matched up is .540 for the home team given the Log5 formula. Running a simulation for a seven game series indicates that the team with home field advantage wins just over 51% of the time. The same holds true in a 5 game series. So given two average teams the home field advantage doesn't seem to be that significant.

Wild Card Team's Chances
Another question that comes up in relation to playoff series is how often inferior teams like a Wild Card teams would beat the best team in the league. To see how often this is the case I simulated that my Wild Card team played .540 ball at home and .490 on the road (83 wins) while my "best" team or division winner played .650 at home and .550 on the road (97 wins). With that configuration the Wild Card team still won 31% of the time in a five game series.

The lesson is that even through baseball is the "game of the long season" as George Will says, the best teams still have a considerable chance of getting beat in any playoff series just as they do in a single game. I think this point should take the edge off the criticism the Braves have taken for only winning one World Series while winning 13 consecutive division titles and especially on the A's for supposedly not being able to win while employing a "Moneyball" approach. Overall, the addition of the Wild Card adds excitement to the end of the season for many teams (Cubs, Padres, Astros, Rangers, Red Sox, and A's this season) at the cost of correlating the winner of the World Series more closely with the team who garnered the best season record. Take your pick.

How Probable Was the BoSox Comeback?

That seems to be the question on everyone's mind today. To have some fun with that question I constructed a simulator in Visual Basic .NET that plays seven games series in a 2-3-2 format. I calculated the probability of each team winning their home games using the log5 method described by Bill James in the 1981 Baseball Abstract and documented by Tom Tippett at Diamond Mind Baseball here.

           A - (A * B) 

WPct = -----------------        

       A + B - (2 * A * B)

So if TeamA played .550 ball at home and TeamB played .450 on the road the probability of TeamA winning a game at home would be .599 (.55-(.55*.45))/(.55+.45-(2*.55*.45)). Interestingly, I also found a slightly different formula by Rodney Sparapani posted this April that gives the same results.

For the 2004 season the Yankees played .704 ball at home, .543 on the road while the Red Sox played .679 at home and .531 on the road. Using the log5 formula for home games then the Yankees had a probablity of winning of .677 against the Red Sox while the Red Sox had a probability of .643 at Fenway Park against the Yankees.

I then used the random number generator to simulate the outcome of the contest and record the number of victories for each side and in how many of the them the team who did not have home field advantage (the Red Sox in this case) one the last 4 games of the series.

Drum roll please....

In 100,000 ALCS matchups the results were:

Yankees: 60,109
Red Sox: 39,891

So the Yankees win about 60% of the time and the Red Sox 40%. In those 100,000 contests the Red Sox won the series after going down 3-0 754 times or .754% of the time or once every 132 series. The Yankees took the first three games 16,701 times and so the Red Sox made their comeback 4.5% of the time. That's very close to the actual number of times that the feat has now been accomplished - 1 out of 26 or 3.8%.

As an aside the Yankees swept the series 5,789 times while the Red Sox swept it 4,269 times. Here is the complete breakdown:

In case you're interested here are the probabilities for the Red Sox facing either the Astros or Cardinals.

Red Sox versus Astros = Red Sox win 60.5% of the time
Red Sox versus Cardinals = Cardinals win 56.3% of the time

For those interested the VB .NET code to run each trial is as follows:

Module Module1



    Public outcomes As New ListDictionary





    Public Sub main()

        outcomes.Add("40", 0)

        outcomes.Add("41", 0)

        outcomes.Add("42", 0)

        outcomes.Add("43", 0)

        outcomes.Add("04", 0)

        outcomes.Add("14", 0)

        outcomes.Add("24", 0)

        outcomes.Add("34", 0)

        Application.Run(New Form1)

    End Sub



    Public Function RunTrial(ByVal team1 As Team, _

      ByVal team2 As Team) As Results



        Randomize()



        Dim team1Won, team2Won As Integer

        Dim team1Home As Decimal

        Dim team2Home As Decimal

        Dim scores As String

        ' odds of team1 winning their home games

        team1Home = (team1.HomeWPct - (team2.AwayWPct * team1.HomeWPct)) / _

         ((team1.HomeWPct + team2.AwayWPct - (2 * team1.HomeWPct * team2.AwayWPct)))

        'team1Home = (team1.HomeWPct * (1 - team2.AwayWPct)) / _

        ' ((team1.HomeWPct * (1 - team2.AwayWPct)) + ((1 - team1.HomeWPct) * team2.AwayWPct))

        ' odds of team2 winning their home games

        team2Home = (team2.HomeWPct - (team1.AwayWPct * team2.HomeWPct)) / _

         ((team2.HomeWPct + team1.AwayWPct - (2 * team2.HomeWPct * team1.AwayWPct)))



        Dim i As Integer

        For i = 1 To 7  '7 game series, 2,3,2



            ' team1 has the homefield advantage



            Select Case i

                Case 1, 2, 6, 7

                    If PlayGame(team1Home) Then

                        ' team1 won

                        team1Won += 1

                        scores &= "1"

                    Else

                        team2Won += 1

                        scores &= "2"

                    End If

                Case 3, 4, 5

                    If PlayGame(team2Home) Then

                        ' team2 won

                        team2Won += 1

                        scores &= "2"

                    Else

                        team1Won += 1

                        scores &= "1"

                    End If

            End Select



            If team1Won = 4 Or team2Won = 4 Then

                ' series over

                Return New Results(team1Won, team2Won, scores)

            End If



        Next

    End Function



    Public Function PlayGame(ByVal prob As Decimal) As Boolean

        ' choose a random number between 0 and 1

        ' if <= prob then game is won so return true else return false

        If Rnd(1) <= prob Then

            Return True

        Else

            Return False

        End If



    End Function



End Module



Public Class Team

    Public Sub New(ByVal Home As Decimal, ByVal Away As Decimal, _

     ByVal name As String)

        HomeWPct = Home

        AwayWPct = Away

        TeamName = name

    End Sub

    Public HomeWPct As Decimal

    Public AwayWPct As Decimal

    Public TeamName As String

End Class



Public Class Results

    Public Sub New(ByVal team1 As Integer, ByVal team2 As Integer, _

     ByVal scores As String)

        Team1Won = team1

        Team2Won = team2

        Games = scores

        outcomes(team1.ToString + team2.ToString) += 1

    End Sub

    Public Team1Won As Integer

    Public Team2Won As Integer

    Public Games As String

End Class

A Victory for Sabermetrics?

David Pinto over at Baseball Musings writes about the sabermetric tide in baseball given the success of the Red Sox. One of the commentors to that post asked:

"doesn't the spread of sabermetric ideas mean that the market inefficiencies of the past will be competed away soon and there will be no more possibilities for progress? Or are there a host of new sabermetric discoveries to be made?"

Well, this season the Red Sox and A's, rather than progress through new sabermetric insights, tried instead to exploit the undervaluing of defense as the value of on base percentage and OPS begins to be understood as pointed out by Peter Gammons and Ken Rosenthal. Billy Beane also pointed this out in a recent interview.

However, as I've said before I think the inherent structure of the game of baseball ultimately limits the possibilities for progress. Using the Batting Runs formula, for example, the value of a homerun or a stolen base or a walk has changed only slightly since 1900. From the offensive perspective it isn't like someone will suddenly learn that stolen bases indeed are more valuable than power hitting. And even in the big picture sabermetricians pretty well understand the relative values of offense and defense (split into pitching and fielding). As a result sabermetrics will become more specialized and so I wouldn't look for "a host" of new sabermetric breakthroughs. In addition, taking advantage of what is currently undervalued can only get you so far if what is undervalued is not as valuable in an absolute sense. Right now we're in a time when some teams can and do exploit the market but with the spread of sabermetrics this advantage will be lessened.

To me, one of the last big frontiers is valuing defense more precisely. There's alot of disagreement as to how many runs a really good shortstop saves over an average one. Getting a defensive run measure to the same visibility as OPS and deprecating fielding percentage would be a big win for sabermetrics and for baseball in general.