FREE hit counter and Internet traffic statistics from

Sunday, October 31, 2004

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.

Friday, October 29, 2004

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.

Thursday, October 28, 2004

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"?

Wednesday, October 27, 2004

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.

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.

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.

Tuesday, October 26, 2004

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.

Monday, October 25, 2004

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.

Sunday, October 24, 2004

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".

Saturday, October 23, 2004

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.

Friday, October 22, 2004

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.

Thursday, October 21, 2004

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


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"
team2Won += 1
scores &= "2"
End If
Case 3, 4, 5
If PlayGame(team2Home) Then
' team2 won
team2Won += 1
scores &= "2"
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

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
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.

ALCS Recap

The Red Sox completed their more than improbable comeback last night with a 10-3 victory over the Yankees. 25 other teams had gotten down 0-3 in a best of seven but only the Red Sox even forced a game 7, let alone won it. A few observations on game 7 and the series.

  • Like many I was surprised that the Yankees did not have a better approach to Curt Schilling in game 6. They were not patient nor did they bunt forcing Schilling to throw only 99 pitches through 7 innings and never testing his bad ankle. When a pitcher is clearly injured you need to wear him down, which the Yankees seemed unwilling to do.
  • Games 6 and 7 weren't really the problem for the Yankees. Games 4 and 5 were. In game 4 they had a 4-3 going into the bottom of the 9th when a Mariano Rivera walk turned into a run to tie the game. In game 5 they held a 4-2 lead in the bottom of the eighth before David Ortiz homered off of Tom Gordon and Rivera gave up the sacrifice fly to Trot Nixon to tie the game. Perhaps Rivera should have been brought in in the 8th inning of game 5 instead of waiting.
  • In game 7 I was shocked to see Pedro Martinez on the mound to start the 7th inning. He was coming back on only one day's rest having thrown 111 pitches in game 5. Presumably he would pitch either game 1 or game 2 of the World Series. When he came in he was not sharp at all but seemed to pick up the velocity after he let in the 2 runs, striking out John Olerud and retiring Miguel Cairo. Regardless of the outcome that was a bad decision by manager Terry Francona. Derek Lowe had only thrown 69 pitches and was in command. It worked out but I don't understand it at all.
  • Throughout the series Al Leiter added alot with his commentary and showed what thinking pitchers are thinking about during a game. His comments in game 7 about the Yankees pitching pattern to Olrando Cabrera were especially interesting. He noted that the Yankees seemed to try and get him out on fastballs although Leiter knows from experience and backed it up with statistics that Cabrera is a fastball hitter hitting .213 on breaking balls and .297 on fastballs. That may explain part of the reason Cabrera hit .379 in the series.
  • On the contrary the Yankees had an excellent approach to pitching Mark Bellhorn. They pounded him inside both low and high. His homerun in game 6 was on a pitch out of the strike zone away and just a little up and his homerun in game 7 was pitch left out over the plate. Interestingly, both Tim McCarver and Joe Buck seemed critical of the decision to bat Bellhorn second in the lineup, emphasizing the fact that he struck out with a man on second and nobody out in the first inning therefore failing to move the runner over. To me this is an example of the Red Sox employing the strategy of "be the house". Yes, Bellhorn strikes out alot (177 times, tops in the AL not tops in the majors as McCarver said last night) but he also walks alot (88 times). Over the course of a season his 88 walks and .444 slugging percentage are going to move over alot of runners while his strikeouts are going to result in fewer double plays (he hit into 8). I'll take that tradeoff any day, especially if the alternative is to bat Cabrera second who has a .316 career OBP and grounded in 16 double plays in 2004.
  • As noted by the broadcast team last night the Yankees got 3.3 innings, 6 hits, 8 runs, and 7 walks out of $25M worth of pitchers in Kevin Brown and Javier Vazquez. Many will use this as proof that money doesn't win championships. The payroll ranking of the eight teams that made the playoffs are 1,2,3,7,8,11,12,19. The fact is that large payrolls result in many more playoff appearances but because of chance in short playoff series don't guarantee championships. Albert and Bennet in Curve Ball constructed a model of team performance and through a simulation concluded that the best team in any given season has a 98% chance of making the playoffs but only a 21% chance of winning the World Series.
  • I'm not sure that Joe Torre shouldn't have brought in Mariano Rivera in the 2nd inning when the game was on the line. That would have been a bold move. Vazquez did not pitch all that well in game 3 going 4.1 innings and giving up 4 runs and repeated that trick last night.
  • David Ortiz deserved the ALCS MVP award. All of his three homeruns were huge not to mention his game-winning single in the 14th inning of game 5 while hitting .387 and driving in 11 runs.
  • George Steinbrenner is sure to shake things up in the Bronx. I wouldn't be surprised to see a change of pitching coaches but although that's where it will start it'll likely only be the beginning.
  • Best Tim McCarver quote of the series - "The riptide of big innings are walks"
  • I agree with Will Carroll who notes that for a team with a really big payroll the Yankees had several obvious holes in their lineup during the series. Batting Kenny Lofton at DH and the combination of Tony Clark and John Olerud at first base as well as Miguel Cairo seems strange for a team with that much money. I don't mind Ruben Sierra at DH so much.

It's been a long week of baseball. One more night with the NLCS game 7. It's hard to bet against Roger Clemens.

Wednesday, October 20, 2004

ARod and Interference

For those interested here is the relevant passage in the rule book relating to last night's interference call on Alex Rodriguez.

"(a) Offensive interference is an act by the team at bat which interferes with, obstructs, impedes, hinders or confuses any fielder attempting to make a play. If the umpire declares the batter, batter runner, or a runner out for interference, all other runners shall return to the last base that was in the judgment of the umpire, legally touched at the time of the interference, unless otherwise provided by these rules. In the event the batter runner has not reached first base, all runners shall return to the base last occupied at the time of the pitch."

This is a part of rule 2 and was clearly violated by ARod. However, as Craig Burley points out the umpires also use a manual that interprets various rules which says in section 6.1:

"while contact may occur between a fielder and runner during a tag attempt, a runner is not allowed to use his hands or arms to commit an obviously malicious or unsportsmanlike act such as grabbing, tackling, intentionally slapping at the baseball, punching, kicking, flagrantly using his arms or forearms, etc. to commit an intentional act of interference unrelated to running the bases."

This also makes it clear that the umpires were correct.

The Federal Marriage Amendment

Robert Bork has a nice piece in First Things defending the Federal Marriage Amendment now before the Congress which reads:

"Marriage in the United States shall consist only of the union of a man and a woman. Neither this Constitution nor the constitution of any state shall be construed to require that marital status or the legal incidents thereof be conferred upon unmarried couples or groups."

Bork argues against other social conservatives such as George Will and Charles Krauthammer who think it unwise to amend the Constitution for this, or it appears, any reason. Bork then goes on to explore other possible wordings of an amendment and the consequences of homosexual marriage on the culture.

In some opposition to an amendment, as when Krauthammer says "for me the sanctity of the Constitution trumps everything" I see an unhealthy veneration of the Constitution that appears to have grown in the last 80 years. This "sanctity" of the Constitution has had the effect of making it increasingly unlikely that the Constitution will be amended. The irony is that over time more and more interpretations by courts have only the slightest connection with the text itself and are rather based on the whim of a few people. It is just such a situation that calls out for the process of amendment. A first step is to once again realize that the Constitution is a human document and that it's interpretation occasionally needs to be clarified by the will of the people.

And because the amendment will ultimately fail not because of its content but because of the Constitution's "sanctity" homosexual marriage in the states is a forgone conclusion. Bork outlines the undeniable scenario that will unfold:

"A homosexual couple will marry in Massachusetts, move to another state (say, Texas), and claim the status and benefits of marriage there. They will cite the Full Faith and Credit Clause of Article IV of the Constitution, which declares that states must accept the public acts of every other state. Texas will refuse recognition, relying on the federal Defense of Marriage Act (DOMA), passed in reliance on Article IV's further provision that Congress may prescribe the effect of such out-of-state acts. The couple will respond with a challenge to DOMA under the federal Due Process and Equal Protection Clauses. The Supreme Court will then uphold their challenge by finding a federal constitutional right to same-sex marriage that invalidates DOMA. The FMA would prevent this almost-certain outcome. Instead of state-by-state experimentation, we are going to have a uniform rule one way or the other: homosexual marriage everywhere or nowhere. The choice is that stark and judges are forcing us to make it."

Given the past behavior of the Supreme Court, can anyone honestly reason it will go down any other way?

My own view has been that homosexual marriage in isolation should probably be approved. After all, almost everyone agrees that some form of civil union is desirable in the interests of financial and legal fairness and once you go that far, civil marriage is largely a distinction without a difference. But once you go there (and why I don't think we should even if it's the "fair" thing to do), then marriage has lost any mooring it once had and can reasonably be conceived to mean absolutely anything (the same argument can be used against civil unions). I see no compelling reason why a young man may not "marry" an elderly woman for financial interests or a woman marry her son, or a group of people marry for financial and legal protection, or people "marrying" and divorcing the same or different people on a semi-annual basis in order to receive tax breaks. It is the symbolic link with child-rearing that is the basis for marriage as it now exists.

Bork addresses the argument that such arrangements couldn't or wouldn't happen.

"Many consider such hypotheticals ridiculous, claiming that no one would want to be in a group marriage. The fact is that some people do, and they are urging that it be accepted. There is a movement for polyamory - sexual arrangements, including marriage, among three or more persons. The outlandishness of such notions is no guarantee that they will not become serious possibilities or actualities in the not-too-distant future. Ten years ago, the idea of a marriage between two men seemed preposterous, not something we needed to concern ourselves with. With same-sex marriage a line is being crossed, and no other line to separate moral and immoral consensual sex will hold."

Conservatives such as Thomas Sowell often define the difference between themselves and liberals by saying that conservatives take seriously the law of unintended consequences. Sever the link between marriage and the family and I'm betting you'll see that law unleashed.

Tuesday, October 19, 2004

Excellent Umpiring

Two times in tonight's game between the Yankees and Red Sox the umpiring crew got together when a call was disputed, talked it over, and got the call correct. The first time was on the 3-run homerun by Mark Bellhorn that actually hit a fan before falling back onto the field of play and the second time when Alex Rodriguez swatted the ball out of Bronson Arroyo's glove in the bottom of the 8th. Kudos to the crew, who did the correct thing and got it right both times.

Up until just a few years ago it was not common for crews to do this. The umpire who made the original call usually stuck to his guns and wouldn't ask for help.


There was an interesting piece in The New York Times on September 19th by Alan Schwarz titled "Ball Four! Take Your Measly Base, Slugger". Schwarz is the author of The Numbers Game. In the piece Schwarz discusses the 1.433 OPS of Barry Bonds (at the time of the article - Barry has since broken his own 2002 record for OPS with 1.422) and how David Neft, the former vice president for research at Gannett, devised OAPS (On-base advantage plus slugging percentage) in order to "acknowledge this strategic aspect of the game: how walks are, to varying degrees, conscious choices by pitchers to avoid the potential damage done by slugging."

To take this into account Neft subtracts the batter's slugging percentage from 1 and uses this in the calculation of what he calls "on base advantage". Basically, this is an acknowledgment that there is an opportunity cost associated with taking a walk and that pitchers sometimes choose to walk a batter based on the potential damage pitching to the batter could do. So in practice this means that if a batter had 240 total bases, 80 walks, and 150 hits in 500 at bats his OBA would be .397, his SLUG .480, and his OPS .876. His OA would then be .330 since his walks would be worth only 52% of normal (1-.48) and his OAPS .810.

For a slugger like Bonds the difference between his OBA and OA will grow proportionately with his walk total. Whereas in our average player the difference was only .024, for Bonds it's more like .35 - fifteen times the difference and has the effect of bringing his OAPS down to around 1.07 or so. The following chart illustrates how OPS continues to rise more sharply as a batter accumulates walks while OAPS has a much smaller slope, rewarding batters less for each walk.

This approach also seems to hold up fairly well in computer models as noted by Schwarz:

"Mark Pankin, a 59-year-old investment adviser and avid baseball statistics researcher in Arlington, Va., plugged Neft's concept into his computer model and found it held up. Though the average walk costs a pitcher 0.33 runs, Bonds's walks each cost 0.17, with other players' figures going up as their slugging percentage goes down: Beltre (0.25), Guerrero (0.27) , up to the notoriously nonslugging David Eckstein of the Angels (0.36). 'It can be a meaningful difference: about 40 percent from Beltre to Eckstein,' Pankin said."

What Pankin is saying is that when Bonds doesn't walk, his plate appearances are worth an average of .16 runs. As a result, when a pitcher walks him it increases the run potential .17 runs (.33 - .16). For Eckstein on the other hand his runs per plate appearance are -.03 and so when a pitcher walks him it increases the run potential by .36 runs (.33-(-.03)). In other words it is relatively less costly to walk Bonds than it is to walk Eckstein. And of course whether you want to roll the dice and see if Bonds will make an out depends in large part whether there are runners on base, hence the strategic nature of many of his walks.

However, there is something that doesn't quite sit right about this. I don't really like the idea of punishing a hitter because they have a high slugging percentage.

One way to correct this would be to only weight Bonds' intentional walks using the formula suggested by Neft. After all, it is in these situations when we know that the defense chose a strategy of avoidance. Since 120 of Bonds 232 walks were intentional, they should be counted at .188 giving Bonds effectively 135 walks (.188*120+112) or valuing each walk at .58. Guerrero on the other hand had 14 IBB and 38 regular walks and so his walks would be valued at .84 (((14*.401)+38)/52).

But of course making this correction doesn't acknowledge the times a hitter is pitched around resulting in a "regular" walk. And for those hitters who never get an intentional walk their walks will always be valued the same as a base hit in the OPS calculation, something we know from Batting Runs that is not correct. Walks are 70% as valuable as singles overall, being worth .33 runs with singles at .47. A better approach overall would simply be to use Batting Runs with a weight such as .17 or so for the intentional walks.

In the end of course, one of the main strengths of OPS is that it is good for back of the envelope calculations and so introducing more complexity into it defeats some of its purpose.

Monday, October 18, 2004

Kauffman Park Effects 2004

Since the season is over for the Royals I thought I'd update the Kauffman Stadium run scoring spreadsheet that I started before the season started and blogged about previously.

My interest in this began when considering how the fences being moved back 10 feet at the K last winter would affect the run scoring at the park. So here are the updated numbers:

	Home				Away			Index		

Games Royals Opp Opp%+ Games Royals Opp Opp%+ Royals Opp Overall
2004 80 338 426 26% 82 382 479 25% -9% -9% -9%
2003 80 433 512 18% 82 403 355 -12% 10% 48% 28%
2002 81 434 505 16% 81 303 386 27% 43% 31% 36%
2001 81 382 485 27% 81 347 373 7% 10% 30% 20%
2000 81 451 488 8% 81 428 442 3% 5% 10% 8%
1999 80 441 449 2% 81 415 472 14% 8% -4% 2%
1998 80 353 492 39% 81 461 407 -12% -22% 22% -1%
1997 80 387 434 12% 81 360 386 7% 9% 14% 11%
1996 80 372 369 -1% 81 374 417 11% 1% -10% -5%
1995 72 285 346 21% 72 344 345 0% -17% 0% -8%
1994 59 325 287 -12% 58 249 245 -2% 28% 15% 22%
1993 81 370 354 -4% 81 305 340 11% 21% 4% 12%
1992 81 314 346 10% 81 296 331 12% 6% 5% 5%
1991 81 344 378 10% 81 383 344 -10% -10% 10% -1%

91-94 302 1353 1365 1% 301 1233 1260 2% 9% 8% 9%
95-03 715 3538 4080 15% 721 3435 3583 4% 4% 15% 9%

As you might have expected the end result is that fewer runs were scored at Kauffman Stadium this season than on the road to the tune of 9% - obviously a big difference from the trend of 2001-2003 when about 26% more runs were scored at the K and the historical trend of +9% since 1991. One shudders to think how many runs Darrell May and Brian Anderson might have given up with the fences at their 2003 distances. As it was they gave up 38 and 33 homeruns respectively, the former setting a Royals record.

However, these quick and dirty numbers don't translate directly into park factors used by sabermetricians to normalize statistics such as OPS and Runs Created. The calculation of BPF (Batter Park Factor) and PPF (Pitcher Park Factor) is rather complicated and a complete explanation can be found on using the same basic formula as Total Baseball and originally documented in The Hidden Game of Baseball.

Suffice it to say the BPF and PPF also take into account things like:

1) the innings pitched difference between home and road games (a good team at home will get fewer at bats and thus score fewer runs than on the road)
2) the impact of the team's park on the park factors of other teams
3) the fact that hitters don't get to bat against their own pitchers and vice versa
4) and that a player only plays half his games at his home park.

In addition they are typically calculated using averages over several seasons (I think it might make more sense to use weighted averages since I would assume that weather patterns varied by groups of years as well as single years). This is important since there is a large element of variation in run totals in a park from season to season based on weather, individual players, and simply luck. So I wouldn't be surprised if run scoring increased at the K next year since we had a cooler and wetter summer in KC than in years past.

So the BPF and PPF for these seasons from, which uses a 3 year average, actually calculate to:

2004 95 96
2003 113 112
2002 117 115
2001 110 109
2000 104 103
1999 101 101
1998 104 105
1997 102 103
1996 97 98
1995 103 103
1994 104 104
1993 104 105
1992 103 103
1991 100 101

Obviously this tends to even out the fluctuations between 1994-95 and 1997-98. And it would appear that the factors of 95/96 for 2004 may not be the result of a three year average. If they were the BPF would have to have been very low indeed. If not, then this makes sense when configuration changes are made to the park as was the case at the K this season.

Triples Galore

In response to a question on SABR-L I dug into retrosheet data for 1992 (I now have the 2003 data but haven't loaded it yet courtesy of the Stats Software group on Yahoo). The questioner asked how often triples drove in runs, how often the batter hitting the triple scored, and how often both occurred. Here's what I came up with:

Lg 3b RBI Score3b Pct 3bScored Pct 3bRbiScore Pct
NL 459 289 207 45.1% 316 68.8% 117 25.5%
AL 386 264 187 48.4% 252 65.3% 93 24.1%

Where Score3b is the number of times a triple drove in at least one run, 3bScored is the number of times the batter who hit the triple scored, and 3bRbiScore is the number of times the batter drove in a run and later scored in the inning.

If I did the calculation correctly (this was my first effort at doing inter-inning analysis with retrosheet data) it is suprising that 46% of triples ended up scoring a run or more since the OBP is roughly .330. That means that triples are hit more frequently with men on base than you would expect. The percentage of batters hitting triples that score seems about right (67%) when looking at run expectancy tables.

Sunday, October 17, 2004

Advanced .NET Compact Framework Development

Here is a PPT talk that I'll be giving at the Wichita .NET User's Group in a couple of weeks. It covers several advanced .NET Compact Framework development techniques incuding P/Invoke, Detecting Network Presence, and making Smart Devices Smart Clients.

A Study of 1 Peter

The small group my wife and I attend are doing a 9-week study on 1 Peter. This year I'm leading the group and so have prepared a few notes each week in preparation for the time meeting. For those interested I've placed the notes I use here for download:

Week 1: Introduction and Background
Week 2: 1 Peter 1:1-13 A Precious Salvation
Week 3: 1 Peter 1:14-25 A New Way of Life
Week 4: 1 Peter 2:1-10 A Chosen Priesthood
Week 5: 1 Peter 2:11–2:25 Submission to Rulers and Masters
Week 6: 1 Peter 3:1–3:12 Wives and Husbands
Week 7: 1 Peter 3:13–4:6 Doing Good: The Promise of Vindication
Week 8: 1 Peter 4:7-19 Mutual Love: The Key to Christian Community in the End Times
Week 9: 1 Peter 5:1-14 The Responsibilities of a Church in the Midst of Trials and Concluding Remarks

The outline I'm following was based on one created by Daniel B. Wallace, Ph.D. Professor of New Testament Studies Dallas Theological Seminary.

Disclaimer: I have no formal theological training and so read through these at your own risk. I did try and document from where some of the background material is taken from for each week so you can find the original source yourself. I generally come from an evangelical perspective but I tend to differ in areas such as eschatology and inerrancy.

Saturday, October 16, 2004

A Brief History of Run Estimation: Batting Runs

The following is the second article in my series on the sabermetric history of run estimation. This article covers Pete Palmer's Batting Runs, a component of the Linear Weights system.

Batting Runs, a linear run estimator, was developed by Pete Palmer in the 1970s and was introduced as a part of his Linear Weights (LWTS) system to the world in his and John Thorn's 1984 book The Hidden Game of Baseball, like Bill Jame's Baseball Abstracts, one of the preeminent documents in the history of sabermetrics. Palmer went on to apply his linear weights system to defense and pitching and derive his Total Player Rating (TPR) system that was tracked in Total Baseball and continues as Batter-Fielder Wins (BFR) and Pitcher Wins (PW) in the 2004 edition of The Baseball Encyclopedia.

However, the history of Batting Runs and Linear Weights actually goes back much further.

As documented by Alan Schwarz in his excellent book The Numbers Game, F.C. Lane, the editor of the Baseball Magazine from 1912-1937 was actually the pioneer of linear weights when he observed that batting average was an inadequate way of measuring the contribution individual players make to winning baseball games by remarking in 1916,

"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..."

So Lane took it upon himself to correct the situation and kept track of the results of 1,000 hits and their results in order to assign them coefficients to use in an equation he developed. The simple equation was:

Total Run Value = (1B*a)+(2B*b)+(3B*c)+(HR*d)

The values for a,b,c, and d he assigned were .30, .60, .90, and 1.15. The core of Lane's observations of the 1,000 hits being that the hits were not only valuable for the obviously different number of bases gained by each, but there was also a component of advancement value that contributed to run creation. Later Lane also assigned a value of .164 to walks, a value now recognized as too low by half but revolutionary for its time by crediting a walk on the batter's part as valuable at all.

It must also be remembered that Lane's innovation came in a time when batting average, made official way back in 1876, was the only way most people had ever evaluated offensive players. It is true that Henry Chadwick developed a stat in the 1860s he called "Total Bases Per Game", which was slugging perentage with a different denominator, but it didn't really catch on and slugging percentage was not made official in the National League until 1923 and the American League until 1946.

Lane used his formula to compare Brooklyn firstbaseman and former batting champion Jake Daubert to Phillie's slugger Gavvy Cravath, who had hit 24 homeruns in 1915. Not suprisingly, Lane's analysis showed that Cravath was the more valuable player with a Total Run Value of 79 versus 62 for Daubert.

Lane went on to adjust his formula and eventually settled on the following:

Total Run Value = (1B*.457)+(2B*.786)+(3B*1.15)+(HR*1.55)+(BB*.164)

Unfortunately, Lane's pioneering work was all but forgotten soon after.

In the mid 1950s George Lindsey, a military officer, listened to and watched around 400 baseball games and from what he learned he began submitting articles to the statistical journal Operations Research on various aspects of baseball strategy. With the help of his retired father their combined scoring efforts produced the 1963 article "An Investigation of Strategies in Baseball", another of sabermetric's founding documents. In that article Lindsey produced the first Run Expectancy table, a table that showed how many runs were expected to score from any of the 24 base/out combinations (I use a similar table in my Big League Pocket Manager application for the Pocket PC to calculate the break-even probabilities for various strategies).

O/B 0 1 2 3 1,2 1,3 2,3 Full
0 0.46 0.81 1.19 1.39 1.47 1.94 1.96 2.22
1 0.24 0.50 0.67 0.98 0.94 1.12 1.56 1.64
2 0.10 0.22 0.30 0.36 0.40 0.53 0.69 0.82

From here it was a simple step to calculate the run expectancy before an offensive event occurred, the run expectancy after, and along with the typical advancement on singles and doubles and the frequency of the base/out combinations (which Lindsey also tracked), compute the run values or weights for each offensive event. Lindsey came up with .41 for singles, .82 for doubles, 1.06 for triples, and 1.42 for homeruns - very similar to what Lane had done 40 years earlier.

Interestingly, Lindsey like Lane then used his system to compare a singles hitter, in this case the Tiger's Harvey Kuenn who had won the 1959 AL batting championship hitting .353, with a homerun hitter, the Indians Rocky Colavito who had hit 42 homeruns. This comparison had a bit more riding on it as the two were traded for each other. Colavito came out on top 114.5 to 112.6.

Using Run Expectancy and advancement tables like those calculated by Lindsey is only one way of calculating run values for various offensive events. And this brings us back to Batting Runs and Pete Palmer.

In 1978 Pete Palmer ran a computer simulation of "all major-league games played since 1901." From that simulation Palmer tabulated the frequencies of the offensive events and by assigning advancement values based on observation of 100 World Series games was able to calculate the expected run values for each event. The formula he devised was:

Batting Runs = (.46*1B)+(.80*2B)+(1.02*3B)+(1.40*HR)+(.33*(BB+HBP))+(.30*SB)+(-.60*CS)+(-.25*(AB-H))-(.50*OOB)

What is interesting about this formula first is that it includes hit by pitch (HBP) and stolen bases and of course that the weights are similar to those calculated by both Lane and Lindsey. It's real import, however, is that for the first time the number of outs (AB-H, CS, and OOB or "outs on base") the player is responsible for is included and given a coefficient. Like other offensive events, outs have a run value, it is simply the case that the run value is negative since outs decrease the opportunity for scoring runs by either ending an inning or moving the team in that direction. Typically, OOB is difficult if not impossible to find for individuals without play-by-play data but for teams is simple to calculate as OOB = H+BB+HBP-LOB-R-CS.

Stolen bases and caught stealing can also be taken out of the Batting Runs formula and be calculated separately as Stolen Base Runs (SBR) or Base Stealing Runs (BSR) as (.30*SB)-(.60*CS). Originally, the value of the stolen base and caught stealing was set at around .20 and -.35 respectively. However, Palmer was convinced by Dave Smith of Retrosheet to increase both the positive and negative impacts of the stolen base on the basis that they occur in situations where games are more in question. In other words, stolen bases are strategically more important and so have a greater impact on wins and losses. Not many people seem to buy this argument since runs and not wins are what is being calculated. Apparently, Palmer agreed and so in The 2004 Baseball Encyclopedia BSR is simply calculated as (.22*SB)-(.38*CS).

The most important fact about Batting Runs is that because of the inclusion of negative values for outs Batting Runs is a measure of the "net runs produced above average" in a given offensive context. In other words, a Batting Runs value of 55 means that the batter produced 55 runs above what an average batter would have produced given the same opportunities, which means given the same number of outs consumed. Of course, this also means that a player can be assigned negative Batting Runs indicating they performed below average. Batting Runs, therefore cannot be compared with Runs Created without making adjustments. That adjustment is to reduce the value of the out from around -.25 to -.10 or -.09. The basis for this is straightforward. The value of an out (or any offensive event for that matter) can be thought of as the sum of the value the out in moving runners over and the value of ending the inning. Using the run environment of 4.3 runs per game (the average runs per game from 1901-1977) each out is worth -.16 runs in terms of its inning-ending value. Subtracting -.16 from -.25 yields a value of -.09 as the value of the out related to moving runners along. By using -.09 as the value for outs, Batting Runs can be compared to Runs Created.

It's also important to keep in mind that technically the Batting Runs formula shown above is valid only for a given offensive context, namely the 4.3 runs per game of 1901-1977. Palmer and Thorn show in The Hidden Game several sets of weights by period (1901-20, 1921-40, 1941-60, and 1961-77). Fortunately, these values are very similar, something Palmer apparently did not expect, thinking that in the "deadball era" the relative value of a stolen base might be significantly greater and homerun smaller (they were but only very slightly, for example the homerun going from 1.36 in the earliest period to 1.42 in the latest and the stolen base going from .20 to .19).

As a result, Palmer was able to present a single formula and use the value of the out to adjust for differences by era. Some out values for different eras as noted in Curve Ball and The Hidden Game are:

-.24 for 1901-1920
-.30 for 1921-1940
-.27 for 1941-1960
-.25 for 1961-1977

In the modern era Palmer then recommends that a value of -.25 value be used when pitcher's hitting is included (for example in the NL) while a value of -.27 is recommended when the DH is employed since making an out is more costly when the run environment expands as it does when pitchers are not hitting.

Batting Runs has also been adjusted slightly throughout the years using different weights. For example, the formula in the 1989 edition of Total Baseball was:

BR = (.47*1B)+(.78*2B)+(1.09*3B)+(1.40*HR)+(.33*(BB+HBP))+(.30*SB)+(-.60*CS)+(-.25*(AB-H))

And the formula in the 2004 edition of The Baseball Encyclopedia reduces the weights of the extra base hits by including their value into the value for hits since singles are not weighted separately:

BR = (.47*H)+(.38*2B)+(.55*3B)+(.93*HR)+(.33*(BB+HBP))+(.22*SB)+(-.38*CS)-(ABF*(AB-H))

Also included here is ABF, or the "league batting factor". This is essentially a custom "out" value for the league context to ensure that the average batter's Batting Runs equal zero for the given league and year. It is calculated using league totals as:

ABF =((.33*(BB+HBP))+(.47*H)+(.38*2B)+(.55*3B)+(.93*HR))/(AB-(LGF*H))

For example, the ABF in the NL for 2003 was .28 and in the NL for 1968 was .23 since the increased offensive context of 2003 dictates that an out cost a team more potential runs than it did in 1969.

LGF in the calculation of ABF is the league factor designed to increase the number of Batting Runs for leagues deemed inferior to the typical major-league. It equals 1 expect when it is:

Union Association (1884) = .8
Federal League (1914-15) = .9

In reality, the linear weights associated with Batting Runs differ not only by era but also by league and for each league by each individual team and for each team by position in the batting order. In other words, in order to caclulate how many runs an individual player is responsible for it would be necessary to calculate weights for each offensive event that were particular to his team and position in the batting order. However, because of the complexity of making such calculations and because creating custom linear weights at the lower levels reduces their usefulness for comparison across teams, leagues, and eras, most sabermetricians use a single formula and adjust the outs value based on era or league. For an interesting discussion of creating custom linear weights see Tangotiger's site.

Another area for refinement in the era of Barry Bonds is separating the value of a regular base on balls from an intentional walk, and for that matter hit-by-pitch. The general consensus is that a regular walk has a weight around .31 while an intentional walk is around .18 and a HBP slightly more than a regular walk (since walks occur disproportionately with two outs and when first base is empty).

From the beginning adjustments have been made to Batting Runs. The most obvious, and one that Palmer and Thorn discuss in The Hidden Game is to take the batter's home park context into consideration. To do so they first calculate the BPF or Batter's Park Factor. This number is based on the number of runs scored in the park versus the number of runs scored in road games and takes into account the fact that hitters don't have to face their own pitchers. BPF is centered on 1 and so an above average hitter's park will have value slightly above 1 such as 1.04 while a pitcher's park will have a BPF of under one, say .96.

In order then to calculate the Adjusted Batting Runs or ABR the following calculation is used:


Here BR is the unadjusted Batting Runs, RPA is the number of runs per plate appearance for the league, and PA is the plate appearances for the batter. For example, if the player had 55.0 batting runs in 700 plate appearances while playing in a pitcher's park with a BPF of .92 in a league like the 2003 National League where .122 runs were scored per plate appearance, the ABR would be 55-((.92-1)*.122*700/.92) = 58.6.

A second derivative is a conversion from Batting Runs to wins, or Batting Wins. This statistic is based on Palmer's empirical observation that on average a win is purchased at the cost of 10 extra runs. In other words, if a player contributed 10 Adjusted Batting Runs, then he was worth 1 extra win to his team. Of course, the number of runs per win varies with the league context and can be calculated as:

RPW = 10*Sqrt(RPI)

RPI or Runs per Inning here is the runs scored by both teams per inning. So for a league that scores 4.5 runs per game, the two teams combined score 1 run per inning, the square root of which is 1, multiplied times 10 equals 10. As a result, in lean offensive times like the 1968 NL the RPW will be around 8.75 while in good offensive times like the 2003 NL it will be closer to 10.5.

It is then a simple matter then to divide the Adjusted Batting Runs by RPW to get the Batting Wins. The formula used in the 2004 edition of The Baseball Encyclopedia is:

BW = ABR/(10*Sqrt(RPI+(ABR/G/9)))

In this case the runs per inning of the player is added to the runs per inning for the league to take into consideration the increased or decreased offensive context that the player contributes.