The Curious Case of Mark Teahen

With Craig Brown's excellent review of Mark Teahen published a couple weeks ago, I thought it would be appropriate to re-publish my take on Baseball Prospectus regarding Teahen published around the same time as Brown's first piece back in August of 2006. Obviously, things haven't turned out so well for Teahen and so far in 2008 the prognosis isn't really any better. Still, it's always instructive to look at what we got wrong and not just what we got right and so without further ado...

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August 31, 2006
Schrodinger's Bat
The Curious Case of Mark Teahen

"I think it's well-documented how I feel about [Teahen], and how I feel about him as a ballplayer. I don’t need to add anything to that discussion." --Former Royals General Manager Allard Baird, perhaps with an "I told you so" when asked about the third baseman's breakthrough season.

On August 22^nd of this season, Mark Teahen, Royals third baseman and former centerpiece of the deal that sent Carlos Beltran to Houston at the trading deadline in 2004, stepped in against the Indians' Cliff Lee in the first inning. Teahen would blast a two-run home run, his 16^th of the year. Rather than call it a day, Teahen would add two doubles and a single, steal two bases (one of third base), and score the go-ahead run in a 5-2 Royals victory.

My, how times have changed.

At this time last year, eight total bases in one game would have seemed like a pipe dream for a player many were starting to consider a bust, and nothing more than a product of overblown Moneyball hype. No longer: going into Tuesday's action, Teahen was hitting .296/.368/.535 overall, and had hit an especially robust .337/.421/.633 with ten home runs since the All-Star break. That adds up to a WARP1 of 5.3 and an Equivalent Average of .305, two numbers that suggest that Teahen, at least, might heal one of the many wounds of Royals fans, and in a small way redeem the reputation of former GM Allard Baird.

Beyond the raw performance, what we really want to know is what's behind his turnaround, and whether or not we can expect this kind of performance to continue. This week, we'll address both by revisiting the themes of an article I wrote last season.

Where He's Been
The primary question about Teahen, even before he was drafted, was when or if the 6'3" 210-pounder would develop power. Teahen had always hit the ball the other way with a swing he mastered in innumerable childhood wiffle-ball games played against his brothers. In Moneyball, Michael Lewis used Teahen as an example of the new thinking in player development by relating a conversation between then-scouting director Eric Kubota, a scout, and GM Billy Beane. In Lewis' version, Beane ends the speculation about Teahen by noting that "power is something that can be acquired. Good hitters develop power. Power hitters don't become good hitters."

The A's drafted Teahen in the first round with the 39^th pick of the 2002 draft, even though he had hit just ten homeruns in over 600 plate appearances during his three seasons at St. Mary's College of California. The A's attempted to help him develop power by getting him to pull the ball, according to Lewis:

To teach him how to pull the ball, the Oakland staff took Teahen into a room and showed him tapes of Jason Giambi. Giambi once had been just like him, they said: a third baseman who hit well but not powerfully. At the end of his first season, Oakland sent Teahen to a training center in Florida with instructions to gain 15 pounds and drop his body fat from 15 percent to 10 percent. He made a halfhearted stab at it—and put on fat. ("I'm not sure how you do that, gain 15 pounds and lose all that body fat," he says. "It'd be a lot easier if they didn't include the body-fat part of it.") The extra weight made him feel clunky. And the attempt to pull the ball felt wrong. He dropped the weight, and kept on hitting the ball the other way. He didn't want to be Jason Giambi. He wanted to be Mark Teahen.

After that experiment failed and he was traded to the Royals in the Beltran deal, his new team also attempted to get him to pull the ball, sitting him down with no less an authority on hitting than Hall of Famer George Brett. Brett introduced Teahen to the Charley Lau approach to hitting for a couple of days. At the time, that didn't seem to quite have the intended results either:

For two days, with Brett looking on, Teahen went into the Triple-A batter's box and cantilevered backward, bat lowered and tucked tightly against his back shoulder. Just like George Brett! Then Brett left--and Teahen went right back to hitting a baseball the way he always had. "Two days!" Brett said, six months later, not knowing whether to laugh or scream. "That kid, he did what I showed him for two days…Then the moment I left he went back to doing it his way."

As a result, up until this year Kubota's skepticism about Teahen seemed to be well-justified. In 1,468 minor league plate appearances, Teahen hit a grand total of 18 home runs, one more than he has this season in a quarter of the plate appearances, although 14 of those came in 2004 while he split time between Double- and Triple-A. All told, he put up a career minor league slugging percentage of just .409. Annointed as the Royals' third baseman in spring training last season, he continued his light-hitting ways by hitting a meager .246/.309/.376 in 491 plate appearances.

All of this led our PECOTA system to list his top five comparables coming into 2006 a squad of non-stars:

Jim Mason

Mike Darr

Bobby Smith

Lee Stevens

Travis Lee

That's not an impressive group, to say the least, although Jim Edmonds comes in as Teahen's seventh comparable, and Larry Walker shows up at 11. In addition, the five-year forecast never had him above 12 home runs or a .448 slugging percentage, and he was given a dangerously high attrition rate of 23%. At best, that forecast made him a serviceable player, worth around two to three wins per year, but certainly unspectacular. It was a projection of a player vulnerable to, in an evolutionary sense, being selected out of the majors as a third basemen or corner outfielder.

Given this scenario and the similar low-wattage disappointments trailing another hyped third base prospect, Sean Burroughs (who has since been released by the Devil Rays after hitting just .214 in 37 games at Durham), I wrote a piece last July that took a look at both of their performances up to that time, and tried to find comparable players using Isolated Power (ISO) to get a historical sense of just what they were up against. Basically, the idea was to use ISO (slugging percentage minus batting average, providing a measure of the number of extra bases a player generates) to see how frequently players that matched their profile (defined as 1,000 or more at bats plus walks before the age of 24) went on to develop greater than average power. I also normalized ISO to both park and league by creating Normalized ISO (NISO) for the comparisons.

What I found was that there did appear to be some precedent for players like Teahen increasing their power, notably infielders Roy Smalley, Lou Whitaker, Toby Harrah, and George Brett, and outfielders Kirby Puckett and Roberto Clemente. I also found that players who made the largest gains in ISO after their Age-24 season typically make great gains between 24 and 27, and reach their peak performance by 28 before beginning a slow, gradual descent.

What He's Doing
As Royals fans well know, the change in Teahen correlates with his demotion to Omaha on May 6^th. When sent down, he was hitting just .195 (15 for 77) with two home runs. Down in Omaha, he worked with hitting instructor Terry Bradshaw, providing strong support that in this case correlation is indeed causation:

Omaha hitting instructor Terry Bradshaw made a video of Teahen’s good at-bats from last year. What better way to teach a stubborn student than to let him learn from himself? The mechanical changes were subtle. They shortened Teahen’s swing, kept his hands back, and made a minor adjustment with his hips that allowed him to hit inside pitches better.

Once he did that, the Royals had no choice but to call him back up. He was 28 for 56 with a 1.107 slugging percentage and .606 on-base percentage in his last 17 games in Omaha.

In addition, Teahen revealed in an online chat last month that Bradshaw emphasized that he start using his legs more. As Teahen himself says, "That has resulted in harder contact and ultimately pulling the ball more often."

Although Brett may have thought that his advice had no effect, it now appears that Teahen absorbed what the Hall of Famer was teaching, and has been working on incorporating it into his approach:

I took what he told me and tried to find out mechanically what I could do to get that same effect. I wasn’t going to look like George Brett at the plate, but I was going to try to use some of his ideas to get me in that same position.

The results are fascinating. Using data from the excellent FanGraphs site we can see that the combination of subtle mechanical changes, more emphasis on using his legs to generate torque, and confidence has led to a sea change in how Teahen puts the ball in play.

Year      GB/FB    LD%    GB%    FB%  HR/FB
-------------------------------------------
2005       2.22  23.5%  52.8%  23.8%   8.6%
2006       1.39  14.6%  49.7%  35.8%  16.5%

The result is that his line drives are turning into fly balls (up over 50%), and those fly balls are being driven out of the park or deep into the gaps. His profile has turned from one common to a contact hitter to one that looks more like the Phillies' Ryan Howard, albeit with a few more ground balls. In the meantime, Teahen's batting average on balls in play is at .336, somewhat higher than the league average (around .300). Coupled with his relatively low line-drive percentage, it remains to be seen whether his refinements will allow him to maintain a BABIP that high, or whether he'll regress somewhat. Keep in mind that we're still talking only about a few hundred plate appearances since he was recalled from Omaha.

It's also clear that despite Teahen's self-proclaimed increased propensity for pulling the ball, he's still being true to his natural hitting style for the most part, and is not simply looking to yank the ball down the line at every opportunity. The following chart from MLB.com tracking his home runs and doubles at Kauffman Stadium this season indicates that his power is to all fields, especially to left-center:



The following chart tracking 15 of his 17 home runs (two couldn't be located using the interface) provides a similar picture:



Where He's Going?
So given the apparent turnaround, can history provide any guide to what we might expect from Teahen from here on out?

To help answer that question, I did what any good performance analyst might do: I looked for comparable players. I was particularly interested in whether Teahen's newfound power was a good bet to last. To try and get a feel for this, I created a list of players who'd had between 400 and 600 at-bats plus walks before their Age-24 season, who had debuted after the 1945 season, and who had in those opportunities recorded a Normalized ISO between 65% and 100% of league average. In other words, these were players who didn't show much power before their 24^th birthday, but who had nevertheless accumulated a fairly significant number of at bats by that time. This produced a list of 90 players, ranging from Preston Ward (who debuted in April 1948) to Teahen and J.J. Hardy (who both debuted last season). This is a more targeted study than the one done in the previous article. I used these particular criteria because Teahen sits squarely in the middle, with 487 at-bats plus walks and a NISO of .828 before his Age-24 season, figures that ranked him 36^th on the list.

Of the 88 players who debuted before 2005, 77 of them are no longer active but went on to play past their Age-23 season, and as a group they lasted an average of another 8.3 years and recorded an NISO of .869. As a group, here's a chart reflecting their aging pattern with regards to NISO; the yellow line is the three-year moving average:



Keep in mind that this graph includes a heavy dose of selection bias, as more players are included in the Age 24-31 categories, after which many of the players are out of the majors, finally leaving a core group of pretty decent players who continue to play into their late 30s. Beyond the pretty common observation that these types of players don't tend to last past their early 30s, the chart shows that these players as a group tend to increase their power a bit more slowly than is typical, and don't peak until around their 30^the birthday, whereas the total population normally reaches their peak at ages 27-29. Unfortunately, it also indicates that as a group these guys never reach a league-average NISO.

That grim observation aside, all is not lost. The good news is that in terms of increasing isolated power, Teahen's good enough to rank near the very top of the list. The following are the ten players among these Teahen comparables who ended with the highest NISOs through 2005:

Name                Bats   Seasons   AB+BB   AVG    SLUG   ISO    NISO
-----------------------------------------------------------------------
Todd Hundley          B         11    3706   .239   .464   .225   1.477
Tony Batista          R          9    4090   .251   .466   .215   1.341
Dave Duncan           R          7    2560   .223   .373   .150   1.290
Daryl Boston          L          9    2313   .253   .425   .172   1.284
Davey Johnson         R         12    4772   .262   .412   .150   1.269
Mike Sweeney          R          8    4182   .309   .513   .204   1.259
Torii Hunter          R          6    3140   .269   .470   .201   1.242
Dmitri Young          B          8    3900   .294   .491   .197   1.232
Dave Nilsson          L          6    2585   .291   .480   .188   1.188
Nick Johnson          L          3    1218   .278   .457   .179   1.136

As you can see, there are some encouraging signs here, particularly in the cases of guys like Davey Johnson, Mike Sweeney, Dmitri Young, and Nick Johnson making the list. At this point, Teahen would rank second, with a NISO past his Age-23 season of 1.37. This is much better company to be in than the preseason PECOTA comparables we listed previously, or even most of the rest of the 88 comparables found by this method.

There is certainly no magic that will tell us the future, but from a historical perspective, what we can say is that there is some precedent for the kind of transformation we seem to be witnessing, although the magnitude of Teahen's big step forward is not exactly typical. Combined with the anecdotal and statistical evidence of his changed approach, Teahen's improvement is therefore not likely a mirage predicated on small sample size. If he continues performing even close to the level of his last three months, he'll finally fulfill the expectations of Billy Beane and Allard Baird.

I think Royals fans can be cautiously optimistic, with the hope that in the years to come the controversy surrounding Teahen will not be whether he'll develop power, but how the team will accommodate two good young hitters at the hot corner once Alex Gordon is ready for the big leagues. That's the kind of problem everyone would like to have.

Heading to Steel Town

Today my column on Baseball Prospectus did not feature any new analysis or the usually endless tables overflowing with numbers and headed with three-letter acronyms. No, today marked the 100th and (at least for now) final Schrodinger's Bat column, marked with the title "Opus 100".

The column does not require a subscription and so you can read it for yourself but in the final section I briefly discuss the reason that this centennial edition is the last in the series.

To borrow from that bit...I'm leaving BP to join the front office of the Pittsburgh Pirates to become their Director of Baseball Systems Development. In that capacity I'll be assisting the excellent staff--including Kyle Stark, Bryan Minniti, Greg Smith, and Joe Delli Carri, under the direction of General Manager Neal Huntington--in building systems to support and inform the decision-making process of the baseball operations staff. All of those individuals mentioned, and many others, have made me feel more than welcome, and I'm thrilled to start the process of integrating the array of quantitative and qualitative information in a way that makes both even more instructive.

While I'm very excited at the new challenges and opportunities, I'm also a little sad as I say goodbye to Compassion International, where I've worked as a software architect for the last three years. Beyond the successes of the team in building a service oriented infrastructure that I've been blessed to be a part of, working at Compassion has truly been a wonderful experience. The dedication, intelligence, and vision of the organization and its employees to release children from poverty in Jesus' name is truly inspiring. It really is a great place to work and hey, I hear they might be looking for someone :)

Historical SFR

A couple days late in my summary of this week's effort on Baseball Prospectus but this week I ran the Simple Fielding Runs (SFR) system against Retrosheet data from 1988-1998. This was possible without modifying the system since the relevant hit type and fielder data is present for those eleven seasons (in the same ratios as available for 2003 through 2007 for the major leagues and 2005-2007 for the minor leagues).

Although you'll need to read the piece to get all the details, suffice it to say that Ozzie Smith, Cal Ripken, Mark Lemke, Ryne Sandberg, Matt Williams, John Olerud, and Mark Grace all come out looking pretty good as you might expect.

A reader asks, however, how Roberto Alomar and Omar Vizquel look and so here's a look at their complete data calculated for SFR thus far.

Roberto Alomar, 1988-2004 at Second Base
Year    Team       Age   Balls Runners    Diff     SFR    Rate
1988    SDN         20     624     126       8     5.9    1.06
1989    SDN         21     672     153      -4    -2.8    0.98
1990    SDN         22     593     138      -9    -7.2    0.93
1991    TOR         23     744     192      10     7.2    1.05
1992    TOR         24     619     167      -4    -3.3    0.97
1993    TOR         25     650     161      -6    -4.8    0.96
1994    TOR         26     395     101      -3    -1.9    0.97
1995    TOR         27     564     127       2     1.7    1.02
1996    BAL         28     605     130      15    11.1    1.11
1997    BAL         29     383      76      19    14.0    1.25
1998    BAL         30     587     144      15    10.9    1.10
2003    CHA/NYN     35     523     148     -22   -16.7    0.85
2004    ARI/CHA     36     125      37      -6    -4.4    0.84

                          7083    1699      13     9.6    1.01

Interestingly, while SFR didn't like Alomar much in San Diego and Toronto, it did in his three years in Baltimore. Keep in mind that for infielders SFR does not take into account park effects and that both the shortstop and first baseman have an impact on the second baseman since the system parcels out balls assigned to each via overall distributions. Both of these may play a factor here although I haven't researched Baltimore particularly although I did note that Sean Smith's system incldues a similar disparity. Overall Alomar rates out at +9.6 runs and a rate (computed as the ratio of expected runners reached to actual runners) just above average at 1.01.

Omar Vizquel, 1989-2007 at Shortstop
Year    Team       Age   Balls Runners    Diff     SFR    Rate
1989    SEA         22     557     130       9     6.6    1.07
1990    SEA         23     356      90       0     0.1    1.00
1991    SEA         24     609     152      13     9.5    1.08
1992    SEA         25     656     189       1     1.0    1.01
1993    SEA         26     719     188       3     2.6    1.02
1994    CLE         27     293      70      10     7.3    1.14
1995    CLE         28     570     133      18    13.4    1.13
1996    CLE         29     655     168       5     4.2    1.03
1997    CLE         30     633     142      15    11.2    1.10
1998    CLE         31     656     185      14    10.5    1.08
2003    CLE         36     295      59      14    10.4    1.24
2004    CLE         37     597     159      -3    -2.6    0.98
2005    SFN         38     654     153      13     9.4    1.08
2006    SFN         39     590     147       9     7.0    1.06
2007    SFN         40     639     134      38    28.5    1.29

                          8478    2097     159     119    1.08

Vizquel is predictably excellent for most seasons and rated highest last year although once again, his third baseman certainy had some influence.

Those interested in this topic should definitely check out Sean Smith's work at The Hardball Times where he expands his TotalZone system and provides lots of interesting results.

A Common Theme

Coincidentally, the John Dewan stat of the week this week happens to correspond quite nicely with my Schrodinger's Bat column titled "Clearing the Decks" posted today on Baseball Prospectus. John talks about the best bunters of 2007 and in my column I do a little of that in relation to the Tattered Cover book signing that I pariticpated in several weeks ago before moving on to the minor leagues best bunters from 2005 through 2007.

In additon I take a look at the concept of "free bases" recently discussed by Rangers' staff as well as the recent 2008 Scout's Honor Results posted on MLB.com. It's in that section that I revisit the topic of bunting a little and have this to say on the scout's choices in that category.

Best Bunter: Juan Pierre, with Ichiro Suzuki runner-up. Near and dear to the first topic discussed this week. While Pierre is the most prolific bunter over the past six years (320 attempts), his success rate ranks 16th out of the 18 players with 75 or more attempts during that span, with a success rate of 41 percent. Suzuki doesn't bunt nearly as often, but does succeed more frequently at 59 percent in 59 attempts. No, Willy Taveras would clearly be the better choice with Luis Castillo (54 percent in 84 attempts) and Corey Patterson (51 percent in 128 attempts) undoubtedly better as well.

Of course I critique a few of the other choices as well...

Baseball's Trifecta

This article originally appeared on Baseball Prospectus on September 28, 2006.

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September 28, 2006

Schrodinger's Bat: Baseball's Trifecta
by Dan Fox

"I think if you come to the ballpark and you see Carl hit a triple, you've had a pretty good day. It's pretty much a signature play for him, because when he hits the ball down the line, or in the gap, he's thinking three. He never thinks two. He breaks triple. He wants triple, he takes triple."

--Devil Rays manager Joe Maddon after Carl Crawford's triple on September 24.

"Hey, big mouth, how do you spell triple?"

--Shoeless Joe Jackson, to a heckling Cleveland fan who taunted him by asking if he could spell "illiterate." This was his response after hitting a triple.

In the bottom of the sixth inning of last Sunday's Yankees/Devil Rays game, Carl Crawford pulled Mike Myers' 1-0 slider into the gap in right-center. The ball skidded past Bobby Abreu, and by the time he retrieved it and hit the cutoff man, both runners had scored and Crawford had coasted into third. It was his 15th triple of the season.

As much as I disdain more or less arbitrary statistical milestones, the hit did draw some attention, since it made Crawford the first player in 76 years to hit at least 15 triples in three straight seasons. In that year, 1930, no fewer than three players were finishing a run of three or more years with 15 triples or more:

                 1930  1929  1928  1927  1926
---------------------------------------------
Earle Combs        22    15    21    23
Paul Waner         18    15    19    18    22
Charlie Gehringer  15    19    16

By comparison, Crawford hit 19 triples in 2004, 15 last year, and now 15 this season. When asked after the game why he thought it had been so long since a player accomplished the feat, Crawford replied, "There are fast guys in the game who can hit, so I have no clue why guys haven't done it. That's not a stat that you go out and try to do every year. That's a stat that just happens."

Crawford's achievement and his comment provide a springboard for this week's column, where we'll discuss triples and their accompanying historical trends.

Historically Speaking

The simple and somewhat tautological answer to Crawford's consternation regarding the lack of triples is that the triple has become increasingly rare over time. And just as a rising tide lifts all boats, a low tide grounds them. The following graph shows the number of triples per 500 at-bats plus walks for each year from 1901 through 2005:



Notice that, as it did for offense in general, the robust environment of 1930 marked the high point for triples, with 6.8 triples hit per 500 AB+BB. The rate dropped immiediatly thereafter, to 5.7 in 1931 and 1932, and it never again reached as high as 5.3. It now seems to have stabilized at around 2.5.

If there are fewer triples being hit, then it becomes less likely that an individual player will be able to hit 15 in three consecutive seasons. For example, a player who hits 15 triples would have a rate of 12.5 per 500 AB+BB. In 1930, a player who hit triples at 1.8 times the rate of the average player would end up with 15 triples, and eleven of the 73 players with 500 or more AB+BB hit 15 or more triples in 1930. In 2005, however, a 15-triple player would have to hit triples at a rate more than five times that of the average player, and just two players (Crawford and Jose Reyes, who hit 17) out of 140 with 500 or more AB+BB could do that. It should be noted that 2005 was a comparatively good year for three-baggers: since 1992, there have been ten seasons in which no player has hit 15 triples. In contrast, when 10-15% of the players hit 15 or more triples every year, there is a very good chance that one or more of those players will repeat for three consecutive years.

As an aside, the general reduction in triples makes the performance of Cory Sullivan on April 9 even more of a fluke. In the top of the fifth inning, Sullivan hit two triples in a seven-run outburst that helped the Rockies beat Jake Peavy and the Padres 10-4. Those two triples tied a record held by ten others, although most recently accomplished by the Senators' Gil Coan in 1951.

The graph also shows the spike in triples that occurred between the years 1974 and 1980. As you can see, triples had been declining steadily since 1930, reaching a low of 2.72 in 1973. From there they began to climb again, reaching a high point of 3.71 in 1977 before gradually declining to settle back down at the 1973 level by 1986. Note that 1977, like 1930, was a relatively big offensive year, with teams scoring 4.47 runs per game. Offensive levels continued to rise throughout the period, and so it can't simply be chalked up to more hits resulting in more triples. But since there weren't new parks being introduced, and expansion occurred in the middle of the spike and not at its start, it's not obvious what might have caused it the outburst.

At first blush, one might posit that there was a general trend towards valuing speed that began in the early to mid-1970s, as young players like Ron LeFlore, Tim Raines, Willie Wilson, and Omar Moreno began to establish themselves. The increase in stolen bases, however, is more gradual than that for triples, and actually began around 1959 (with the "Go-Go Sox" and Maury Wills playing a large part) with a steeper increase in the mid-1970s that peaked in another year that was good for offense, 1987, as shown in the following graph:



While all of this is interesting, it kind of tiptoes around the answer that Crawford is looking for (he probably doesn't really care, but play along). Although there doesn't appear to be consensus among the analytical community, the following are the theories most often discussed as to why the triple has become relatively rare:

• Better Fielders. One of the more interesting questions is to consider how the game has changed as the players have become more athletic. Clearly the speed, strength, size and athletic ability of the average professional baseball player in 2005 exceed that of one in 1920. The question is, how does this affect the game and the evaluation of performance? This was recently touched on by Phil Birnbaum on his Sabermetric Research blog, and was the subject of a thought-provoking chapter by Nate Silver in Baseball Between the Numbers.
  
  As an example of such an effect, the late Stephen Jay Gould argued that a rising level of play inching closer to the "right-wall" of human ability coupled with stabilization of the game itself have conspired to decrease the variability in seasonal batting averages, making it far more difficult to hit .400 now than in years past. The epitome of Gould's argument is that Tony Gwynn had less opportunity than Ty Cobb to exploit the inferiority of others.
  
  Something like this may be happening with triples as well. The theory is that as fielders have become bigger, faster, and boast better throwing arms, would-be triple hitters have had a more difficult time exploiting their opponents, and thus rack up fewer three-baggers. In addition, the standardization of positioning (including the idea that outfielders played shallower in the past) and cutoffs have added to the difficulty. Although baserunners have also become faster, this theory would argue that the improvement in fielding ability and techniques has outstripped the increase in baserunner speed.
  
  
• Park Configuration. This is a corollary to the first theory. Early in the century, ballpark dimensions were far less standardized than today. For example, the Huntington Avenue Grounds where the Red Sox played from 1901-1911 featured a left-center field fence 440 feet away, and a centerfield wall 530 feet from home plate from 1901-1907, and then at 635 feet starting in 1908. Similarly, the center field fence at Forbes Field was 462 feet away in 1909, and at the Polo Grounds, center field ranged from 430 feet in 1931 to 505 feet in 1949. Don't forget that while these and other ballparks in the two eight-team leagues had one or more long distances, they also had lots of corners and edges that made for unpredictable caroms. All of this adds up to situations which surely allowed hitters more opportunity to leg out triples.
  
  Over time, standard dimensions (335/375/400/375/335) made their way into the game, diminishing the opportunity for strange bounces and balls rolling towards distant fences with outfielders in hot pursuit. For my money, the combination of this and the first cause probably explain the lion's share of the overall historical trend.
  
  
• Risk Aversion. As mentioned previously, as offensive levels rise, the relative importance of stolen bases decrease. The same reason causes triples to decline in value; the marginal benefit of stretching a double into a triple is lessened as the probability of scoring from second base increases. A quick look at Run Expectancy Matrices from various years would bear this out as well as the graph presented in my column on Win Expectancy. The argument, then, is that as offensive levels have risen over time, triples have decreased as a result of their lessening strategic importance.
  
  While the premise of this theory is certainly true, one doubts whether calculations like this are taken into account either consciously or subconsciously. More problematic, however, is the fact that runs per game have not increased over time, therefore cutting the legs out from under this theory. Contrary to the steadily downward-sloping line in the first graph, run scoring was actually higher throughout the 1920s and into the early 1930s than at any other time, and after diminishing to reach its low point in 1968 (3.42 runs per game per team), it has steadily increased since then:
  
  
  
  
• Player Aging. No discussion of triples would be complete without at least a brief look at the effect of age. As Clay Davenport noted in his essay "Graying the Game" in Baseball Prospectus 2002, and subsequently reinforced by Nate Silver last season, the player population is aging, and has been for quite some time. This has an impact on triples, since older players lose foot speed and don't hit as many as younger ones do. The graph below shows triples per 500 AB+BB for all players since 1901, player-seasons from 1901-1935 and seasons from 1936-2005:
  
  
  
  Even at a time when triples were much more common (the orange line), triples peaked at age 22 and steadily declined through age 40. You'll also notice that the slope of the line for players in the first part of the 20th century is not quite so steep as it is for those since. I also find it very interesting that the slope of the line from ages 22 through 35 for all players is very nearly straight, indicating an extremely uniform decrease with age.
  
  Clearly, players don't hit as many triples as they get older, but the general aging of the player population cannot account for the overall decrease in triples. Just considering players 25 years old or younger, those who played since 1936 hit triples at a rate of 3.72 per 500 AB+BB, while those who played before 1936 hit them at a rate of 6.73. Keep in mind that it's also very likely that the average speed of players 25 years old and younger in the major leagues today is greater than that in the Deadball Era, meaning that other factors such as fielding prowess and changing park configurations are much more important to the overall trend.
  

"How do you spell triple?"

The triple is often called the most exciting play in baseball, and for good reason. There is no play that involves as many players, lasts as long, and concludes so often with a bang-bang crescendo. As we've seen, there are a variety of reasons that have conspired to make it a much rarer event today than it was in days past. These include increased standardization and ability on defense, less variability in park dimensions, risk aversion, and perhaps an aging player population. Whatever the combination and relative importance of these different causes, rather than wring our hands at its disappearance, let's instead appreciate the feat for its increased difficulty and marvel at those, like Carl Crawford, who can do it with regularity.

The Phone Books Are In! The Phone Books Are In!

Ok, so it's not quite a Steve Martin moment but I was excited to see this at my local Borders bookstore today. Good stuff.

Oh, and tomorrow night I'll be joining Christina Kahrl and Nate Silver at The Tattered Cover in LoDo to talk about the book and the Rockies. Hope to see you there.

VORPies and Scrappers

Here are a couple of by now dated but still interesting articles...

Cubs' Theriot measures success in different ways. Bruce Miles talks about Ryan Theriot and how he's never been a numbers guy and how numbers don't tell the entire story etc. Personally, I like this article and couldn't agree more with the author. Miles mentions that Baseball Prospectus PECOTA has Theriot projected for an OBP of .330 and quotes Theriot as saying:

I'm going to give everything I've got. And I'm not afraid to fail. I think I'll do what it takes to do something great and help the team win. I take pride in my defense. Either you've got to drive them in or you've got to save a run.

I think it's easier for me to save them than drive them in. I'm realistic about my game. I think I know what I can and can't do. I know my limitations.

Offensively Theriot played very well until a September slump which could be attributed both to a little fatigue in his first full season or an indication that the league has caught up with him. It'll be interesting to see if either of those play out in 2008. Defensively SFR had Theriot at +4.8 at short in 2007 (399 balls assigned) and +2.3 at second base (100 balls). At third he was -0.8 in a really small sample (15 balls). SFR also had him at +0.7 in 2006 at second base (101 balls) and so overall defensively, and although Theriot's not a number's guy, I'd have to say that the numbers agree that he can help the team win with his glove. Incidentally, SFR had Brian Roberts at +7.6 in 2007, +1.2 in 2006, and -1.2 in 2005 at second base.

VORPies?. I'm still trying to figure out just what a "VORPy" is but Jon Heyman tweaks them a little in discussing Jimmy Rollins and his MVP award in 2007. But again, this article to me makes some good points including the ideas that Rollins should get a little boost over David Wright because of his defense (and playing a more difficult position) and baserunning but of course all of these things can be quantified. Wright's VORP was 81.1, Rollins was 66.1 and these numbers as Heyman rightly points out are park adjusted. So was Rollins 15 runs better on defense and baserunning? SFR has Rollins at +5.0 and Wright at +3.2 and so Rollins makes up a little there. On the bases Rollins was at +7.2 and Wright at +2.5 and so there's another few runs which when combined with his defense essentially allows Rollins to make up about half the difference. But the MVP is not all about numbers either and winning and leadership, I think, should definitely matter. In the end, when you factor these things in it seems to me like these guys are in the same vicinity and so it's not as if Rollins was a really poor choice. Matt Holliday, with his 75.0 VORP and pretty decent defense in 2007 should no doubt also have been considered. And by the way, Heyman talks about Hanley Ramirez a little whose 89.5 VORP led all National Leaguers. I had him at +1.8 in baserunning but at -17.5 runs with the glove in SFR. By all accounts his defense really is poor and so it comes off as kind of disingenuous for Heyman not to mention that. But on the topics of the Gold Glove and Rookie of the Year...well, don't get me started.

Baserunning for the Ages

I've been writing mostly about defense over at Baseball Prospectus and here in the past couple of months and so I thought I'd revisit the topic of baserunning today.

Although in my column I talked about the greatest baserunners of the Retrosheet era and here have extolled the virtues of Tim Raines, Robin Yount and others, I noticed that I've failed in either venue to list the top and bottom single seasons of that era.

So today here are the top and bottom 50 baserunning seasons in terms of total Equivalent Baserunning Runs (EqBRR). And don't forget that an essay describing the system and its metrics titled "The Tortoise, the Hare, and Juan Pierre" appears in Baseball Prospectus 2008, which I'm told, is shipping now. Also, I'll be talking about the book with Christina Kahrl and Nate Silver Wednesday, March 5th at 7:30 pm at the Tattered Cover Bookstore in Historic LoDo in Denver.

First, the top 50 seasons.

Name                Year    EqGAR  EqSBR  EqAAR  EqHAR  EqOAR TotOpps   EqBRR EqBRRate
Maury Wills         1962      0.8   13.8    2.3    3.6    0.1    848     20.6     1.26
Willie Wilson       1980      0.5   10.0    4.2    3.9    0.5    741     19.1     1.35
Rickey Henderson    1985      2.6    9.8    1.0    3.1    2.3    663     18.8     1.43
Vince Coleman       1986      0.0   11.0    0.3    0.9    4.2    627     16.4     1.26
Willie Wilson       1979      2.1    9.2    0.7    2.8    0.9    563     15.7     1.33
Eric Davis          1986     -0.3   10.2    0.5    1.7    3.2    403     15.3     1.55
Rickey Henderson    1988      2.3    9.0    1.3   -2.0    3.8    650     14.4     1.27
Vince Coleman       1987      2.5    7.1    1.2    2.4    0.8    723     14.1     1.28
Tim Raines Sr       1983      0.9    7.6    1.8    2.7    0.6    762     13.6     1.22
Bobby Bonds         1972      2.0    6.0    1.6    3.6    0.5    517     13.6     1.42
Kenny Lofton        1993      1.5    8.1   -0.1    4.3   -0.5    717     13.3     1.17
Lonnie Smith        1985      2.8    1.4    2.5    2.9    3.1    460     12.8     1.85
Willie Wilson       1987      0.4    7.1    0.6    3.9    0.7    581     12.6     1.24
Juan Pierre         2007      0.3    4.2    1.9    5.0    0.6    666     12.0     1.40
Davey Lopes         1978      0.6    5.8    1.9    1.4    2.1    580     11.8     1.24
Vince Coleman       1985      1.2   10.7    0.7    0.6   -1.4    665     11.8     1.06
Rickey Henderson    1983      0.9    7.8    1.3    0.1    1.6    609     11.7     1.17
Gary Pettis         1985      2.1    7.4    0.7    0.2    1.3    470     11.7     1.31
Johnny Damon        2000      3.1    2.7   -0.7    4.2    2.2    743     11.5     1.33
Ron LeFlore         1979      2.3    5.6    1.3    1.9    0.4    602     11.5     1.30
Davey Lopes         1975      0.4    8.6   -1.3    2.2    1.4    685     11.4     1.14
Barry Larkin        1995      1.3    5.5    1.2    1.3    1.9    526     11.2     1.31
Tim Raines Sr       1985      1.6    9.4    0.8   -0.6    0.0    726     11.2     1.08
Willie Wilson       1983      1.9    7.0   -0.6    1.4    1.5    532     11.2     1.24
Ivan DeJesus        1978      1.0    2.2    1.7    4.5    1.7    625     11.1     1.38
Hanley Ramirez      2006      3.1    1.7    1.3    3.5    1.5    576     11.0     1.50
Joe Morgan          1975      0.8    6.3    0.9    2.0    0.9    618     10.8     1.27
Ron LeFlore         1980      0.1   11.0    0.3   -0.1   -0.5    611     10.7     0.99
Tim Raines Sr       1987     -0.5    7.2    0.3    2.5    0.9    567     10.4     1.17
Ray Durham          1998      1.2    2.0    1.8    3.6    1.8    611     10.4     1.37
Juan Pierre         2005      3.6    1.7   -0.3    2.5    2.9    665     10.4     1.43
Chone Figgins       2005      4.4    0.7    1.9    2.5    0.8    619     10.3     1.43
Marquis Grissom     1992     -0.3    6.5    2.1    0.1    1.8    567     10.2     1.19
Rickey Henderson    1984      0.9    2.4    2.1    3.9    0.9    599     10.2     1.31
Tim Raines Sr       1982      3.3    5.7   -0.2    1.2    0.1    626     10.1     1.25
Tim Raines Sr       1992      0.3    5.3    1.5    3.0    0.1    669     10.1     1.24
Al Wiggins          1983      0.3    4.1    0.9    0.4    4.4    582     10.0     1.29
Bert Campaneris     1969      1.3    5.8   -0.5    2.5    0.8    565      9.9     1.29
Kenny Lofton        1994      1.7    4.5   -1.1    3.4    1.4    574      9.9     1.23
Ron LeFlore         1978      2.3    5.2    0.6    2.3   -0.6    720      9.9     1.20
Chone Figgins       2006      2.1    0.8    1.6    4.9    0.4    577      9.9     1.48
Omar Moreno         1979      1.5    3.8    0.7    3.0    0.8    619      9.8     1.29
Scott Podsednik     2003      1.8    4.6    1.0    3.2   -0.6    542      9.8     1.34
Joe Morgan          1976      0.1    5.5    0.4    2.7    1.0    504      9.7     1.28
Tom Goodwin         2000      1.0    3.9    1.3    2.9    0.5    445      9.7     1.37
Milt Cuyler         1991      0.9    3.1    2.0    0.8    2.8    438      9.7     1.47
Davey Lopes         1976      0.6    7.3    0.5    1.7   -0.5    508      9.7     1.12
Willie Wilson       1984      1.7    5.1    2.1    0.8   -0.1    530      9.7     1.24
Tony Gwynn          1987      0.3    2.0    1.4    3.5    2.3    682      9.6     1.36
Luis Castillo       2007      1.0    0.6    1.1    3.1    3.8    528      9.6     1.51

As you can probably tell most of these top 50 are driven by high EqSBR scores with Maury Wills 1962 season at the top of the heap. There were a few players though, like Lonnie Smith in 1985 who excelled despite pedestrian work stealing bases. Related to that point you'll also notice that the final column we have a rate statistic titled EqBRRate. I explained the idea behind it in the column cited above.

...it turns out that when many folks talk about baserunning, they're not really thinking about discretionary stolen base attempts, but instead that combination of speed, risk taking, and judgment that goes into evaluating situations, and that when aggregated leads us to assert that a particular player is a good baserunner. Since EqSBR is primarily comprised of stolen base attempts (with a few pickoffs thrown in) our new rate statistic, which we'll christen Equivalent Baserunning Rate (EqBRRate), will omit this aspect.

So...we'll define EqBRRate as the ratio of actual or total runs to expected runs contributed across the four remaining metrics. Since both values for individual opportunities consider the context and are weighted appropriately (an EqOAR opportunity has both a lower expected and usually actual run value associated with it than an opportunity of EqHAR) and since we're eliminating EqSBR, both weaknesses discussed above addressed. To illustrate how this works, let's consider Chone Figgins' 2007 season:

Metric    Opps  TotRuns ExpRuns
EqOAR      314      0.1     1.2
EqGAR       31      3.2     2.6
EqAAR       44      5.7     4.7
EqHAR       53     10.1     5.6
           442     19.0    14.2

Taking the context of the opportunities into account, we would have expected Figgins to net +14.2 runs across the four metrics, but he actually contributed +19.0 runs. When we divide the total by the expected we get a ratio of 1.34, indicating that he contributed, or manufactured if you will, 34 percent more runs than expected.

So as you can see Smith's 1985 season actually comes out on top with a EqBRRate of 1.85 easily topping the 1986 season of Eric Davis at 1.55. The lowest rate out of the top 50 is Ron LeFlore's 1980 season where he was actually below 1.00 at 0.99 but made the top 50 by virtue of his 11.0 EqSBR.

And now the bottom 50...

Name                Year    EqGAR  EqSBR  EqAAR  EqHAR  EqOAR TotOpps   EqBRR EqBRRate
Carlos Delgado      2007     -0.4   -0.2   -2.9   -3.6   -0.4    394     -7.5     0.41
Jose Offerman       1992      0.5   -4.9   -1.3   -1.1   -0.7    505     -7.5     0.86
Eddie Murray        1990     -1.2   -4.2    0.2   -3.5    1.1    521     -7.5     0.82
Scott Cooper        1994      0.1   -2.3   -0.4   -5.2    0.3    306     -7.5     0.45
Rick Wilkins        1996     -0.4   -1.7   -1.3   -4.3    0.2    264     -7.6     0.41
Pat Burrell         2005     -0.5   -0.2   -0.7   -5.6   -0.7    368     -7.6     0.42
Randy Milligan      1991     -0.5   -3.7   -0.5   -2.1   -0.8    414     -7.6     0.67
Manny Trillo        1982     -0.1   -4.1   -1.9   -1.9    0.3    430     -7.6     0.72
Larry Sheets        1988     -0.7   -4.3   -0.8   -1.8   -0.2    286     -7.7     0.58
Bill Freehan        1971     -1.1   -3.1   -1.8   -1.7   -0.1    331     -7.8     0.43
Dave Parker         1977     -0.4   -6.4   -0.9    0.7   -0.8    531     -7.8     0.93
Jorge Posada        2007     -1.3   -0.1   -0.7   -4.2   -1.6    507     -7.8     0.59
Ted Simmons         1975     -1.5   -1.7    0.3   -4.8   -0.2    573     -7.9     0.72
Ed Bailey           1963      0.0   -3.9   -0.4   -3.3   -0.4    231     -7.9     0.35
Gene Richards       1982     -1.3   -4.8    0.0   -2.0    0.1    455     -8.0     0.81
Jim Thome           2004     -0.5   -1.4   -3.2   -3.2    0.3    436     -8.0     0.59
David Justice       1997     -0.7   -3.3   -0.3   -3.0   -0.7    398     -8.0     0.61
Dan Meyer           1977     -0.9   -2.0   -1.3   -4.6    0.7    409     -8.1     0.60
Jim Norris          1977     -0.1   -3.8    0.2   -2.9   -1.5    447     -8.1     0.73
Felix Jose          1991     -1.8   -3.5   -2.5    0.7   -1.0    482     -8.1     0.62
Lance Parrish       1979      0.0   -3.7   -2.6   -1.5   -0.4    361     -8.1     0.62
Steve Garvey        1980     -0.4   -5.5   -0.9   -0.8   -0.6    467     -8.1     0.78
Steve Henderson     1983      0.2   -7.5    0.6   -0.7   -0.8    362     -8.2     0.93
Carlos Delgado      2000     -0.6   -1.4   -1.4   -3.6   -1.1    618     -8.2     0.58
Al Oliver           1977     -0.1   -7.0   -0.2   -0.1   -0.8    474     -8.2     0.88
Tom Foley           1988     -0.1   -4.4   -0.4   -1.6   -1.7    279     -8.3     0.53
Dale Berra          1984      1.2   -2.8   -0.9   -5.2   -0.7    297     -8.4     0.57
Tommy McCraw        1972     -0.5   -5.9   -1.5   -0.5    0.0    299     -8.4     0.76
Joe Cunningham      1959     -0.8   -2.3    0.4   -5.3   -0.4    504     -8.5     0.60
Pete O'Brien        1984     -0.4   -3.1   -1.4   -2.9   -0.6    428     -8.5     0.52
Kenny Lofton        1997      0.4   -9.4   -0.1    0.6    0.0    539     -8.5     1.06
Frank Thomas        2000     -1.0   -1.6   -1.6   -3.4   -1.0    535     -8.6     0.47
Harold Reynolds     1988     -0.7   -7.8    1.0   -1.2    0.0    535     -8.7     0.95
Eddie Yost          1957      0.3   -5.4   -0.9   -2.8    0.0    394     -8.7     0.62
Joe Morgan          1980     -0.2   -2.0   -0.3   -6.5    0.3    434     -8.8     0.55
Clete Boyer         1970      0.6   -1.6   -0.2   -6.9   -0.8    307     -8.8     0.21
Ed Kranepool        1967     -0.8   -1.9   -0.1   -5.7   -0.4    323     -8.8     0.39
Mike Hargrove       1979     -1.8   -2.3   -0.2   -4.2   -0.5    522     -8.8     0.69
Jose Cruz           1977     -0.1   -8.3    0.5   -1.3    0.3    483     -8.9     0.95
Ernie Whitt         1989     -1.4   -1.0   -1.7   -4.0   -0.9    313     -9.0     0.34
Harmon Killebrew    1970     -0.8   -2.1   -0.7   -4.6   -1.0    435     -9.0     0.56
Tom Pagnozzi        1991     -1.5   -4.8   -0.7   -1.5   -0.8    391     -9.3     0.61
Bob Kearney         1984     -0.1   -2.6   -2.0   -3.8   -0.9    290     -9.4     0.29
Ryan Garko          2007     -1.0   -0.4    0.2   -7.7   -0.5    403     -9.4     0.32
Rod Carew           1982      0.1   -5.5   -0.2   -3.2   -0.7    558     -9.5     0.71
Tom Brunansky       1992     -0.6   -3.1   -1.8   -3.4   -0.7    373     -9.6     0.43
Todd Zeile          1997     -0.5   -4.8    0.0   -4.5   -0.4    484    -10.2     0.64
Mike Epstein        1971     -0.2   -2.5   -2.4   -4.4   -1.1    311    -10.6     0.38
Todd Zeile          1992     -0.7   -4.0   -1.1   -5.4    0.0    425    -11.2     0.52
Tony Bernazard      1984     -0.1   -6.9   -0.3   -3.4   -0.6    364    -11.2     0.62

There are some real "ice wagons" here (in the parlance of the dead ball era referring to poor baserunners) of course although many of these as well are here because they did so poorly in EqSBR (Tony Bernazard, Jose Cruz, and Kenny Lofton are three notable examples). The Indians Ryan Garko makes the list with his 2007 campaign primarily because he was thrown out trying to advance on hits five times - all at the plate - on his way to an historic -7.7 runs on EqHAR.

From a pure baserunning perspective Clete Boyer with his 1970 campaign ranks dead last at 0.21 with Bob Kearney in 1984 at 0.29 and Garko close behind. Lofton's 1997 season is the only one with a rate of 1.00 or higher at 1.06 but his EqSBR of -9.4 sinks him.

Outfield Defense Redux

I've made some changes to the SFR system for outfielders based on excellent feedback from readers and others that I discuss in today's column appropriately titled "Back to the Drawing Board". One of the things you'll notice is that my correlations for right fielders (primarily because of Brian Giles and Juan Encarnacion) with UZR for the 2003 through 2006 period are very poor. Not sure why but I noticed that Sean Smith apparently has similar issues. Overall, I like the system better and it seems to handle Manny Ramirez better and correlates pretty well with UZR overall.

As a bonus you can now download a spreadsheet with version 1.0 of SFR for the infielders that includes 2007 minor league data.

Baseball Prospectus Top 100

At Baseball Prospectus today we published our top 100 prospects list as compiled by Keving Goldstein. Jay Bruce leads the field and below is the list ordered by team so you can count and debate your favorites. In terms of sheer numbers the A's, Rangers, and Red Sox each have seven prospects in the list while the White Sox, Blue Jays, Indians, Mets, Tigers, and Astros have one a piece.

Rank/Name              Pos     Team
27. Nick Adenhart      rhp     Angels
38. Brandon Wood       3b/ss   Angels
59. Jordan Walden      rhp     Angels
89. Hank Conger        c       Angels
54. J.R. Towles        c       Astros
22. Daric Barton       1b      Athletics
26. Carlos Gonzalez    of      Athletics
46. Fautino de los San rhp     Athletics
50. Brett Anderson     lhp     Athletics
56. Gio Gonzalez       lhp     Athletics
98. Trevor Cahill      rhp     Athletics
99. Chris Carter       1b      Athletics
7.  Travis Snider       of     Blue Jays
17. Jordan Schafer     of      Braves
36. Jason Heyward      of      Braves
63. Brent Lillibridge  ss      Braves
70. Brandon Jones      of      Braves
83. Gorkys Hernandez   of      Braves
86. Jair Jurrjens      rhp     Braves
31. Matt LaPorta       of      Brewers
42. Manny Parra        lhp     Brewers
76. Jeremy Jeffress    rhp     Brewers
8.  Colby Rasmus        of     Cardinals
69. Chris Perez        rhp     Cardinals
71. Bryan Anderson     c       Cardinals
37. Geovany Soto       c       Cubs
45. Josh Vitters       3b      Cubs
40. Jacob McGee        lhp     Devil Rays
20. Jarrod Parker      rhp     Diamondbacks
64. Gerardo Parra      of      Diamondbacks
90. Max Scherzer       rhp     Diamondbacks
5.  Clayton Kershaw     lhp    Dodgers
14. Andy LaRoche       3b      Dodgers
32. Chin-Lung Hu       ss      Dodgers
66. Scott Elbert       lhp     Dodgers
78. Wes Hodges         3b      Georgia Tech
29. Angel Villalona    3b      Giants
84. Henry Sosa         rhp     Giants
52. Adam Miller        rhp     Indians
33. Jeff Clement       c       Mariners
44. Chris Tillman      rhp     Mariners
55. Carlos Triunfel    ss      Mariners
93. Wladimir Balentien of      Mariners
10. Cameron Maybin     of      Marlins
88. Chris Volstad      rhp     Marlins
51. Fernando Martinez  of      Mets
28. Chris Marrero      of/1b   Nationals
35. Ross Detwiler      rhp     Nationals
81. Michael Burgess    of      Nationals
12. Matt Wieters       c       Orioles
75. Chorye Spoone      rhp     Orioles
85. Radhames Liz       rhp     Orioles
23. Chase Headley      3b      Padres
39. Matt Antonelli     2b      Padres
61. Matt Latos         rhp     Padres
68. Carlos Carrasco    rhp     Phillies
96. Joe Savery         lhp     Phillies
24. Andrew McCutchen   of      Pirates
43. Steven Pearce      1b      Pirates
94. Neil Walker        3b      Pirates
30. Neftali Feliz      rhp     Rangers
49. Eric Hurley        rhp     Rangers
58. Elvis Andrus       ss      Rangers
62. Engel Beltre       of      Rangers
73. Michael Main       rhp     Rangers
74. Chris Davis        3b      Rangers
77. Taylor Teagarden   c       Rangers
3.  Evan Longoria       3b     Rays
6.  David Price         lhp    Rays
15. Wade Davis         rhp     Rays
18. Desmond Jennings   of      Rays
25. Reid Brignac       ss      Rays
2.  Clay Buchholz       rhp    Red Sox
16. Jacoby Ellsbury    of      Red Sox
53. Justin Masterson   rhp     Red Sox
57. Jed Lowrie         ss      Red Sox
60. Ryan Kalish        of      Red Sox
95. Michael Bowden     rhp     Red Sox
100.Lars Anderson     1b       Red Sox
1.  Jay Bruce           of     Reds
9.  Homer Bailey        rhp    Reds
21. Joey Votto         1b      Reds
41. Johnny Cueto       rhp     Reds
13. Franklin Morales   lhp     Rockies
80. Chris Nelson       ss      Rockies
82. Greg Reynolds      rhp     Rockies
91. Casey Weathers     rhp     Rockies
92. Dexter Fowler      of      Rockies
19. Mike Moustakas     ss      Royals
72. Luke Hochevar      rhp     Royals
11. Rick Porcello      rhp     Tigers
65. Carlos Gomez       of      Twins
79. Deolis Guerra      rhp     Twins
97. Ben Revere         of      Twins
87. Aaron Poreda       lhp     White Sox
4.  Joba Chamberlain    rhp    Yankees
34. Ian Kennedy        rhp     Yankees
47. Austin Jackson     of      Yankees
48. Jose Tabata        of      Yankees
67. Alan Horne         rhp     Yankees

The Moral Hazards of the Hit Batsmen

This the final in a series of three columns I wrote for BP on the topic of hit batsmen. You can find the other two on this blog as well. It appeared on May 18, 2006

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Schrodinger's Bat:The Moral Hazards of the Hit Batsmen
by Dan Fox

"The designated hitter rule is like letting someone else take Wilt Chamberlain's free throws."

--Rick Wise (1974)

In the previous two weeks, we’ve been looking at historical hit by pitch rates and their trends, and investigating a variety of theories that have tried to explain the fluctuation of those rates. We’ve looked at a wide variety of theories that account for factors such as aluminum bats at the amateur level, changes in the strike zone, the increase in body armor, intimidation, retaliation, and even the win expectancy of the hit batsmen. While individual theories may lack explanatory power for a specific period of time, taken together they do provide insight into the sometimes opposing forces that underlie trends in baseball's complex competitive environment.

There is one trend, however, that we failed to discuss. So this week we’ll take a look at the difference in league rates of hit batsmen since the introduction of the designated hitter in 1973. This topic has been taken up before, so we’ll start by covering some of the old ground, and then hopefully add something new to the discussion.

Setting a Baseline
Before we discuss what the impact of the DH on HBP rates might be, let’s lay out the raw facts that have inspired so much conjecture. The following graph shows the percentage of AL hit batsmen per 1,000 plate appearances as opposed to the NL since the DH was adopted in the American League in 1973. The shaded line is a three-year moving average.



What this shows is that from 1973 until the mid 1990s the rate of hit batsmen in the AL was anywhere between 3% and 30% higher than in the NL. While that’s a wide range, more typical values are between 10% and 20%, with the average during the period being 17%:

1973    9.3%    1990   19.0%
1974   14.0%    1991   18.6%
1975    7.8%    1992   20.0%
1976   17.3%    1993    9.4%
1977   17.2%    1994   -7.6%
1978   12.5%    1995   -6.7%
1979    8.4%    1996    2.5%
1980   24.2%    1997  -15.9%
1981   22.8%    1998    4.4%
1982    3.2%    1999   10.2%
1983   19.1%    2000  -17.6%
1984   29.7%    2001    7.0%
1985   21.5%    2002    7.4%
1986   26.5%    2003    3.4%
1987   16.7%    2004    7.7%
1988   20.9%    2005   -5.6%
1989   22.9%

Around 1994, things began to change and in the following dozen years HBP rates in the NL actually surpassed those in the AL five times, including in 2005 where 9.52 batters were hit per 1,000 PA in the AL, against 10.05 in the NL.

So in fact, there are actually two questions that we can ask about this trend. First, what accounts for the difference in rates of hit batsmen during the twenty-year period following the introduction of the DH (1973-1993), and secondly, what caused those differences to shrink in the period after 1993?

A Moral Hazard or More Opportunity?
As mentioned in the introduction, the topic of league differences in HBP rate have been researched in the past. Most recently, Lee A. Freeman wrote an excellent article titled "The Effect of the Designated Hitter Rule on Hit Batsmen" in Volume 33 of The Baseball Research Journal. In it, Freeman provided a short synopsis of the previous work, citing articles in the journal Economic Inquiry in 1997 and 1998, as well as a follow-up in a 2004 issue of the Journal of Sports Economics.

Prior to Freeman’s paper the two theories that had been bandied about to explain the difference (at least from 1973 until the mid 1990s) were the "moral hazard theory" and the "lineup composition theory." The former theory argues that because American League pitchers needn’t fear retaliation with the presence of the DH, they are more apt to hit opposing batters since they don’t bear the costs of their actions directly. The latter theory also argues from a cost-benefit basis, although differently--AL pitchers hit more batters because the cost in terms of run scoring when hitting a DH is so much less than hitting a pitcher. This follows from the fact that the designated hitter is much more likely to be an offensive producer than your typical weak-hitting full-time hurler.

As a variation of the lineup composition theory, Freeman contended that more hit batsmen in the AL can be explained largely (but not totally, as he rightly cautions against single-theory explanations) simply by more "true" hitters coming to bat in the AL. In his words:

American League pitchers are not given the opportunity during a game to 'ease up' their delivery to the opposing pitcher. As a result, AL pitchers are likely to 'want' or 'need' to pitch inside to more batters during the course of a game, thereby increasing the chances of these batters being hit by a pitch.

Through an analysis of average HBP per season and per team, both before and after the introduction of the DH, Freeman concludes that there is no statistical significance (at the .001 or .005 levels) to the differences in hit batsmen across the two leagues once you adjust the averages for the fact that in the AL approximately 12.5% more true hitters come to the plate in the DH era.

What this analysis lacks, as admitted by Freeman himself, is a more granular accounting for the differences in the number of "true" hitters, and instead relies on a quick and dirty approximation. Using Retrosheet data, we can address that weakness in the study.

The following table shows the percentage of plate appearances consumed by each fielding position, along with the HBP per 1,000 plate appearances for both the AL and NL in the period 1973-1993.

        <----AL---->   <----NL----->
               HBP /           HBP /
POS     PAPct   1000   PAPct    1000
------------------------------------
 P       0.0%    0.0    6.8%     2.2
 C      10.1%    6.3   10.4%     4.9
1B      11.1%    4.9   11.3%     4.8
2B      10.9%    5.0   11.2%     4.7
3B      10.8%    5.3   11.1%     5.7
SS      10.3%    4.8   10.8%     3.7
LF      11.2%    6.2   11.4%     5.0
CF      11.4%    5.2   11.5%     4.7
RF      11.0%    5.6   11.3%     4.3
DH      11.2%    6.1     -        -
PH       2.0%    4.9    4.2%     3.7

TOTAL            5.5             4.5

In total, AL hitters were hit at a rate 20.8% higher than NL hitters.

As you can see, in the AL designated hitters consumed 11.2% of the plate appearances, and were hit at a rate of 6.1 times per 1,000 PA. Both totals are among the highest for AL hitters. So, while the DH might be the equivalent of someone else taking Wilt's free throws, the price the DH pays is some additional pain.

On the other side of the fence, NL pitchers consumed just 6.8% of the plate appearances, and were hit just 2.2 times per 1,000 PA. Interestingly, although the percentage of plate appearances for AL pitchers is rounded to 0%, they actually came to the plate 79 times, mostly as the result of games where the AL team lost their DH as a result of the DH assuming a defensive position per rule 6.10.

So, rather than seeing Freeman's 12.5% more "true" hitters in the AL, in actuality AL pitchers see around 7% more true hitters when you subtract the pitchers from the NL totals. However, Freeman also noted that pinch-hitters are often used for pitchers in the NL, and this is borne out by the fact that pinch-hitters came to the plate more than twice as often in the NL (4.2%) than in the AL (2.0%). Freeman also speculated that pinch-hitters are not as likely to get hit since they are often weaker hitters than players in the regular lineup (it should be noted that as reported in The Book, there is also a "pinch-hitting penalty" that drags down performance). The lesser rate of hit batsmen for pinch hitters is verified by the data. So, assuming that the NL rate of pinch-hitting was the same as the AL rate, and throwing the remainder of the NL pinch-hitters into the bucket of poor hitters with the pitchers, we can estimate that the AL pitchers see approximately 9% more true hitters than pitchers.

The difference between Freeman's estimate and the actual numbers lies in the fact that the vast majority of pitchers hit ninth, Dontrelle Willis being the most recent occasional exception. Hitting from the last slot in the order, pitchers therefore come to the plate less frequently than position players.

To adjust for that, given the data in the above table, we can now make an estimate for the true differences in hit batsmen by controlling for pitcher plate appearances. One simple way to do this is to estimate what would happen if all pitcher and pinch-hitter plate appearances in the NL were consumed by a true hitter whose rate of getting hit was relatively as high as a designated hitter's in the AL. This means that 11% of the NL plate appearances (6.8% + 4.2%) will be assigned a new HBP rate based on the difference between a DH and the rest of the positions in the AL. To do so we'll first calculate the ratio of the DH rate (6.1) to the non-DH rate (5.4) as 1.13. If we assume that true hitters in the NL consuming those plate appearances would have produced 13% more hit by pitches than the non-pitchers and pinch-hitters (which turns out to be 5.4 HBP/1000 PA), then the average for the NL would jump 30% from 4.5 hit batsmen per 1,000 PA to 4.8. As a result, instead of a 20.8% advantage for the AL during the period, the true advantage is around 13.6%.

So while accounting for a different lineup composition in the AL helps level the playing field, it obviously doesn't account for the entire difference, as Freeman concluded. We're still left with around two-thirds of our original difference between the leagues. Does that mean we're left with the moral hazard theory to explain the remaining difference?

Readers familiar with this subject will note that this cursory analysis lines up nicely with the fine work done by J.C. Bradbury and Douglas Drinen in a paper titled "Identifying Moral Hazard: A Natural Experiment in Major League Baseball" (warning: .pdf). In that paper, using data from 1989-1992 compared against 1969 plus 1972-1974, the authors conclude that:

"Controlling for variables that proxy batter quality, pitcher quality, retaliation, and game situation we find that the DH rule increases the likelihood that any batter will be hit during a plate appearance between 11 and 17 percent. This explains approximately 60 to 80 percent of the differential in the hit batsmen rate between leagues."

But there are also two additional theories to consider.

If you look back at the previous articles in this series you'll notice that the rate of hit batsmen in the AL actually surpasses that of the NL prior to the introduction of the DH. In fact, beginning in 1967, the rate of AL hit batsmen to NL went as follows:

1967  11.5%
1968  18.1%
1969  -1.5%
1970  10.1%
1971   8.3%
1972  11.0%

During this six-year period the differences in the AL rate with the pitcher hitting were not much different than those immediately after the introduction of the DH. What this indicates is that hit batsmen were already more frequent in the junior circuit. Perhaps some of this remaining difference lies elsewhere.

As mentioned last week, one of the factors that may influence hit batsmen is the definition (both written and as interpreted) of the strike zone. There is of course anecdotal evidence that the strike zone varied in the two leagues primarily as the result of AL umpires using the old-style "balloon" chest protector that forced them to stand more upright and therefore call more high strikes. And although by around 1983 AL umpires were also using the inside chest protector popularized by Bill Klem, they may have retained their traditional strike zone for some years. But still, outside of concocting what Stephen Jay Gould would call a "just-so story," there is no clear connection between high strikes and hit batsmen. A related hypothesis might be that the AL, being known as more of a curveball league, induced more hit batsmen since curveballs are inherently more difficult to control than fastballs. But both of these theories are difficult to quantify.

A more straightforward idea is that one or two individuals skewed the numbers for this time period, accounting for the remaining difference between the leagues. This follows the dictum that when what you're measuring has inherently low frequencies, you should always be aware of a small number of samples having a large influence on the data.

As most readers have already guessed, when you're talking about hitters and HBPs during this period, Don Baylor and Chet Lemon are two players who immediately spring to mind. Both played their entire careers in the AL, with Baylor suiting up for the Orioles, A's, Angels, Yankees, Red Sox, and Twins from 1970-88, and Lemon for the White Sox and Tigers from 1975-90. Baylor was hit 257 times in 8,888 plate appearances (defined simply as hits plus walks plus HBP for this analysis) from 1973 through 1988, for an astounding rate of 28.9 per 1,000 PA--tops during the period and ranking him 15th for players since 1901. Lemon was hit 151 times in 7,768 PA for a rate of 19.4. If these two players' rates are adjusted down to the average for the period, the overall rate for the AL drops from 5.5 to 5.3 and therefore accounts for about 4% of the remaining difference.

In summary then, from an initial difference of nearly 21% in the rate of hit batsmen between the two leagues in the 1973-1993 period, just over 7% can be accounted for by the presence of more true hitters in the lineup and another 4% by two hitters who were exceptionally "gifted" at getting plunked. This still leaves ample room for the moral hazard theory, a theory that incorporates differences in the two leagues relating to strike zone or styles of play, or a combination of all of the above to operate.

Evening the Score
The second question introduced above is related to the disappearance of the difference in rate of hit batsmen between the two leagues, beginning in 1994. Since that time, the National League has actually topped the American League in five of the twelve years, as shown in the previous table.

What can account for this dramatic shrinking of differences between the two leagues?

First, let's take a look at the same table for the years 1994-2005 as we did for the preceding years.

        <----AL---->   <----NL----->
               HBP /           HBP /
POS     PAPct   1000   PAPct    1000
------------------------------------
P        0.4%    1.4    5.9%     3.3
C       10.1%   11.1   10.5%    12.8
1B      11.1%   10.7   11.2%    10.5
2B      11.0%   10.6   11.5%    13.1
3B      10.8%    9.3   11.1%     9.8
SS      10.9%   10.3   11.1%     8.5
LF      11.2%    8.9   11.3%    10.5
CF      11.3%    8.5   11.5%    10.0
RF      11.0%    9.8   11.3%    10.7
DH      10.4%   10.2    0.5%    12.2
PH       1.6%    8.4    4.2%    10.0

TOTAL            9.9            10.3

What you'll notice is that the NL has outpaced the AL since 1994 despite leading in a minority of those seasons. This data set now includes interleague games, so a DH is listed in the NL column, and pitchers in the AL with the rate of hit batsmen for NL DHs even higher than that for the NL, and the rate for AL pitchers lower than in the NL. Of course, both leagues saw massive increases in their rates reflected as well.

In a follow-up paper (another .pdf) also published in 2004 Bradbury and Drinen conclude that during the entire history of the DH, batters were about 8% more likely to be hit in games where the DH was played accounting for around half of the difference between the leagues. However, when looking only at 1994-2005 data and breaking down the data into games played with the DH and those without we find the following:

        <----DH---->   <---NO DH---->
               HBP /           HBP /
POS     PAPct   1000   PAPct    1000
-------------------------------------
P        0.0%    0.0    6.2%     2.8
C       10.1%   10.0   10.5%    11.0
1B      11.1%    9.6   11.2%     9.0
2B      11.0%    9.6   11.5%    11.2
3B      10.8%    8.4   11.1%     8.4
SS      10.8%    9.1   11.1%     7.5
LF      11.2%    8.1   11.3%     9.0
CF      11.3%    7.8   11.6%     8.5
RF      11.0%    8.8   11.3%     9.2
DH      11.2%    9.0     -        -
PH       1.4%    7.9    4.3%     8.6

TOTAL            8.9             8.8

Here there is only a 1% overall difference. If one were to "correct" the data to account for lineup composition, as we did with the 1973-1993 data, you would find that games in which the DH was not in force produced 8.1% more hit batsmen per 1000 plate appearances than games without the DH. Truly, this is a large shift, for which we can offer three possible explanations.

First, as with the 1973-1993 data, we may be seeing the influence of one or several extreme players. It just so happens that during this period the NL has been blessed with a trio of the most-frequently hit batters in the history of baseball in Jason Kendall (except 2005), Craig Biggio, and Fernando Vina (except 1995-1997 and 2004). A clue to their contribution can be seen in the previous table, where the rates for second baseman and catchers are conspicuously high in the NL. Overall, their rates during that time…

          PA  HBP  HBP/1000
---------------------------
Kendall 5908  197    33.3
Vina    4633  154    33.2
Biggio  7930  245    30.9

Don Baylor has nothing on these guys.
If we adjust these three players' rates down to the league average for the period it drops the overall NL rate 4.3%, down to 9.8, just under the AL rate. Even so, this doesn't fully account for the fact that, given the lineup composition theory, we should see even fewer hit batsmen in the NL.

A second theory, and one proposed by Bradbury and Drinen in their follow-up paper, targeted the expansions of 1993 and 1998 as possible factors. Although discussed in the first article in this series, this theory does accurately predict a larger increase in HBP in the NL than in the AL in 1993-1994 because of the asymmetrical nature of the expansion draft. In 1993, the HBP rate rose 7.3% in the AL and 21.6% in the NL, and for 1994 it was -6.0% and 11.6%. In the years following 1994 the rate increases evened out. But even so, one wouldn't think that NL pitchers would go on hitting more batters even after the affects of expansion were absorbed as they did in 1997 and 2000.

The final theory, and one also proposed by Bradbury and Drinen, is that the implementation of the "double-warning rule" (8.02(d)) in the winter of 1993 had an immediate impact. Essentially, this rule raised the costs for teams hitting opposing batters, and placed that cost squarely on the pitcher and manager, both of whom can be immediately ejected from the game. One result is that AL pitchers now have a greater fear of hitting batters in retaliation lest they be ejected, thereby lowering their rate of hit batsmen. At the same time, it could be argued (as Brady and Drinen do) that NL pitchers have less fear of retaliation under the double-warning rule, since they know that the opposing team dare not hit them or their teammates or suffer the cost. The combination of more fear by AL pitchers and less fear by NL pitchers could together be responsible for essentially erasing the gap between the leagues.

Take Your Base
One of the reasons so many of us love baseball is that while it is seemingly simple, it is also a very human activity with naturally endless complexity. In this series of articles, I hope that we've highlighted some of that complexity in a statistically small but interesting part of the game. But while I for one love big-picture analysis, there's nothing more exciting than getting caught up in the one-on-one confrontations between pitcher and batter that are really the source of our ruminations.