Archive for March, 2004

Changing the Walk Rule

I’m about 10 days behind the baseball blogosphere in discussing this interview with Bill James in The American Enterprise magazine. The most interesting statement by James was his one suggested rule change to improve baseball.

I suggest a batter should be able to decline a walk. Not only an intentional walk, but any walk. The batter’s team should able to say, “No thanks, I don’t want that walk.” And if you walk him again, he goes to second base and anybody already on moves up two bases. The reason that should be the rule is because the walk was created to force the pitcher to throw hittable pitches to the batter. That is the walk’s natural function. To allow the walk to become something the defense can use to its advantage with no response from the offense is illogical and counterproductive.

This reminded me of a similar rule suggestion by Brad DeLong in October 2002.

After much meditation, I have decided that baseball needs only two changes in order to become a great sport:

— A twenty-five second pitch-hit clock–with a called ball or strike against whoever violates it.
A walk on a 4-0 count is not a one-base but a two-base walk.

It is crystal clear why these two changes would greatly improve the game. It would speed it up–which is important. And it would eliminate the boring and unfair practice of depriving the best hitters of chances to show their stuff.
Emphasis added.

Though James and DeLong suggest slightly different rules, they basically want the same thing: a two-base walk to prevent pitchers from using a walk to punish a good hitter. I predict the following implications from such a rule change.

1) Wage disparities across hitters will grow. One reason that Bonds is not paid more than he is for his ability is that pitchers can simply not pitch to him. If you raise the cost of walking Bonds, he will see more pitches and produce more offense. Hence, he will be receive a higher wage. Now, this does not bother me, nor is it likely to bother Bill James. But if you don’t like it when A-Rod earns 10-times more than the average player, you ought not like this rule.

2) The game will become less of a team game. Rather than having to sign good hitters to bat Bonds around when he is walked, you are more able to rely on Bonds generating his own scoring. Again, this will transfer income from mid-level players to superstars, but I think the real change is how it will affect the play of the game. A good team can consist of a one or two stars and others rather than needing 5 or 6 solid hitters to be dispersed through the line-up to prevent the pitch-around strategy.

3) Defense will get better, because the defensive specialists with weak bats will induce fewer pitch-arounds. They will be less of a drain on offense.

4) There will be more foul balls, because hitters will foul off strikes just to earn two-base walks.

I will admit that the effects are likely to be small but noticeable. I don’t like the rule change, but not because of any of these implications. I don’t see anything unnatural with a pitcher choosing to walk a batter. The costs and benefits of walking are what they are, and pitchers respond accordingly. Is it really less exciting to allow a pitcher to choose between pitching to Bonds with one man on and pitching to Santiago with two men on? That sounds like a sporting risk. The pitcher gets to decide the speed and location, why not who to pitch to when you have a base open?

Update: Skip has some more thoughts on the issue.

The Gains from Trades

Matthew Namee writes about the wheeling and dealings of Billy Beane and his stathead friends. Beane, J.P. Ricciardi, Theo Epstein, and now Paul DePodesta all share similar philosophies on baseball. This got me thinking, “why is it that these guys trade with each other so much?” Is it some conspiracy, coincidence, or just friends wanting to deal with friends?

Well, I think there is another option that is related to friendship. These are the few GMs in the league who value player qualities in the same way. If they value players differently (I mean from a different evaluation perspective), some trades that ought to take place will not. For example, let’s say Beane eyes a traditional “leadoff-man” speedster for defensive purposes on a team in desperate need of some relief pitching. Beane wants the guy to bat eighth and save some runs in center. Beane is willing to part with a relief pitcher with few saves but a great K/BB ratio. An upgrade for both teams. Were Beane on the other team he would make the trade in a second. The trade would make both teams better off. But, the old school GM complains that “there is no way I am going to give my leadoff-man who can steal lots of bases and manufacture runs for anything less than a dominant closer.” Of course, this is when Beane offers him a high save closer he’s built up by pitching in the 9th inning with three-run leads, and laughs. But this will only work for so long , as GMs begin to realize they are getting screwed and refuse to do business with the A’s. No such problem exists when Beane can work with GMs who evaluate talent in a similar way. These guys are bound to trade with each other because they are the only ones who can see unrealized gains from trade from the same perspective.

I went Googling on the web and here is what a I found. Beane’s explanation seems to support this.

“We have similar beliefs and knowing each other allows us to make deals [quickly]. With J.P. and Theo, I can get a deal done in five minutes.”

And Ricciardi feels similarly,

“In trades with Billy, or anybody else, we don’t mind trading away a good player, as long as we get a good player back. We never feel like it’s about pulling a fast one.”

Just as Star Wars fans can trade replica lightsabers more easily at the Bi-Mon-Sci-Fi-Con than at a flea market, Beane & Co. can swap players much easier amongst themselves. Maybe this explains why Beane let some of his “secrets” out in Moneyball. If current GMs won’t trade with him, maybe some tight-wad owners might read the book and hire him some trading partners.

BTW, I doubt this is an original idea, and it has probably been hashed out on Primer somewhere. If you know of any discussions of this, please send me links.

How Does this Site Look?

Thanks to all of you who have written to me about the site. I have had a few complaints about how this page looks in Safari and Netscape. Thank you for informing me of this. I have been using this template on my old site and I was unaware of the problems. I took down the “Old Fishinghat” pictures, which ought to help, but I am afraid my patch job of CSS will have to stay until I can fix the problem. If you are having problems viewing the site please let me know the problem and your browser in the comments of this post. That way others can confirm or deny the problem. Then, when I get a spare moment I can work on fixing the problems. Sorry for the mess, but please bear with me if you can.

The DH and Hit Batters

An article on a paper by Doug Drinen and myself on the hit batsmen difference between the AL and NL has just hit the web. I wouldn’t have known except that Baseball Primer has already started a thread on it. I don’t have much time to write on it now, thanks to a lunch committee beating (I mean meeting), but I may write more on this later. Here is a link to the original paper.

Update: I have a few more links to pass along. The main story appears on the Inside Science News Service of the American Institute of Physics (go figure). Also, here is an earlier wire story from Dick Jones Communications. If you have not checked out the thread on Primer linked above, there was a very interesting discussion of the paper there yesterday.

Update: The Globe and Mail has also picked up the story.

Welcome to Sabernomics

In the past few months I have written many posts about economics in baseball at Old Fishinghat. I have enjoyed writing about baseball so much that I decided to devote an entire weblog to it. I may post on various other topics related to other sports and economics, but the main focus of the site will be baseball as viewed by an economist. I still have Old Fishinghat for general ranting.

So what is sabernomics? Simply put, sabernomics is the study of economics in and of the game of baseball. I very much enjoy sabermetrics and economics. Sabermetricians strive to find objective knowledge about baseball, often using mathematics and statistics as tools. Economists study human beings striving to maximize utility subject to constraints on action, also often employing mathematics and statistics. In other words, economists concentrate on how human beings respond to changes in the rules of the game. Baseball, like all sports, provides a natural laboratory for economic study as a result of the obvious goals of participants and constraints on action imposed by its rules and institutions. This is what interests me. Sabermetricians are also interested in such issues, but the scope of sabermetrics is much broader than the economics of baseball. MLEs and UZRs interest me as a fan, but not as an economist; therefore, I probably will not use this site to debate the usefulness of these statistics. You might say that sabernomics is a subfield of sabermetrics, a subfield of economics, or maybe it is just a domain name that was available for purchase at a low price. Regardless, I will use this site to post my thoughts on baseball that interest me as an economist.

On the right sidebar I have posted links to some studies that I have done on Old Fishinghat that are relevant to this site. I have also transferred several of the posts to this site if you want to see what I write about. I have enabled comments and trackbacks to facilitate discussion. Please, feel free to chime in with your thoughts and suggestions to specific posts. I hope you enjoy the site.

Measuring the Quality of Competition in MLB

This article by Chris Dial caused me to revisit some of my thinking about the quality of competition in baseball over time. Judging player ability over time when player performance is a function of other participants in the game is not easy. For example, in sports such as running, where the outcome is measured by time, it is very easy to compare athletes over time using absolute measures of performance. The runner with the fastest time is clearly the best. However, sports such as baseball, where outcomes are a function of the relative performance of players, comparing abilities becomes much more difficult. While Babe Ruth was the greatest hitter of his era it does not mean that he is any better than the players in today’s game. The pitchers of today differ from the pitchers of Ruth’s era. While Ruth may have dominated in his own time, few would argue that this beer-swilling slugger would be the same player in today’s game. But, it is possible that Ruth performed better against his competition than Barry Bonds does to his.

So if we cannot use absolute statistics to measure achievement, how can we compare player performance across eras. Stephen Jay Gould suggests such a method: compare the distribution of playing talent in the game. The talent spectrum in baseball ranges from AAA call-ups to superstars. As the talent pool expands more fringe players enter the game. This means that the best hitters (pitchers) in the league get more opportunities against low-quality pitchers (hitters), giving the best players a greater opportunity to excel. Gould takes his argument a step further to say that the compression of talent in today’s game — due to the rising population compared to stagnant number of teams — reduces the occurrence of abnormal excellence. He views the decreased dispersion, as measured by the standard deviation of several baseball statistics, as the reason that no player has batted .400 since Ted Williams in 1941.

I decided to use Gould’s argument in a different way. I want to see how competitive the game was, as measured by talent dispersion, during different eras in baseball history. I am curious as to the quality of the game as measured by the distance between the best and the worst players. An instructive example occurs every four years in soccer with the World Cup. The best players in major leagues around the world form all-star teams by country and compete. I am not a huge soccer fan, but I have watched both MLS and World Cup soccer. There is huge difference in quality of play, with the World Cup being at a much higher level of play. This makes me wonder, has the talent distribution in baseball become more like the World Cup over time, as Gould predicts?

First, I want to look at the percent of the US population playing Major League Baseball over time. This table lists the population per MLB player at the start of each decade.

Date		Pop/Player Ratio
1900		238,163
1910		288,214
1920		265,054
1930		308,007
1940		330,411
1950		378,314
1960		358,646
1970		338,687
1980		348,532
1990		382,631
2000		375,229
		
Century		328,353
Post-1940	 352,557 

Since 1940 MLB has been above the average ratio of the century, but it has not continually increased. Why not? Expansion. Also, I am excluding some other important measures that understate dispersion in the early part of the century such as racial segregation and the lack of international players. However, this may be counterbalanced by the emergence of other sports with which baseball competes for talent. Therefore, I am not sure how useful this information is.

Second, I want to directly examine the dispersion of baseball talent in hitting and pitching. Instead of using the pure standard deviation of baseball statistics, I am going to use the coefficient of variation (CoV) as a measure of dispersion. The CoV is simply the SD/Mean, and it is superior to the non-normalized SD because it is not biased by the mean. For example, a year with a high mean batting average is likely to have a higher SD of batting average than a year with a low batting average. Using the Lahman database I use all pitchers that face at least 50 batters and players that have 100 at-bats to calculate the CoV of quasi-OBP allowed [(hits +walks)/(AB+walks)] and batter OPS for all pitchers and hitters. I would prefer to calculate OPS against for pitchers, but this data needed to calculated this is not in the Lahman data. I pick the cut-off of 50 and 100 for pitchers and batters to cut-out the players who do not have enough observations to for reliable statistics, but I don’t want to cut out all of the fringe players. I set a lower standard for pitchers, because raising the cut-off excludes a good number of relief pitchers. This figure lists this dispersion by decade relative to the 1920-2003 average. Higher bars mean greater dispersion, lower bars mean more similarity across players.

One thing that is quite interesting is the difference in fluctuations across hitters and pitchers. They do not seem to move together. For example, in the 1980s and 1990s hitters were not widely dispersed though pitchers were very dispersed. This leaves a few questions to ponder.

1) Why does the dispersion of hitting and pitching talent differ? If it were just the result of changes in the size of the population from which MLB draws players, they should move together.

2) How can baseball fans use this data to compare individual players across eras? Though pitching talent is more dispersed than in Ruth’s era, the average offense of the league is much higher now. How can we combine both of these metrics to compare players from different eras to each other versus their competition? Bonds has done well in an era of pitchers that are on average worse than Ruth’s pitchers, and the modern day pitchers are much more varied in quality. I want to give Ruth the edge here — not because I like him, but because it seems the right thing to do — but I would like a more objective way to quantify this. Maybe the historical win shares database will do it, but I don’t know.

Finally, I would like to figure out which decade from the past is most like today in terms of the quality of competition. The clear winner is the 1950s, certainly a good decade for baseball. Hitting and pitching dispersion were very similar to today, and Steve Treder seems to like it for some other reasons. It is also interesting that the population to player ratio of today is very similar to 1950.

Age and Pitching Performance

After looking into the aging patterns of hitters, the next step is to look at pitchers. How does pitcher performance improve and decline with age? I used the same regression technique I used for hitters to estimate the effect of age on pitching performance using this model.

ERA+ or K/BB+ = X(Age) + B1(Lag of ERA+ or K/BB+) + B2 (# Batters Faced by Pitcher) + V (player constants) + e

ERA+ is the pitcher’s season ERA divided by the league ERA that season multiplied by 100; where 100 is a league average pitcher for that season. K/BB+ is the pitcher’s strikeout-to-walk ratio for the season divided by the league average and multiplied by 100. The “plus” method is a good way to pull out year-to-year differences in the observations. ERA is the normal standard by which most fans judge pitcher performance. I admit I could have used the DIPS ERA, but I did not want to calculate it going back to 1980. I think when you look at performance over time there is not that much of a need to make the correction, so I will not expend the effort. Instead I will use another good metric of pitching performance, the strikeout-to-walk ratio. As Skip discussed the other day, in 1974 Gerald Scully first noticed this metric to be an important measure of pitcher quality, and Bill James agrees. X is a vector of coefficients for different degrees of polynomials of Age (Age, Age^2, Age^3, etc.). V is a vector for individual player constants to factor out any individual player characteristics not included in the model (i.e. this is a fixed-effects model). The two control variables I include are the previous year’s performance in ERA+ or K/BB+ to proxy pitcher quality and # of batters faced by pitchers in a given season to proxy for injury.

For a sample I use individual players by season from 1980-2003. Data is from the Lahman Database. I include only pitchers who start at least 10 games in any season of observation. I tried using a wider sample of pitchers initially, but the inclusion of relief pitchers seems to make estimating the model very difficult. This is probably a good thing since starting pitchers and relief pitchers have almost completely distinct roles. It is also important to note that the league averages I use to calculate ERA+ and K/BB+ are the average of all players starting 10 games or more in that particular season. I estimate the model using the xtregar command in Stata, which basically estimates the coefficients using OLS but corrects for serial correlation.

Here are the fitted plots on three samples of pitchers for both measures of pitching performance: the entire sample of pitchers, those pitchers with below 100+ careers , and those with above 100+ careers.

The best fit for ERA+ is quartic, or adding the polynomials from Age to Age ^4 ; thereforefore, the minimums I report are rough visual estimates. Many thanks to an altruistic reader who tried to help me minimize the function by hand, but it was too much of a pain (we need Mathematica). Pitcher ERA+ is minimized at about 28-29 for the good (below 100) pitchers, 26-27 for the entire sample, and seems to be ever rising for the not-so-good (above 100) pitchers.



The best fit for K/BB+ was quadratic, and therefore easy to maximize. Pitcher K/BB+ is maximized at 29.67 for the good (above 100) pitchers, 28.58 for the entire sample, and 25.66 for the not-so-good (below 100) pitchers.



From this, I think it is safe to say that the best estimate of peak pitching performance is a little more than 28. It is a little higher for good pitchers, and a little earlier for lower quality pitchers. This is not surprising since high-quality pitchers will have more opportunities to pitch as they get older than low-quality pitchers. Below I include the regression tables for those who are interested. I do not report the standard errors. All of the statistics are statistically significant at the 1% level in the K/BB+ model. For ERA+ the coefficients are statistically significant for the entire sample model at the 5% level or less; however, when I break the sample up, some of the coefficients on the higher-orders of age are not statistically significant. I am still working on this a bit, but I just want to post what I have. Please feel free to lend me your thoughts or suggestions.


Variable ALL ERA+ < 100 ERA+ > 100
Age 24.22148 22.96265 32.37705
Age^2 -1.369466 -1.25484 -2.218376
Age^3 0.0315969 0.0275669 0.0604417
Age^4 -0.0002519 -0.0002059 -0.0005627
Lag(ERA+) -0.2734865 -0.2851918 -0.280756
BFP -0.0430742 -0.0340235 -0.0566215
R-sq. 0.28 0.24 0.37
Obs. 1911 1251 660
Players 448 234 214
Peak Age 26-27 28-29 early 20s
Variable ALL K/BB+ > 100 K/BB+ < 100
Age 7.265849 8.569231 5.124458
Age^2 -0.127119 -0.1444294 -0.0998337
Lag(K/BB+) -0.1721541 -0.1464887 -0.2262057
BFP 0.041634 0.0500489 0.0318835
R-sq. 0.13 0.12 0.18
Obs. 1911 987 924
Players 448 144 264
Peak Age 28.58 29.67 25.66

More on Age and Batting Performance

Since my last posts (here and here) I have received several excellent suggestions on how to modify the model. First, I want to break down the player/age effect by different types of players. Though I discussed this below, the age-performance curves make it clear that there is not much difference in aging patterns across differently-abled players. The three classifications of players with career OPS+s of <90, >90 & <110, and >110.

Second, Skip suggested that I incorporate some higher polynomials in the estimates. While the quadratic is certainly preferred to the linear estimate, other polynomials may provide even better estimates. And he was right, because adding the cubed or third degree of age to the regression model has an interesting effect. While the R-sq. did not change much (.0086) the cubed term was statistically significant, and the estimated peak age shifted from 29 to about 27.

As you can see, adding the cube of age looks very different. (Note, adding the 4th and 5th powers did not help). I am less concerned about the different peaks and the rate of decline among the two estimates. From about 28 on, the estimates are very similar. The interesting part is the early career. In the cubed model players start just below their peak before declining, while in the squared model players improve quite a bit before they decline. I would also like to point out that this fitted prediction includes controls for the number of ABs in a season, to attempt to control for injury problems.

So which model do you like? Wade Boggs or Chipper Jones?

Age and Batting Performance Continued

Since my earlier post, I have had some more time to analyze the data and examine a few other studies on aging in baseball. The literature tends to support the conventional wisdom that players peak around 27. Here are some links to studies and their predictions of peak age. Keep in mind that this is a brief summary on my part and my reporting does not reflect the caveats of the authors. I think all of these studies are good and anyone who is interested in the issue should read them.

Bill James (from the 1982 BJHA): 27 is the peak including all offense and defense. This is a must-read article if you can get your hands on it. Luckily, I have a friend who loaned me his tattered copy.
David Luciani: 24-26
Don Malcolm: Doesn’t really take a stand on this issue, but it is an interesting study on age and performance by hitting components.
Tangotiger: 27
Keith Woolner: 25-28, but probably a little less than 27.

Given my earlier results, I was a bit concerned. My model seems to produce different conclusions, but I have quite a bit of confidence in my empirical approach. So, I decided to break out the numbers in several different ways. The two most logical ways to parse the data are by player quality and career length. Recall, I only include player seasons where the batter has more the 300 ABs. The first table reports the results for players with career OPS+s of <80, <90, <100, >100, >110, and >120.


Variable All Players <90 <100 >100 >110 >120
Age 8.876 7.792 8.737 9.109 9.953 10.275
Age^2 -0.152 -0.135 -0.149 -0.156 -0.170 -0.162
Lag(OPS+) -0.261 -0.253 -0.303 -0.242 -0.226 -0.109
R-sq. 0.3 0.35 0.35 0.27 0.32 0.33
Obs. 2848 321 1203 1645 576 151
Players 621 103 332 289 79 21
Peak Age 29.21 28.88 29.37 29.2 29.28 31.62

The results indicate that players of different quality age the same, except for the superstars (>120). While most other players peak at age 29, the superstars peak between 31 and 32.

Now, I want to estimate the model on players with different career lengths. Maybe there is some bias from bad players leaving early and good players sticking around. In all of these samples I include players with at least two consecutive seasons with 300 ABs. The career seaons categories are 5 or less, 10 or less, 5 or more, 10 or more, and 15 or more.


Variable All Players 5- 10- 5+ 10+ 15+
Age 8.876 12.212 9.780 8.872 8.906 9.414
Age^2 -0.152 -0.238 -0.177 -0.152 -0.150 -0.155
Lag(OPS+) -0.261 -0.452 -0.299 -0.259 -0.228 -0.340
R-sq. 0.3 0.4 0.32 0.31 0.28 0.23
Obs. 2848 434 1755 2651 1307 252
Players 621 250 515 467 135 18
Peak Age 29.21 25.64 27.57 29.22 29.62 30.29

Players with shorter careers seem to peak earlier than players with longer careers. This is not surprising since these players are likely to be the weakest of the talent pool, plus they do not get the opportunity to improve since they are no longer in the league. But, that number 29 keeps popping up as the peak age for players, and this runs against the conventional wisdom.

I have three explanations for my difference. First, I use OPS as a measure of offense, and most of the studies discussed above use other measures. If you think OPS is a bad measure of offense, then my study probably doesn’t mean that much to you. Second, I focus on a relatively modern sample, in which players are playing longer due to better nutrition, conditioning, and medical technology. Third, I may have made a data error somewhere in the mix. While I doubt this, I do plan to double-check my numbers to make sure I did not make a mistake in generating. I will update this if I find out this is the case. I plan to think more on the subject, and I hope others do as well. Please feel free to pass along any comments.

Age and Batting Performance in MLB

I was curious about the peak age of performance for baseball players. A Google search revealed a few studies, but they didn’t handle the question the way I would. So I thought I would try it my way. I am not saying those studies are bad, I plan to read several over the weekend.

Using the Lahman database, I used a sample of every player in MLB that had 300 at-bats in a season from 1980-2003. If a player failed to get 300 ABs in a season, he was dropped from the analysis for that season and the season that followed (because I am using lags), but he was then returned when he had 300 ABs. I picked this time period because, I am not interested in aging patterns from the past at this moment. Using Stata I estimated the following equation using the xtregar command (this is basically an OLS estimate with a correction for first-order autocorrelation). The unit of observation is a player in a season.

OPS+ = B1 (Age) + B2 (Age^2) + B3 (Lag of OPS+) + B4 (League OPS for that year) + V (player constants) + e

OPS+ is simple the OPS of a player relative to the average OPS of the league in that year. This measure is NOT park-adjusted. V is a vector of fixed effects to control for individual player attributes. I’ll spare presenting the numerical results for the moment, but I will tell you that the peak age of OPS + for the sample is about 29. Plugging in the average numbers for the Lag and League OPS variables the table below plots the estimated OPS+ by age.

Interesting. The general wisdom on this stuff is that the peak age is closer to 27. I will have to think more on it.

Update: Here are the coefficient estimates. All are statistically significant at the 1% level except League OPS, which is significant at just about the 5% level. I also report a second specification with League OPS dropped.


Variable Coefficient Coefficient
Age 8.051103 8.876295
Age^2 -0.1400366 -0.1519125
Lag(OPS+) -0.2633548 -0.2610575
League OPS 18.8625
R-sq. 0.31 0.3
Obs. 2848 2848
Players 621 621
Peak Age 28.75 29.21

There is still more to come.