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.

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