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January 5, 2006

Crooked Numbers

Double Play Thursday

by James Click

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When you spend way too much time talking about baseball with people, a lot of time there are little questions thrown out here and there that aren't thoroughly answered, but are also not quite worthy of the full length discussion and exploration that a column requires. With most people, these questions become a column of bullet points or small notes, with others a full length feature piece. But with me, they become rambling incoherent gibberish mixed in with a few tables. Or, if you're lucky, a two-for-one column.

Part 1:

Joe Sheehan mentioned difficulties with sample size in his last column, specifically with regards to how long it takes before we know how good a team truly is. Noted among the examples were the A's, Indians, and Astros, three teams who struggled to score runs, at least early in the season. While Rany Jazayerli has covered how much faith to put into the first few games of the season in detail, maybe there's something to the idea that teams in low-scoring environments tend to have a higher variability as the season goes on. Perhaps the suppression of runs lends more luck to the outcome of games and a larger sample size is required to determine the true winning percentage of those teams.

To answer this, teams from 1972-2005 were grouped by their total runs and runs allowed into three levels with one-third of the league in each level each season. Then their final winning percentage was compared to their winning percentage after 30, 45, and 60 games. Averaging the differences between those yields the following:


Run Env  After 30    After 45    After 60
High       .071        .053        .043
Mid        .063        .047        .042
Low        .067        .055        .042

As expected, the difference decreases as the games sampled increases. However, teams in low-scoring environments don't show a significantly higher variance than ones in higher situations. So there's little reason to think that we know less about the Astros after a certain number of games than we do about the Red Sox.

However, instead of looking at the total variance, looking at the average change in winning percentages reveals something interesting.


Run Env  After 30    After 45    After 60
High      -.004       -.006       -.005
Mid        .005        .001       -.001
Low        .002        .007        .006

Teams in high run scoring environments see a steady decrease in winning percentage while those in lower run scoring environments see a steady increase. While the trend is slight--somewhere around one to one-and-a-half games on the season--it raising interesting questions about player durability in higher run scoring environments or other factors in play.

Part 2 (completely unrelated to Part 1):

Something that's come up in discussions before is the aspect of players changing leagues. Typically the thought process is that pitchers may benefit from a league switch while batters do not, a theory stemming from the idea that the pitcher is trying to deceive the batters and the more times batters have seen a pitcher, the better they will perform. While that aspect of performance is up for debate over the course of repeated batter-pitcher matchups, there may be something to the idea that switching leagues can affect performance of batters or pitchers on a macro level.

Rather than looking at this trend on a general level, it's more interesting to check it out in different eras, particularly with regards to free agency and interleague play. With the advent of these two changes--not to mention winter leagues, video equipment, etc--players in different leagues see each other much more often than they used to. As a result, we would expect modern players to be able to deal with a transition from league to league better than players in the past.

The table below contains the average change in OPS for all players who totaled at least 1,000 AB in three consecutive seasons in one league and then totaled at least 400 AB in another the next year. The "Pre" group is all players 1945-1974, the "FA" group is 1975-1996, and the "Inter" group is 1997-2004. (Obviously 1975 wasn't a clean break from the previous period as 1997 was, but since free agency gradually took hold over the late-70s and early-80s, there's not single season to select as when one data set should end and another begin.)


Period   Players  Delta OPS
Pre        34       .013
FA         97       .004
Inter      59      -.002

As much as that looks like a steady trend moving against the way we would expect, changing the years between the eras just slightly completely changes the conclusions. For example, here are the same numbers, but with the eras changed to 1945-1970, 1971-1990, and 1991-2004:


Period   Players  Delta OPS
Pre        25       .003
FA         77      -.001
Inter      88       .008

The problem is that the difference between the eras is so small that moving one or two players from one era to another changes the rankings of the eras. As such, there doesn't appear to be a tangible change between the performances of batters who changed leagues before and after free agency and interleague play. While there seems to be a slight increase (.004) on the whole among batters who change leagues, that change is so small that it could easily be caused by any number of factors for which this study has not accounted.

On the flip side are the pitchers:


Period   Players  Delta ERA
Pre         78      -0.03
FA         136      -0.02
Inter       57       0.08

Once again, there appears to be a smooth trend working here. However, let's change the years between the eras just a little and see what happens.


Period   Players  Delta ERA
Pre         53     -0.02
FA         122     -0.04
Inter       96      0.06

This time the interleague period still shows up as distinct from the other two eras, but the difference isn't large enough to draw any broad conclusions about pitchers having a harder time changing leagues in the last two decades than they have for the previous few.

It stands to reason that players should have an easier time switching leagues these days mainly due to the greater mix of players seen every year as a result of free agency and interleague play. However, because there doesn't seem to be any consistent problem switching leagues in the first place, it's hard to make that disappear with the advent of modern player movement and scheduling.

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