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# League Difficulty (Part 4)

by David Gassko
April 16, 2007

In today's article on league difficulty, I wrote that The Book recommended adding 400 plate appearances of average performance to a player's record when regressing to the mean. It turns out I was mistaken, as the authors use different numbers in different parts of the book, but I am told by Tom Tango, one of the authors, that I should be adding more like 220 plate appearances. Of course, that changes our results a bit.

The following graph presents the results using three different methods. The green line represents the method proposed by Dick Cramer, and used by Clay Davenport of Baseball Prospectus, which we examined in part one of the series. The blue line is the conclusion we came to last week, in part two. The red line, which is the correct measure of evolving league difficulty (assuming I didn't make another mistake somewhere), takes into account the corrections mentioned in today's column, with regression to the mean reduced from 400 plate appearances to 220.

As you can see, without accounting for aging and regression to the mean, we still strongly overstate the effects of improving quality of play, though perhaps not quite as much as it might have appeared last week. What I find most interesting is that even according to the new method, over the past 15 years, the quality of competition has been essentially flat. I think it's pretty clear that we are hitting some kind of wall of physical ability.

For posterity, I'm also posting a graph for each separate league. For a larger version, simply click on the picture:

David Gassko is a former consultant to a major league team. He welcomes comments via e-mail.