Friday, March 29, 2013
Historical replacement level
Someone asked me if I had faith that the replacement level is constant enough that awarding 0.206 wins per team game is fine. I don't know the answer to that. One thing that I would expect however is if you take all the negative wins of players in each season and add them up, that that should remain fairly constant year to year. If for example you have 1000 wins to hand out, then maybe expecting 1200 wins among players with greater than 0 WAR and -200 wins among players with less than 0 WAR. I don't know that it should be +1200/-200 or +1150/-150 or whatnot, but I'm pretty sure it should remain constant.
There are two times that I think it should not necessarily be constant: expansion, and changes in games per season. I'd expect for example to see a wider spread, per game, of WAR in 1981 than in other seasons, simply because the signal from the talent can't overcome the random variation? from the smaller samples as much. And, I'd expect that expansion would widen the spread.
Sean and David were nice enough to give me the year-by-year totals. What you see below is the WAR pro-rated per 4860 games, for all the players with negative WAR that year.
We see that indeed in the strike year of 1981, that we see a much wider spread, exactly as expected. (If we had infinite games on the other hand, every player would bottom out at 0 WAR.) 1994 also represents a bottom, but it's not as big a drop because 1993 was an expansion year, and 1995 was not a full-season. 1977 and 1969 also shows a bit of a drop as expansion years, but not as noticeable.
Before 1960, games played was 154 rather than 162, so we'd expect a slightly wider spread. But BR and Fangraphs don't behave consistently there.
We are also limited to the data at hand. The more data, the more the spread. So, since 2002, they use more granular fielding stats, so it allows a larger separation in performance. So, that's another confounding factor, and it may be the reason we see a larger spread, compared to the pre-1988 data when we've got more limited fielding information.
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