THE BOOK--Playing The Percentages In Baseball

I hope I understand the questions, but here are my guess:

1) He Declines
2) Average performance declined, but less than 1 (mean > median)
3) He Declines
4) Average performance declined, but less than 1 (mean > median)

IMO, few(20%) will improve, most will stay the same (55%), a few will decline (20%), some will really decline (5%)

My first inclination is to say that the median will definitely be lower than the mean, simply because the distribution of statistics like you mention are almost certainly skewed.

If a player has a ‘true’ FIP, or anything similar, then from multinomial theory he should have a variance of roughly 0.11, or a standard deviation of about 0.33 (this seems reasonable empirically). I’m going to guess on average a player won’t improve or decline more than about 0.05 points of ‘true’ FIP in any given year, especially at 25, which means declining or improving is almost certainly at a 50/50 split.

I guess my answer is basically that the median will be slightly less than the mean, but decling or improving is a coin toss.

I should add that the variance figure I cited is for 200 IP. It’s obviously bigger for 100 IP (about 0.2 for a sd of about 0.45) or 50 IP (var 0.38 and sd of 0.62). These are approximations, the numbers are different for each pitcher. Regardless, over 50 IP, the probability of decline or improvement from the last season is obviously a crapshoot if you believe my numbers (which are true only if you believe walks, strike outs, home runs, and ‘other’ occur according to a constant multinomial distribution).

wOBA would have been better as a test metric because ERA is not symmetrically distributed, while wOBA would be.

ERA is, basically, wOBA-squared.

Yes, but a symmetrically distributed metric removes the fun of deciphering between 1/2 and 3/4.

If anyone is curious, the variance for wOBA is also convenient to calculate, assuming a multinomial distribution. Excluding SB/CS, it’s something like
800 BF (~200 IP) sd = 0.017
400 BF (~100 IP) sd = 0.024
200 BF (~50 IP) sd = 0.034

This seems reasonable looking at how certain players performed over their career. I would certainly accept the argument that the true variance structure may be different from the multinomial.

Off topic, but Tango, what do you get for the average forecast error from your forecasting challenge? I seem to recall it being about 0.025, which assuming about 600 PA seems reasonable, as injuries and whatnot will increase the variance slightly. If this is the case, it offers some proof that forecasts are about as good as they can get.

Right, it was around .026 I think (for the veteran players), and then it went up from there.  I think for pure-rookies, it was close to .040.

I’m not really concerned about the median/mean thing. And we can use wOBA for the performance metric (that is basically a component ERA).

I just want to know whether you think a 25 year old pitcher will improve or decline, based upon the IP parameters I gave.

Conventional wisdom says that young pitchers improve, right?  Tango, don’t your aging curves for pitchers indicate that 25 year old pitchers improve or at least don’t decline?

Witout looking at comments (yet), here are my answers:
1) he will improve if he was below average and decline if he was above average, but experience will have a small effect that helps him improve. Basically, I’m regressing year n - 1 to average to get my expected performance in year n, and then adjusting that up slightly to account for improvement one would expect from learning and conditioning in a young pitcher.

I’m not sure I understand 2. Sorry.

For 3) smae basic answer, but the error bars are bigger.

By the way, there might be someting I’m missing i these answers. If in year n - 1 pitcher throws 100+ innings but throws 50-100 innings in year n, I’m guessing he got worse in year n. It could just be that he was injured, but IP correlates with overal performance (good pitcher throw more innings) so for those that throw fewer innings in the second year, I’m suspecting a performance deline. (If in (1), the cut off were 180 IP, I’m very likely to bet on “declie” in year 2.)

1) You don’t get to decide whether the pitcher was above or below average in the first year.

2) What makes you think that 100 innings in the first year and 50 in the second, as a minimum, means that our pitcher declined in innings? What if I didn’t mention a minimum at all in year 2?  Would you make the same assumption (that he declined in innings)? If I told you that I looked at all batters who had at least 10 pa in year 1 and at least 5 pa in year 2, would you assume that they had more or less pa in year 2?