THE BOOK--Playing The Percentages In Baseball

Mickey,

I don’t know how meaningful these results are—at a minimum, you need to include minor league data to get rid of some of the selective sampling problem (which frankly is overwhelming right now). Of course players who do not gain much at a young age tend to rise sharply as they reach their peak—otherwise, they wouldn’t stay in the major leagues! The same problem would exist if you included minor league data, of course, but to a lesser extent.

This is very cool stuff, but this is the type of study that I think you can only do rigorously—too much noise otherwise. (And by the way, when you say a player ages well or poorly, I hope you mean their projection improves or declines more or less than expected, not their raw numbers. Otherwise, you’re also conflating regression to the mean with aging in this study, I think.)

I love the idea here, that we might infer the slope based on the trend of the past slope.

The first part seems logical: if Justin Upton spikes to 40 HR this year, it’s not likely that he’ll continue that growth to Age 27 and hit 100.

I think the question implied in the final paragraph here is an interesting one, especially relating back to the discussion of aging models.  The ‘does the player age better at 35 if he aged well at 33’ question seems important to management and contract decisions, even more so than the question of ‘peak age’.  I imagine it may be useful to do some sort of rigorous survival model (i.e. the probability of performance above Level Y at age X, given that he has performed above that level at Age Z).

"The first part seems logical: if Justin Upton spikes to 40 HR this year, it’s not likely that he’ll continue that growth to Age 27 and hit 100.”

Millsy, remember I am using the delta method and skipping a year, so that is not applicable.

If Upton spikes to 40 HR this year and is put into the “ages well group” I am going to look at the difference between next year’s HR rate and the HR rate of the year after that, both of those being independent of the 40 HR year.  He doesn’t have to hit more than 40 HR to “continue to age well.” If he hits 10 HR next year and then 20 the year after that, he will be classified as someone who aged well from Year X to Year X+1 (with Year X+1 being the 40 HR year) and then again from Year X+2 to Year X+1.  That is exactly why I had to skip a year - so it would NOT be obvious that someone who spiked before could not spike again (2 years after that).  I hope that makes sense.

David, yes, there are definitely strong selective sampling issues, especially at the earlier ages.  As I said, I was just quickly playing around with the numbers.

As Tango says, it would be interesting (and useful for teams and for forecasters) to see how past aging trajectories for individual players might portend future trajectories.  I think we have always assumed that because there is so much noise in an individual’s trajectory (which there is), that there isn’t much we can garner from a player’s past trajectories, in terms of predicting his future trajectory.  I think that, because of the low signal to noise ratio in one player’s trajectory over a few years, the best we’ll ever be able to do is maybe tweak the future trajectory just a little bit.  But I think it is possible…

Ah, I see.  I guess I was thinking in absolute terms.