Friday, July 30, 2010

Do younger brothers steal more bases than older brothers? Part IV -- Age vs. SB

A few weeks ago, I wrote a series of posts on an academic paper about siblings and stolen bases. That study claimed that when brothers play in the major leagues, the younger brothers are much more likely -- by an odds ratio of 10 -- to attempt steals more often than their older brothers.

Since then, the authors, Frank J. Sulloway and Richard L. Zweigenhaft, were kind enough to write me to clarify the parts of their methodology I didn't fully understand. They also disagreed with me on a few points, and, on one of those, they're absolutely right.

Previously, I had written,

"It's obvious: if the a player gets called up before his brother *even though he's younger*, he's probably a much better player. In addition, speed is a talent more suited to younger players. So when it comes to attempted steals, you'd expect younger brothers called up early to decimate their older brothers in the steals department."

Seems logical, right? It turns out, however, that it's not true.

For every retired (didn't play in 2009) batter in my database for which I have career SB and CS numbers, I calculated his age as of December 31 of the year he was called up. I expected that players called up very young, like 20 or 21, would have a much higher career steal attempt rate than players who were called up older, like 25 or 26.

Not so. Here are career steal rates for various debut ages, weighted by career length, expressed in (SB+CS) per 200 (H+BB):

17 -- 5.1
18 -- 6.9
19 - 11.3
20 - 14.4
21 - 13.6
22 - 14.0
23 - 14.7
24 - 15.5
25 - 13.4
26 - 14.0
27 - 16.5
28 - 10.2
29 - 11.0
30 - 13.5
31 - 10.3
32 - 17.4
33 - 13.0
34 -- 3.9
35 - 10.5
36 -- 6.1
37 -- 7.4
38 -- 5.3
39 -- 8.4
40 -- 0.0
41 - 14.0

It's pretty flat from 20 to 27 ... there is indeed a dropoff at 28, but few players make their debuts at age 28 or later.

Why does this happen? Isn't it true that young players are faster than old players? Perhaps what's happening is that players who arrive in the major leagues earlier also play longer, which means their extra early high-steal years are balanced out by their extra later low-steal years. I'm not sure that's right, but it's a strong possibility. In any case, my assumption was off the mark, applying as it does only to age 28 and up.

I could have figured out that was the case had I looked at Bill James' rookie study from the 1987 Baseball Abstract. Near the end of page 58, Bill gave a similar chart for hits and stolen bases (but on the total number, not the rate). And it looks like SBs decay not much more than hits or games played.

For instance, consider a 22 year old player compared to one who's 25. The 22-year-old, according to Bill, will wind up with 88 percent more base hits than the 25-year-old (623 divided by 331, on Bill's scale). For stolen bases, the corresponding increase is 84 percent (613 to 334). The two numbers are pretty much the same -- which means, since 1987, we've known that career SB rates don't have a lot to do with callup age.


Anyway, the "odds ratio of 10" finding in the sibling study was based on individual player-to-player comparisons. So, I decided to test those. Suppose you have two players, but one breaks in to the majors at a younger age than the other. What is the chance that the younger callup attempts steals at a higher rate for his career?

To figure that out, I took the 5,742 batters in the study, and compared each one of them to each of the others. I ignored pairs where both players were called up at the same age, and I ignored pairs with the same attempt rate (usually zero).

The results: younger players "won" the steal competition at a 52.9% rate, with a "W-L" record of 7,387,525 wins and 6,569,412 losses.

Young: 7387525-6569412 .529

However: that includes a lot of "cup of coffee" players. If I limit the comparisons to where both players got at least 500 AB for their careers, then, unexpectedly, the older guys actually win:

Young: 1950250-1965161 .498

The difference between those two lines comprises cases when one or both players had a very short career. When that happened, the young guys kicked butt, relatively speaking:

Young: 5437275-4604251 .541

These numbers are important because they represent exactly what the authors of the sibling study did -- compare players directly. My argument was that I believed the younger player would be the "winner" a lot higher than 52.9% of the time. That's not correct. So that part of my argument is wrong, and I appreciate Frank Sulloway and Richie Zweigenhaft pointing that out to me.

Does that mean I now agree with the study's finding that the odds of a player having a higher attempt rate than his brother are 10 times as large when he's a younger sibling? No, I don't. But it does mean that I need to refine my argument, which I will do in a future post.

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