THE BOOK--Playing The Percentages In Baseball

I don’t know if these guys are deeply confused, or deliberately muddying the waters to hide their errors.  But the analysis is just hokum. 

I’m doing this from memory (Phil knows the data 100x better than I do), but the bottom line here is that younger brothers only attempt steals a little bit more than older brothers, as indicated by the fact that just 59% of younger bros. steal more often than their sibling.  But even this overestimates the real difference, for at least 2 reasons:
1) older bros have longer careers, and SBA drop off sharply with age, so their career rate will be lower if you don’t adjust for age;
2) the authors define opportunities as BB, 1B, 2B, and 3B, but since older brothers have much more power on average, a larger share of their estimated opportunities are not true SB opportunities (because it’s an XBH).
I am reasonably sure that once you correct for these, there is no statistically significant difference.

The way the authors invent a big difference is by adjusting for what they call “call-up sequence,” meaning which brother is called up first chronologically.  So, for example, they compare younger brothers called up 1st to older bros called up first.  Guess what?  A younger bro who gets called up before his older brother is usually a very good player, and thus steals much more (same thing if called up the same season).  Now reverse it and compare younger bro called up 2nd (basically average, as almost all younger bros are called up 2nd) to an older bro called up 2nd (a weak player on average)—again, the younger brother is a much better player on average.  This is just a whole lot of words to say nothing of value. 

But in reviewing the data, Phil did discover something very interesting:  younger brothers are significantly worse players on average.  That suggests that players whose older brother played/plays in the majors are given more of a chance to play in MLB than their talent level alone would usually provide.  Cool finding....

The authors mentioned this in their response, calling it the “halo effect”.  I’m not sure if that was their discovery, or Phil’s.

Perhaps the authors did report that finding in the original paper (it’s gated now, and no one should spend 10 cents for this).  On the other hand, the abstract also says “In addition, younger brothers were significantly superior to older brothers in overall batting success.” As I say, this is just a terrible muddle and not worth anyone’s time. The whole notion that brothers’ performance should logically be compared in the same calendar year, with an “adjustment” for who arrived in the majors first, is simply nonsensical.  The bottom line is there’s no there, there.

Right, I agree that the chronological calling up of players seems pretty weird.  I’m not sure why they didn’t just leave it as age based.  Clearly they wouldn’t have done this with uncles/nephews, as almost all uncles are older than their nephews, so they would simply be focusing on their ages.

I don’t get the fascination of the chronological time of being called up as a central point to the study.

In any case, I liked their response overall.  They went pretty in-depth.

Subscribing to the thread.  Will get to all of this next week.  Bad timing.

"I don’t get the fascination of the chronological time of being called up as a central point to the study.”

Probably because it gave them the result they wanted. The lead author’s big theory is birth-order effects, and his work has been criticized for distorting data in order to support that theory (I can’t judge the merits of the criticism, but based on this one paper I find it highly plausible).  If they compare brothers by age, they won’t get much of a birth order effect.

In general, I agree an in-depth response to online criticism deserves praise.  But in this case, I fear the depth is in service of obfuscation rather than clarification. 

And the “halo effect” they describe refers to brothers who were called up second, not to younger brothers.  Their finding is that brothers called up second tend to be worse, which is of course true but meaningless.

Phil responds:

http://sabermetricresearch.blogspot.com/2010/11/do-younger-brothers-steal-more-bases_16.html

As I noted, the “10.58” is not the real odds, but if you take the square root of that, it would (seem to) represent the real odds.  So, that’s 3.25 to 1.

And, presumably, that’s based on having an equal number of younger brothers being called up before the older brother and after.  Maybe, I don’t know.

But, I can buy that explanation, that if you equally weight the callups, and take the square root, then the younger brother has a 76% chance of outstealing the older brother.

Good call.  I think you’re right.  I’ll add that to the post.

VERY good call.  I think that’s the entire problem with the study.  Instead of taking the average of the two different effect sizes, they multiplied them together.

Tango for President!

OK, maybe not.

The 10.58 is not odds.  It’s the factor for how the odds *change* when you switch callup positions.

The idea is that if the younger brother was 1:1 when called up last, he’d be 10.58:1 when called up first.  If he was 1:2 when called up last, he’d be 10.58:2 when called up first.  If he was 10:1 when called up last, he’d be 105.80:1 when called up first.  And so on.

The fact that the square root of 10.58 (3.25) happens to be similar to what our estimate for what the actual odds are (somewhere between 1.4:1 and 5:1) is just coincidence.

The “square root” argument still matters in another context.  The 10.58 applies when you switch brothers ... so, in a sense, it applies to both brothers.  To find the effect on a *single* brother, you’d take the square root. 

I’ve updated my post.  I’m going to have to rewrite it, actually.  There were too many things I was confused about and got wrong.

Right, I never said 10.58 were “odds”.  The square root of 10.58 is the odds.

Go back to my Yanks v Royals example, and looking at their win% based on whether they are in a league of a million teams, or in a league of 2 teams.

The Odds Ratio method works in the former case, but not the latter case.  The authors are applying the Odds Ratio method in the latter case.

I’m saying that even the square root of 10.58 is not the odds.  The square root of 10.58 is the CHANGE in odds when you switch younger and older. 

Imagine that when the younger brother is called up last, he outsteals the older brother 90% of the time: 9:1.

Imagine that when the younger brother is called up first, he outsteals the older brother 98.96% of the time: 95.22:1.

The odds ratio is still 10.58.  The “real” odds ratio is still the square root of that, 3.25.  But the actual odds are well above 90:1.

Last sentence in Phil/12 should be, “But the actual odds are between 9:1 and 95:1.”

Hmmm.... interesting.

Basically, you are saying that if the odds was 90% in one case, and 90% in the other case, then the “odds ratio” would be presented as “1.00”, even if the actual odds is 90%.

***

In that event, this is more like the “splits” we talk about with regards to clutch, or performance by park, etc.

Basically, this “odds ratio” being reported, or whatever it is, is just some intermediary number that is only useful in the context of it actually being applied.

And the final result should be presented as winning odds (head-to-head) so that we all know what we are talking about.

That’s right.  The “odds ratio” is not the odds—it’s how much you increase or decrease the real odds by when you switch from “old called up last” to “young called up first”.

The paper doesn’t talk about the odds much because I don’t think the authors care much.  They only care that “younger” means 10x the odds, because they study siblings.

The title of this post looks quite racist out of context