from Amazon
Wednesday, November 10, 2010
Brothers stealing
The authors responded to Phil about that article. It seems that it’s a question of definitions, as noted on page 10:
Ironically, although odds ratios are often used in an attempt to clarify complex statistical findings, people who are not familiar with them sometimes misinterpret what odds ratios do and do not mean. In our own data for major league brothers, for example, an odds ratio of 10.58 to 1 in favor of younger brothers attempting to steal more bases per opportunity does not mean that younger brothers attempted 10.58 times the number of steals as did their older brothers. Similarly, this statistic also does not mean, as Schwarz (2010) mistakenly reported in the New York Times, that more than 90 percent of younger brothers attempted more steals per opportunity than their own older brothers.
Only 59 percent of younger brothers in our sample attempted more steals per opportunity, although this statistic, uncontrolled for call-up sequence, considerably underestimates the overall effect for this measure, just as computing an odds ratio without regard to call-up sequence underestimates the effect. For example, among the 10 brothers in our study who were called up during the same year—where there is no possible bias owing to callup sequence—80 percent of younger brothers (4 out of 5) attempted more stolen bases per opportunity than their older brothers, yielding a relative risk ratio 4.00 to 1 (80%/20%), and an odds ratio of 16.00 to 1.
I have no idea what the heck they are talking about, other than they may have double-counted. If you have the Yankees with a true talent .667 win% facing the true talent Royals of .333 win%, the Odds Ratio matchup would say that you do .667/.333 (Yankees’ 2:1 odds) divided by .333/.667 (Royals’ 1:2 odds) to give you a 4:1 odds ratio, implying a win% of .800.
If however, your universe of teams is ONLY the Yankees and Royals, and you observe one million games where the Yankees have a .667 win% and, by default, the Royals have a .333 win%, the Odds Ratio would imply a win% of .667 for the Yankees.
So, going back to the authors, it seems to me that when they report an Odds Ratio of 10:1 for younger brothers stealing more, they imply to mean 3.16:1, or 76% as the likelihood of a younger brother stealing more than an older brother. Indeed, why not just report that figure instead? Give us the “win%” of younger v older. We all understand win%.
The authors do a nice job in their response. It would have been nicer if they actually refereced Phil and Guy or whoever by name or handle or even site.