THE BOOK--Playing The Percentages In Baseball

Tuesday, September 28, 2010

Odds Ratio Method: head to head movies

These were the win% of head-to-head matchups of the top 9 movies, in a universe of 34 movies:
v33 Movie
0.797 Major League
0.777 Bull Durham
0.756 The Natural
0.744 Field of Dreams
0.740 Eight Men Out
0.715 Baseball: a film by Ken Burns
0.710 A League of Their Own
0.701 The Sandlot
0.658 Bad News Bears

The header “v33” means “against the other 33 movies in this universe”.

Now, suppose your universe of movies is not 34, but 9 (these 9).  Now, with the Odds Ratio method, it should be easy enough to figure out the chance that each of these movies would best the other 8 in a head-to-head matchup.  This is what it would say:
Odds33 Movie
0.580 Major League
0.551 Bull Durham
0.522 The Natural
0.506 Field of Dreams
0.501 Eight Men Out
0.470 Baseball: a film by Ken Burns
0.464 A League of Their Own
0.452 The Sandlot
0.405 Bad News Bears

But, does anyone believe that The Sandlot would win 45% of the head-to-head matchups of the other 8 movies?  What I think happens is that Sandlot is so different from the others that it beat up on the other 25 movies in the other universe, and once I take those 25 movies out, The Sandlot would be exposed as a bit player.  It’s hard to imagine someone preferring Bull Durham to The Sandlot AND The Sandlot preferred to Field of Dreams.  There is something not very random going on, would be the expectation.  Well, I decided to show the poll with only these 9 movies in the head-to-head matchups, and I got these results:

v8 Movie
0.579 Major League
0.533 Bull Durham
0.564 The Natural
0.575 Field of Dreams
0.507 Eight Men Out
0.473 Baseball: a film by Ken Burns
0.470 A League of Their Own
0.363 The Sandlot
0.364 Bad News Bears

As you can see, there’s some major moving going on.  The Sandlot drops substantially.  Field of Dreams moves up a decent amount.  Field of Dreams had the opposite impact: it didn’t do as well against the other 25 movies as Bull Durham did.  But when faced against its true peers, it bested Bull Durham.

This is similar to say the Russians and Canadians playing hockey tournaments where Russia trounces Italy by a score of 15-1, while Canada wins 12-2.  In reality, those scores tell us virtually nothing about how Russia and Canada would do when they face each other.  And if you have competition that also included Sweden, USA, and Finland, then I would completely discard (not partially) the results against Italy.  Italy is simply no peer to the Russian and Canadian teams, and therefore, provide no information to us as to how Russia would do against Canada.

This I think is what is happening with The Sandlot.  The original chart makes it seem as if it’s pretty close to A League of Their Own, but when placed in a competition of its peers, we see it is nowhere close.  Here’s the full chart, reproduced side-by-side:
v33 Odds33 v8 Movie
0.797 0.580 0.579 Major League
0.777 0.551 0.533 Bull Durham
0.756 0.522 0.564 The Natural
0.744 0.506 0.575 Field of Dreams
0.740 0.501 0.507 Eight Men Out
0.715 0.470 0.473 Baseball: a film by Ken Burns
0.710 0.464 0.470 A League of Their Own
0.701 0.452 0.363 The Sandlot
0.658 0.405 0.364 Bad News Bears