Saturday, April 3, 2010

Opponent-Adjusted Four Factors

This is something I’ve been thinking about for some time, and I finally gave it a shot yesterday.  I should point out right up front that I haven’t done any kind of testing to see if the way I’ve implemented it makes sense, nor checked to see if the adjusted numbers are more predictive than raw Four Factors data.  But I wanted to get a rough draft of the system done before today’s games are underway – I’ll test and tweak in the off season.

My method was basically to reproduce the Pomeroy ratings, except using (for example) offensive and defensive OR% instead of offensive and defensive efficiency.  I tested the method first on efficiency, just to make sure I was able to reproduce Pomeroy’s numbers.  He actually weights the numbers based on how recent the games are, and I didn’t try to mimic that, but my numbers still essentially aligned with his:


That’s the easy part; I’ve done that before.  The trickier part was deciding what value to use for home field advantage for the various factors.  Pomeroy uses 1.4% per team for each number - he adds 1.4% to the home team’s offense and visitor’s defense, and subtracts 1.4% from the home defense and visiting offense.  I don’t know where he got that number, but I was able to roughly reproduce it (1.25%) by looking at only home-and-home games from this season, finding the average overall efficiency, and the average home efficiency, and then taking the square root of the ratio between the two:

( [Ave Home Eff] / [Ave Overall Eff] ) ^ 1/2 = (103.6/101.0)^0.5 = 1.0125

Since this makes sense, and seems to reproduce Pomeroy’s HFA number, I used this method to come up with the HFA adjustments for the Four Factors:

  • eFG%: 1.007
  • TO%: 0.980
  • OR%: 1.007
  • FTR: 1.031

Once I had these, all I had to do was re-do the opponent adjustments using the Four Factors and their HFA’s, instead of the efficiency values.  Then I looked to see if the outputs passed the smell test.  I’d say they look fine; here is a comparison of the raw and adjusted Four Factors rankings for the Final Four participants (click image for larger version):


I highlighted a few of the significant changes.  For the most part, all the teams look better in all the categories, but there are a few exceptions.  Here are a few notes:

  • The only instances where the adjustment moved a team’s ranking down more than a couple spots were Butler’s eFG% and Michigan State’s FTR.
  • Duke and West Virginia’s shooting numbers are not as bad as they seem – the adjustments pull them up to basically even with Butler and MSU.
  • Michigan State’s turnover problem is as bad as it seems – especially with the adjustment improving Butler’s defensive TO%.
  • The best three offensive rebounding teams in the nation are still alive.
  • Butler doesn’t have as much of a defensive rebounding advantage as I thought.
  • The FTR adjustment for MSU is interesting – I’m wondering if that is a result of Big Ten officials “letting them play.”

Of course, now that I have these numbers, the obvious temptation is to use them to predict the Four Factors numbers for tonight’s games.  I of course gave in, but right now I have no faith whatsoever in the accuracy of these.  Just for fun, though:


Eyeballing those, it looks like Butler wins by forcing Michigan State turnovers, and Duke wins by forcing West Virginia into a poor shooting night.  Sounds about right to me.

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