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Hey everyone! I looked around the site to see if this question had been answered before but couldn't find anything. Can someone help me better understand how Ken Pomeroy calculates his adjusted offensive and defensive efficiencies? He gives a brief explanation on his website, but I still have a few questions:

1) Pomeroy says "I compute an adjusted offensive efficiency for each game by multiplying the team’s raw offensive efficiency by the national average efficiency and dividing by the opponent’s adjusted defensive efficiency." But how can you use this method to calculate AdjOffEff if you need AdjDefEff? Where do you start?

2) How does he define "national average efficiency?" Is this value uniform for every game and equal to the average taken at the date of calculation, or does he apply the national average efficiency at the time of each game (i.e. games on different days have different national average efficiencies)? I have the same question for opponent’s adjusted defensive efficiency.

I tried to word these questions as well as I could, but let me know if you need me to clarify my questions. I would greatly appreciate any help you guys have to offer. Thanks!

1.) He divides by the raw def eff iteratively. That's the limit on opponent adjustment.

2.) He probably uses an average of previous season average efficiencies, probably using the current season data (all of it) later in season.

3.) All of this is better done using regression with priors from the previous season.

v-zero wrote:1.) He divides by the raw def eff iteratively. That's the limit on opponent adjustment.

Do you think you could explain this a bit further? I'm sorry if this is a dumb question, but I still can't understand this part of the process.

It's a recursive problem, essentially you start with raw O and raw D and iteratively solve for improved estimates of both. It is similar to the methodology for SRS which is explained for the NFL on sports-reference.

I'm not sure Mr. Pomeroy uses the same style of calculation as SRS...from brief interactions he mentioned that "each level" (opponents' opponents' rating, opponents' opponents' opponents' rating) was worth less and less in the math as it goes deeper. To me that is a flaw - each level should be 100% equal. But what do I know...

i.e. since Efficiency Differential should be estimatable by Team 1 True Rating - Team 2 True Rating

Then something like the following should be true on average:
Team True Rating = Efficiency Differential + Team 2 True Rating
and
Team True Rating = Average of All Eff. Diffs. + Average of All Opponents' True Ratings

so you can see it expanding infinitely, but with equal value assigned to opponents, opponents' opponents' and so on.

TrueRtg = Eff Diff + OppRtg
TrueRtg = Eff Diff + (Opp Eff Diff + Opp's OppTrueRtg)
TrueRtg = Eff Diff + (Opp Eff Diff + (Opp's Opp Eff Diff + Opp's Opp's Opp TrueRtg))

And so on.

What's the difference between these iterative processes and using a simple linear regression with each game in the matrix?

sbs wrote:What's the difference between these iterative processes and using a simple linear regression with each game in the matrix?

There isn't any difference. Both methods are minimizing the squared errors between game outcomes and the predictions made by the individual teams' ratings.

sbs wrote:What's the difference between these iterative processes and using a simple linear regression with each game in the matrix?

So if you were calculating AdjOffEff via SLR, what matrices and values would you use?

Just was thinking about this thread from a while back and thought I'd bump it back up. Could anyone provide a more detailed idea of how these calculations would be done? I'd like to do something like this: http://audacityofhoops.blogspot.com/201 ... ctors.html but unfortunately Hess skips the explanation of this part of the calculations, saying that that's "the easy part."