For all your fancy-pants statistical needs.

Praise for The Basketball Distribution:

"...confusing." - CBS
"...quite the pun master." - ESPN

Point-margin-based Chance of win.

While I think using the four factors can give us a much better picture of point-margin (and therefore, chance of win), let's just look at the 2nd step right now: deriving chance of win from expected point margin.

The Log5 formula used by many people (including Ken Pomeroy) to determine a team's chance of win is fairly accurate. It is based on fitting a model to theoretical results.

Slightly more accurate, I believe, is the LRMC (logistic regression markov chain) steady-state formula, which does the same thing, just to a much higher degree of accuracy; steady-states offer an actual theoretical explanation for the numbers based on team play rather than simply the normal distribution.

For example:
Duke's chances against Maryland, assuming a 2-pt-win-

Log5: 61%
LRMC: 59.8%

Huge difference, huh?

Finally, I must throw in my two cents: empirically, I think it is viable to say that specific teams play more consistently than others. In that way, we can alter win probabilities based on standard deviations of actual minus expected point margin (which explains the basis for this site's creation). Using those numbers (from, we see that:

Duke's standard deviation of actual minus expected point margin is 9.77.
Maryland's standard deviation of actual minus expected point margin is 10.98

By Duke's numbers alone, we see their chance of win as being 58.1%
By Maryland's numbers alone, we see their chance of win as being 42.77%

By averaging these two values in their context (.581 and 1-.4277) we see that Duke's chance of winning should be around 57.7%

This allows us to solve (or at least partially resolve) Pomeroy's two prediction flaws: lack of accounting for consistency, and lack of accounting for diminishing returns. The first is obvious, the second is because team's expected play versus their actual play should reflect the error in his ratings derivations.

If I had enough time to scour through all the teams' data, I could give an adjusted Standard Deviations (or, 'Consistency') value for teams -- adjusting their consistency based on how consistent or inconsistent their opponents play.

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