By taking the simulated # of wins (via kenpom.com's numbers) and average wins for a given seed, we can rate who will have the best performance above what their seed predicts.

Here are the results for the field.

### Quick Math on the bracket

Here is my preliminary results of my bracket simulation, based on stats from Kenpom.com

http://dl.dropbox.com/u/241759/MidwestWest.html

(not yet adjusted for teams' consistency)

http://dl.dropbox.com/u/241759/MidwestWest.html

(not yet adjusted for teams' consistency)

### Game-Changers for NCAA Tourney Teams

Here we'll be taking a look at what is likely to alter a team's predicted final score (based on Ken Pomeroy's rankings - http://kenpom.com and the LRMC's rankings - http://www2.isye.gatech.edu/~jsokol/lrmc/)

The two things we'll be doing:

The two things we'll be doing:

1)We'll describe what part of Ken Pomeroy's Four Factors stats (of a team's opponents) affects the predicted outcome. Relies on = is ranked high in, does not rely on= is ranked low in. All these numbers can be found on the team pages at Kenpom.com

2) We'll measure a team's predictability (in terms of consistency of actual versus expected point margin with an average value of 10.9).

-Predictability: +1.1 points above average

-When opponents' offense relies on heavy free-throw shooting, Duke fares better. (Correlation of +.34)

-When opponents' defense DOES NOT rely on heavy defensive rebounding, Duke fares worse. (Correlation of -.28)

`

-Predictability: -.2 points above average

-When opponents' offense relies on good field-goal shooting, Kansas fares worse. (Correlation of -.43)

-When opponents' offense relies on heavy offensive rebounding, Kansas fares better. (Correlation of +.33)

**-Duke: (#1 Pomeroy, #2 LRMC, #2 bLRMC)**-Predictability: +1.1 points above average

-When opponents' offense relies on heavy free-throw shooting, Duke fares better. (Correlation of +.34)

-When opponents' defense DOES NOT rely on heavy defensive rebounding, Duke fares worse. (Correlation of -.28)

`

**-Kansas: (#2 Pomeroy, #1 LRMC, #1 bLRMC)**-Predictability: -.2 points above average

-When opponents' offense relies on good field-goal shooting, Kansas fares worse. (Correlation of -.43)

-When opponents' offense relies on heavy offensive rebounding, Kansas fares better. (Correlation of +.33)

-When opponents' defense DOES NOT rely on field-goal percentage, Kansas fares worse. (Correlation of -.34)

-Predictability: +.3 points above average

-Predictability: -.5 points above average

**-Wisconsin: (#3 Pomeroy, #13 LRMC, #9 bLRMC)**-Predictability: +.3 points above average

-When opponents' offense relies on good field-goal shooting, Wisconsin fares worse. (Correlation of -.31)

-When opponents' defense relies on field-goal %, Wisconsin fares better. (Correlation of +.24)

-When opponents' defense relies on field-goal %, Wisconsin fares better. (Correlation of +.24)

**-Ohio St: (#4 Pomeroy, #7 LRMC, #5 bLRMC)**-Predictability: -.5 points above average

-When opponents' offense relies on good field-goal shooting, Ohio St. fares better. (Correlation of +.24)

-When opponents' defense DOES NOT rely on field-goal %, Ohio St. fares worse. (Correlation of -.30)

-When opponents' defense DOES NOT rely on field-goal %, Ohio St. fares worse. (Correlation of -.30)

### UPSET WATCH

NCAA tournament upset watch: Murray State and Pittsburgh are the two teams who will likely be mis-seeded the worst: http://dl.dropbox.com/u/241759/upsets.htm

### 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 Kenpom.com), 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.

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 Kenpom.com), 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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