Wednesday, March 31, 2010

Tom Izzo: Is he the real March Magician?



This past week much as been written and talked about Tom Izzo at Michigan State as being the March Magician. The Spartans and Tom Izzo have delivered 6 Final Fours out of the last 13 straight NCAA appearances. Tom Izzo has been head coach at MSU now for only 15 years. The real question I want to answer is how unlikely is this success.

According to Nate Silver at FiveThirtyEight.com, Tom Izzo should have succeeded only twice to the Final Four according to seedings. Nate presents a very interesting logistic regression that ties the seeds to the probability of reaching the final four. According to the seedings the Spartans have over performed. This making the accomplishment of 6 final fours in the last 13 years to be an unusual event.

I did some analysis myself and come to some slightly differing conclusions:

First, you might think going to the NCAA tournament 13 of 15 years is a difficult accomplishment. However with 347 teams in the NCAA Div I someone will due this just by chance and here is why. The selection process gives 30 bids to conference winners and 34 bids at large split among the 8 major conferences. This gives the Big Ten conference about 5.25 bids each year on average. For any given Coach the odds are against you, but remember in the Big Ten there are 11 coaches playing the game and in the 8 conferences about 80 coaches competing against each other. As such the probability that one of these coaches makes 13 out of 15 years is about 0.5102 probability. This is about 1:1 odds. In the end its a good likelihood that somebody does 13 out of 15 years in any 30 year time period.

Now the problem is conditional. Once you are the one who makes a tournament 13/15 years what are your chances of making the final four for 6 or more occasions. It is important to know that of the 347 schools, only 43 of these have made the final four in the past 26 years. Since there are four final four selections each year, then on average these 43 schools have had multiple final four appearances. (Following list is shortened.- Data since 1985)

The average probability of making the final four of the schools from this select group of 43 is approximately 0.205. Now using the binomial distribution function again in Excel for 6 or more final four appearances in 13 trials, the probability of this occurrence is 0.0317.

Since we have two independent events 1) making the NCAA 13/15 years = 0.5102 and 2) winning 6 of 13 final four appearances 0.0317, we multiply the two to obtain our final probability for any coach matching Izzo's accomplishment.

Prob(total) = 0.5102*0.0317=0.0162
Odds = 100/1.62-1 = 60.7:1
(Recognize my figures are not a result of detailed analysis but an estimate. )

In conclusion, Tom Izzo did not really accomplish a very unusual event. Only about 1 in 61. Interpreting this it tells us that given the 15 year career of 60-70 coaches this accomplishment is bound to happen to one of them. A good start to Izzo head coaching career. In fact, certainly this is a lifetime career start for any coach. However it is within the realm of feasibility that it happened. After all 1 in 61 events do occur. If you look at the average frequency that Duke or North Carolina convert to the final four, MSU still lags and is not the best performer by this metric.

So is Tom Izzo the March Magician. Of course he is! Certainly, not only does he benefit from some luck, during March he finds ways to get more out of his team. MSU does still have Magic! Good Luck on Saturday against Butler.
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