What is the Probability of Perfection?

After winning its conference tournament this past weekend, the Wichita State Shockers became the first Division I men’s basketball team to enter March Madness undefeated since the 1991 UNLV Runnin’ Rebels. Wichita State was also the first team to go 30-0 in the regular season.

A feat like this requires some degree of luck. There is never a game in which a team has 100% win certainty, no matter how the weak competition. That said it is certainly a lot easier for a team that plays a weaker strength of schedule to run the table.

The perfect Shockers actually had a very average strength of schedule. According to KenPom.com, Wichita State’s Pythagoras strength of schedule was .531, good for 131^st out of 351 teams. This means, against an average Division One opponent, the Shockers’ competition would win 53.1% of games. This is slightly above average, but not strong nonetheless. On the other hand, Wichita State’s Pythagoras rating is .9403, good for fourth in the country, behind three major powerhouses: Arizona, Louisville and Florida.

So the question remains, how likely was their run?

First, for simplicity sake, let us consider the case where every one of Wichita State’s games was against its average opponent. Their expected win probability could be adjusted to approximately 93.3% using Bill James’s Log5 formula. Developed by the famed sabermetrician, the Log5 formula, weights the winning percentage of each team to develop a single-game win percentage. While the derivation of the formula is complex, the equation is simple:

             A - A * B
  WPct = -----------------
         A + B - 2 * A * B

Given this, the probability that the Shockers go undefeated is simply .93^34, which is 9.4 percent.

Let’s examine each game a little more in depth, however. The Shockers, who have been criticized for their strength of schedule, have indeed played some strong teams including probable tourney teams like Saint Louis and Tennessee an at-large 11-seed (according to Joe Lunardi’s Bracketology). Developed for baseball, Bill James’s formula fails if you assume 1.0 win probability, because clearly team A will always win.

However, if we assume KenPom’s rating is a decent estimation of true winning percentage, then the log5 formula can provide insight into how the shockers did. As I used KenPom’s Pythagoras rating for Wichita State, I also used it for each team they played and applied the log5 formula to each game. I did not count the first game of Wichita State’s season because it was against a non-D1 opponent.

To calculate the probability that Wichita State won all these games, I simply multiplied all these single game probabilities together.

Probability of going undefeated  = 4.37%

Clearly, the Shockers are very lucky. They didn’t suffer injuries to any major players. Also, they are in the Missouri Valley Conference, a conference that is suitably weak to cultivate an undefeated campaign. Nonetheless, Wichita State is a team to reckon with going forward. This season has not been a simple cakewalk for them. Games against Tennessee, Saint Louis and Brigham Young were games that although they were expected to win, posed a significant threat to their perfection.

Unless the selection committee shocks (pun intended) the nation, Wichita State will be a number one seed after reaching the Final Four last season. Will they reach the Final Four once again? That remains to be seen, but just like their perfect season, it will require a lot of skill and a little bit of luck.

by Jacob Lynch, Harvard College