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 131st 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.

Opponent KenPom rating Log5 Win %
Western Kentucky

0.4582

0.94904233

William & Mary

0.4955

0.941302501

Tennessee State

0.2312

0.981264367

Tulsa

0.7062

0.867595933

DePaul

0.4541

0.949835696

Brigham Young

0.8025

0.794925273

Saint Louis

0.8437

0.744757998

Oral Roberts

0.4734

0.946005567

Tennessee

0.8989

0.639179631

Alabama

0.6905

0.875926611

North Carolina Central

0.6793

0.881458018

Davidson

0.6056

0.911170633

Southern Illinois

0.5218

0.935209503

Northern Iowa

0.6733

0.884292074

Illinois State

0.5566

0.926183658

Missouri State

0.5342

0.932128408

Bradley

0.3949

0.960213505

Indiana State

0.6426

0.89754137

Illinois State

0.5566

0.926183658

Drake

0.4278

0.954683114

Loyola (IL)

0.3277

0.969981789

Evansville

0.3991

0.959537799

Indiana State

0.6426

0.89754137

Northern Iowa

0.6733

0.884292074

Southern Illinois

0.5218

0.935209503

Evansville

0.3991

0.959537799

Loyola (IL)

0.3277

0.969981789

Drake

0.4278

0.954683114

Bradley

0.3949

0.960213505

Missouri State

0.5342

0.932128408

Evansville

0.3991

0.959537799

Missouri State

0.5342

0.932128408

Indiana State

0.6426

0.89754137

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

3 thoughts on “What is the Probability of Perfection?

  1. One important thing to also include here that makes Wichita’s run even more impressive is that some of the toughest teams they played were either on a neutral court (BYU) or on the road (Tulsa and more importantly St. Louis), which add a significant level of difficulty to their wins.

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    • Definitely true. You could theoretically adjust the log5 formula to account for the “home-field advantage” The website I pulled the formula from stated that historically the home team wins 54% of the time, but I’m not sure how relevant this is to college basketball.

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  2. Pingback: Wichita State Shockers: How Likely Was Their Undefeated Season? | The Harvard College Sports Analysis Collective

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