Co-authored with Arjun Modi
Going into this past weekend, two Ohio basketball teams were streaking, but within just 24 hours, both streaks were over. On Friday evening, the Cleveland Cavaliers' 26 game losing streak mercifully ended when they beat the Clippers in overtime. On Saturday afternoon, Ohio State's 24 game winning streak ended with a road loss to Wisconsin.
We wanted to know which streak was more improbable -- the Buckeyes' extended winning or the Cavaliers' extended stretch of futility. To calculate the odds of each streak, we used the Pythagorean win expectation formula. The formula gives the odds of winning a single game during the streak based on the number of points scored and allowed during the streak (Cavaliers: 2455 scored, 2810 allowed; Buckeyes: 1868 scored, 1367 allowed).
Using the Pythagorean expectation formula with the appropriate exponents (14 for NBA and 11.5 for college), the single game win probability was 13.1% for the Cavaliers and 96.8% for the Buckeyes. This means that given the points scored and allowed during the streaks, we would expect the Cavaliers to win 3.4 games out of 26 and the Buckeyes to win 23.2 games during a 24 game stretch. Keep in mind that these figures do not adjust for blowout wins/losses (most notable was the Cavaliers' 55 point loss to the Lakers). If we capped wins at 15 or even 20 points for our calculations, the Cavaliers would have had a higher win expectation and the Buckeyes would have had a lower win expectation.
Given this information, the chance that the Cavaliers would lose all 26 games was a paltry 2.6% (.131^26). The Cavaliers did seem to get unlucky as evidenced by the fact that they were actually ahead during in five of the six games before they broke the streak. The Buckeyes streak was not nearly as remarkable given their point differential. Their odds of winning 24 games in a row was 46.3% (.968^24).
For our next test, we wanted to see how the Cavaliers and Buckeyes would fare if they played as poorly/well for an entire season as they did during their streaks.
Assuming the Cavs had the same chance of winning each game, we simulated 100,000 seasons to determine the team's longest losing streak within a season. The results, broken down in the chart above (click on image to enlarge), indicate a franchise bound to endure prolonged streaks of futility. On average, the longest losing streak reached nearly twenty games -- only four teams in NBA history have suffered an in-season losing streak as long. The Cavs, however, relied on a particularly poor string of luck to break the all-time NBA record for consecutive losses. According to the simulations, the team had just an 18.5% chance of losing at least twenty-six games in a row.
Ohio State, on the other hand, embarked on a dominant run to be expected by its out-sized point differential. By basic probability alone, we can calculate the chance of a perfect regular season, with thirty-one games played per this year's schedule, as .968^31 = 37.0%. Simulating 100,00 regular seasons yields a clearer distribution of win streaks and, as a testament to the team's abilities, Ohio State had a 56.6% chance of winning at least twenty-four games in a row. Interestingly enough, the longest winning streak was 24.3 games on average -- in that sense, Ohio State's streak reflects the ordinary accomplishments of an extraordinary team.
So all that leaves is the question of who would win if the Buckeyes played the Cavaliers.
For more analysis like this, check out the Harvard Sports Analysis Collective's site at harvardsportsanalysis.wordpress.com.