Matt Bishop – is a student in my Decision-Making class. Matt is an avid basketball fan and a student of the game. We used the method of indirect comparisons to fill in March Madness brackets; Matt did the heavy lifting, I kind of tagged along. Here is the prediction and a description of the algorithm.
The method of indirect comparisons comes naturally to all of us when attempting to predict the outcome of sports matches. Suppose we are picking a winner between two teams who have previously played. For example, imagine Providence is matched up against Boston College. And suppose they played earlier in the season. This is an easy one: you picked the one that previously won: Providence.
The method of indirect comparisons comes in handy when we are picking bracket matchups between teams that have not played each other during the season. In this situation, the comparison is to a team both have in common; that is to say - to a team that both contenders played earlier in the season.
Again, to continue the example, suppose Providence is playing Seton Hall and they haven’t played before. Both teams however, played Boston College. And both Seton Hall and Providence beat Boston College. But Seton Hall beat them by a larger margin. Thus, Seton Hall moves forward.
One small caveat: in about 5 or so matchups the teams had not played each other nor did they have a third team in common. In these few instances, we picked the winners based on their respective College Basketball Power Indices. Overall, we filled all the brackets using this algorithm.
A quick back-of-the envelope application of the method to the (first round of the) 2016 tournament – suggests that the agreement between predictions and actual results using the method of indirect comparisons was 78 percent. The expected agreement - had we filled the 2016 brackets entirely by chance - was 47 percent. This gives us a kappa of 0.313 – which indicates that there is a “fair” agreement between our predictions and actual results. (I used this online calculator here.)
So there you have it: Villanova and Louisville for the grand prize with Villanova taking it all. The score: 73-64.
In case you are wondering, the method of indirect comparisons is used in the appraisal of comparative risk among competing health-related interventions or treatments. The method of indirect comparisons comes in handy in the absence of head-to-head comparisons between interventions. Here is a good reference.
Just as an interesting aside note that the BPI is a measure of how many points above or below average a team is. In effect, the BPI captures a test against a random opponent. Thus, every time you use the BPI to select a team you are in effect using the method of indirect comparisons. For example: Villanova has a BPI of 20.5; Florida a 17.6 If these two teams were matched up and you picked Villanova on the basis of the BPI score – you have just used the method of indirect comparisons.
arod & matt bishop