The OSCAR Algorithms

Introduction

The ranking of American college football teams has been a deeply contentious issue for over a century. The central problem is that the number of teams (currently 120 in Division I-A) greatly exceeds the number of games each team is able to play each season (about 12). With such a paucity of data, how are we to decide which are the best teams?

Well, one answer is to ask the "experts" - and indeed great importance is placed on the top-25 rankings of coaches and journalists. But of course the judgements of such people can hardly be expected to be purely objective.

Another answer is to write a computer algorithm that looks at all the game results and places the teams in an appropriate ranking order. Does this restore the objectivity to the process? Perhaps surprisingly, the answer is no! Because although a computer executes its algorithm with cold objective efficiency, there are many different ways to write a ranking algorithm. The rankings are thus inevitably influenced by the preferences of the algorithm designer.

The problem is further complicated by the question - on exactly what criteria are the teams being judged in the first place? Should the rankings be a straightforward representation of past results, or should they do their level best to predict the future? It turns out that those two aims are not quite the same - for instance, it very often happens that the Las Vegas line for an upcoming game tilts significantly in favor of a team ranked lower in the polls than its opponent.

There are many choices to be made when designing a ranking algorithm.

One important decision to be made is the degree to which margin of victory should be taken into account. Should the algorithm reward teams that run up the score, or should it ignore the margin of victory completely? Algorithms that take full account of margin of victory tend to be more predictively accurate, but are deemed to be politically incorrect. The algorithms used by the BCS are currently required to ignore the margin of victory.

Another choice to be made is whether or not to include games from the previous season in the calculation. This probably isn't such a good idea for end-of-season rankings, but in September the best way to generate realistic computer rankings is to have a sneaky look at what happened last year.

There are many more considerations. How should home field advantage be taken into account? Should bowl games count for more than regular season games? Should games played last week count for more than games played several weeks ago?