The topic of ranking (or the question “Who’s #1?”) is usually accompanied by the question “Who will win this game?” Granted, ranking does not apply to sports only, but sports is viewed as less academic than most applications. The question of “Who will win?” essentially asks us to somehow identify which team is stronger, better, of higher quality, or is higher ranked. We need to recall that even though we often interchange words “ranking” and “rating,” they do have different meaning. Rating may somehow summarize the quality of a team based on some associated criteria. Ranking is simply an indication of the place in the list that reflects relative importance of teams to each other. The difficulty of this topic is to determine what constitutes quality and importance as far as this particular set of teams is concerned. Ideally, to determine rating we would need to know the characteristics of the perfect team and measure all the teams against it, thus arriving at an absolute measure. Given that we know how far any given team is from the ideal, we can compute the absolute ratings. However, very few (if any) real world applications allow this ideal method. What we are able to do is measure relative difference in quality between teams, thus arriving at a rating based on these relative measurements. Now we are waxing philosophical!
Back to game predictions: This question has two aspects to it, first being “which team in a given competition will win?” and the second being “by how much?” The first is easier to answer. Suppose we pick a method that produces rating scores, a favorite one from the great collection introduced by Dr. Langville and Dr. Meyer. For a game between teams A and B to determine a winner we simply compare each team’s rating scores, rA and rB , the better rated team wins! Now for the by how much, referred to in chapter 9 of Who’s # 1 as point spread: there are many ways to estimate point spread. One of the simplest approaches is to think of the point spread being proportional to the difference between the ratings of the teams. That is, point spread for a game between team A and team B = α|rA − rB |, where α is some constant. In this simplistic point spread approach, the work is concentrated in estimating an appropriate constant α. This constant could be the same for all the games, and could be determined using the previous season, that is the point spreads from the previous season are known and least squares could be a way to approximate α. Another way is to customize α to the pairs of teams. Maybe there is a trend between teams that could be observed across a number of seasons. The described method is simplistic, perhaps it is evident why. For a more in depth discussion do consider the well laid out chapter on point spreads in Who’s #1?