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Friday, October 5, 2007

The Best Possible Ranking (BPR) Explanation

All rankings in college football are subjective, so there is no right or wrong answer, but some systems are more right than others. The Best Possible Ranking (BPR) is, quite simply, the most right possible.

Why? The BPR ranks teams only on wins and losses and the difficulty of their schedule, but does so with minimal data loss. It achieves this through a two step process. First, teams are power-rated using wins and losses, margin of victory (MOV), total yards, turnovers, yards per play, etc. Second, power-ratings are used to evaluate a team's schedule and estimate the difficulty of achieving a team's win/loss record given that schedule. Consequently, each team is ranked exclusively on its wins and losses - that is, of course, the point of sport - but we can better assess the value of those wins. Unlike other non-MOV systems - I use all available data.

The first step in the BPR is important, but not unique. There are literally hundreds of systems for statistically rating teams. The key to the BPR is in the second step. It is motivated by this concept - if team B were to play team A's schedule, what is the probability that B would win more games, the same number of games or fewer games than A.

In the chart above, each line represents a max win frontier. Moving up the y-axis is the probability that the event will occur and across the bottom is the probability that a team will win each game on the schedule (for the sake of this example, we are assuming that the schedule is made up of 12 identical opponents). As we move to the right, the wins come easier, and as we move up the event is more likely. The "event" is the team winning that many games or more. Consequently, lines curve up as we slide to the right - the probability of winning at least that many games increases as the games get easier.

If we were to draw a line horizontally across the chart, any intersecting point would represent an equally likely event. This fact allows us to make some interesting comparisons. For example, as highlighted, it is equally difficult to go undefeated against a schedule of teams you would normally beat 90% of the time (favored by around17.4 points, see chart at bottom) as it is to win at least 11 games against a schedule of teams you would beat 80% of the time (favored by around 11.3). Likewise, it is equally likely that a team will win 1 or more of 12 games against teams it has a 15% chance of beating and that a team will win 4 or more of 12 games against teams it has a 45% chance of beating.

What does this mean? If we have a reliable system for generating power ratings (power ratings are an objective fact, though impossibly difficult to actually measure), and we reduce a team's accomplishments to its wins and losses given the strength of its schedule, we can mathematically, and objectively, deduce national rankings.

It is, quite simply, the Best Possible Ranking.


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