Were we to automate the ranking process, we'd want a set of objective criteria that everyone understands and agrees to and a process for combining them into an ordered list. Division one hockey actually has such a list and process. It goes basically like this:

- Identify "teams under consideration." This just weeds out the bottom of the division, leaving out teams with losing records except for automatic qualifiers and teams rated worse than some rank by the NCAA-calculated RPI
- For each TUC, compare it to each other TUC by each of the pre-defined criteria and assign the one with more points a "pairwise win" (and the other a "pairwise loss")
- For all teams under consideration, calculate the "pairwise winning percentage" the usual way (pairwise wins + ½pairwise ties divided by #compared teams)

It is step 3 that can sometimes cause controversy. When team A and team B have played and team A won both the head to head and the pairwise comparison between the teams, team B can still be ranked higher than team A because it has more pairwise wins against *all the other teams* under consideration than team A. This is not an "error" - it just means that if we compared all *triples* there are more where team B is 2-1 and team A is 1-2 when the triple contains both.

For football, a reasonable implementation is:

1. | Assume that the criteria for considering teams is the same as that for bowl-eligibility. I'd prefer a much stronger test but for the moment it is "have at least a .500 record without counting more than one win against a FCS team." | ||||||||||||||||||

2. |
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3. | List the teams ordered by pairwise winning percentage as defined above. |

**2.c** neatly avoids any specific definition of SOS while still taking schedule strength into account. By just counting *wins* against the "good teams", it gives credit for those without giving credit for just *playing* a tough schedule, which sometimes occurs with rankings that combine SOS with winning percentage formulaically.

**2.d** compares the teams' records over the last four games each played. I chose four because the number of games used in both basketball and baseball represents approximately the last month of the season.

For both **2.e** and **2.f** the idea is that head-to-head and results versus common opponents should take precedence, but when they're not applicable we have to use the rest of the field to make comparisons. Hence the best wins and worst losses are only based upon games that involve teams only one of the pair played. This begs the question, though, as to how to define "best win" and "worst loss."

Note that both the "best win" and "worst loss" could well involve teams not under consideration, soFor our oracle we need some objective ranking of all teams and the best place to look for that is in the computer rankings. We could choose one, choose all or some and take the average or median of the ones we use, or even just use the existing BCS computer summary to form the initial list. I chose to use the Bucklin Majority which is approximately the median of the complete list.someranking of all teams must be aninputto the process.

See the Pairwise Ratings for the 2007 season.