#transitivepropertyisgarbage
My usual rebut to this argument:
We all know that just because A beat B and B beat C does NOT mean that C will lose to A when they play. This is not being debated. Every year there are numerous examples of exactly that. OTOH, when you make these rankings, what are you basing them on? If you are basing them on the games played then you are using the transitive property in one way or another.
My view is this:
The reason for the A>B, B>C, C>A problem is not that the transitive property is garbage. The problem instead is a lack of data:
- Maybe team A played the game of their lives when they beat B?
- Maybe B played a terrible game when they lost to A?
- Maybe B played the game of their lives when they beat C?
- Maybe C played a terrible game when they lost to B?
- Maybe C played the game of their lives when they beat A?
- Maybe A played a terrible game when they lost to C?
IMHO, every team plays within a range. They have great games, good games, average games, bad games, and terrible games. Looking just at one game, Ohio State's one point win in Happy Valley:
If that was a great game for Ohio State and a terrible game for Penn State then:
- Penn State is one of the best teams in the league, and
- Ohio State is no better than middling.
If that was a great game for Penn State and a terrible game for Ohio State then:
- Ohio State is one of the best teams in the league, and
- Penn State is no better than middling.
We don't know until we have enough data (games) to be able to assess these things and determine which games were flukes.