Sunday, December 4, 2022

A Further Explanation of the Calculation

This is how the calculation started in my mind. We are all familiar with a win loss record where an undefeated team has a record of 1.0 and a team that has won half its games has a record of 0.5.

So first step is to give a value for each game a team plays based on a 1 for victory and 0 for a loss, but the to those numbers add the opponent's win-loss record. For example, if you win a game against a team that has a record of 0.5 then the value of that game is 1.5, but if you lose it would be 0.5. By this method, the value of a loss to an undefeated team is the same as a victory over a team that has not won a game; both are 1.0. Now as the year goes on, the value of each game will update based on whether the opponent does well or not. In the example, if that opponent's record later in the season was 0.7, then the value of that game would be 1.7, or if they lost games it would go the other way.

But I added a correction into the calculation that removes the outcome of each game from the opponent's win-loss record, so it doesn't reward a team for losing and doesn't lower the value of a victory. For example, if a team defeats a team that otherwise won all of their games, then the score is 1.0 for the victory plus still 1.0 for the opponent's win-loss record even though they just lost.

So as the year goes on you add up the value for each game played and calculate the average value per game played. I then chose to multiply the average by 100 just to make it easier for people to think about, rather than having that decimal in there. So 100 is the "average" score for a team rather than 1.0. They did something like that for IQ measurements.

At the beginning of the year, every team starts exactly equal and have no score at all. Even after their first game, they are still exactly equal with all having a theoretical score of 1.0. It doesn't matter what conference they are in or estimated rankings at the beginning of the year. Only whether teams win and keep winning or lose and keep losing.

That is how I started it out. My idea was that the non-conference games would mix enough so that it would equalize the scores and pull those who played harder schedules up. When I started in the 1990s the conferences were smaller and everyone was playing more non-conference games. But as the years went on they added more and more FBS teams, conferences expanded, teams played fewer non-conference games, and most big teams routinely began adding FCS teams to the schedule.

So I then added up the collective win-loss record of the each teams opponents to be a surrogate for conference play. With each team playing playing 12 games against other teams that played 12 games, the variation in the win-loss record is low and by the end of the year is almost always between 0.45-0.55 with average being 0.5. I then used that as a factor to increase or decrease the value of the opponent's win-loss record by a small amount based on the win-loss record of all of that opponent's opponents. Here I made a judgement and just added 0.5 to that number to make the average 1.0 and then multiply that number against the the opponent's win-loss record, making it go up and down but by the end of the year accounting for less than 10% of the score. This factor does not include FCS at all, only performance against other FBS teams.

Again to make the value of each game more accurate, I remove the win-loss record of the team from the opponent's opponents win-loss record for each game so that it doesn't alter that game's value, and does not overvalue or undervalue the opponent's score for the for the team's own performance.

I analyzed it and the SEC and Big 10 conferences did on the average have higher scores than than the Sun Belt or Mid-America conferences. But some "power" conference teams were actually not very powerful at all. I actually compared several ways to get to this number. Another technique multiplied the 0.45-0.55 score by 2 which gave greater weight to the opponent's opponents records. The year I tested this was when Utah was undefeated and beat Alabama in the bowl game. That year, the way I ended up doing it better predicted the outcomes of bowl games, where teams from different conferences played each other.

I actually tried to take it to a third level measuring the win-loss records of the opponent's opponent's opponents, but change in score was insignificant, so I stopped it as it is.

Then what to do with FCS teams? At first I excluded them completely since they didn't really mix with FBS enough. But the year Appalachian St beat Michigan, I got annoyed because I felt like Michigan should have accounted for the loss. So I inserted the FCS teams into the calculation, but only with a 0.0 for a loss and 1.0 for a victory. It does not consider the record or power of the FCS team. It was purely an assumption that essentially penalizes teams for playing FCS teams. But now days everyone except Notre Dame plays one FCS team so it kind of balances out... maybe.

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