I have been posting rankings and predictions on the internet since the 1996 football season. I did not start college basketball until 1999-2000. I post both rankings and predictions for the NFL and 1A college football. The rankings and predictions are from two totally separate algorithms that have nothing to do with each other. The rankings are from a retrodictive system and the predictions are from a predictive system. The two type of rankings have different intentions. I first tried to write an advanced retrodictive system when I was about 12 or 13 years old on a Commodore 64. I found the system worked pretty well from what I could tell but the computer was simply to slow to test the system on more than about 40 games or so. I was kicking ideas around in my head but I was unable to test any of them until I went to college and had access to faster systems. The only change to the algorithm since 1997 has been very slight changes to one parameter based on further checking of past data (see description). Here is a description of how my Retrodictive Win Only based ranking system works.
It starts with basic game theory. If you and I bet on flipping a coin then we both have an even chance of winning. The odds are 1:1 so in a fair bet we would put up an even amount of money. However, if you bet me that I couldn't roll a 6 on a standard die the odds against me are 5:1. I would expect you to put up 5 times as much money as I if I were going to take that bet. I have taken the same concept and applied it to football ratings.
In my system you always gain points if you win a game and always lose points if you lose. Margin of victory is not taken into consideration. The system looks at this situation just like I looked at the bets described above. A higher ranked team must put up more points since a higher ranked team should have a better chance of winning. By solving the rankings in this manner it is not easy for a team to cheat the system. A team cannot play a weak schedule and expect a high rating because of a good record. Conversely, a team cannot play a tough schedule and expect their schedule to get them a high rating. It is equally difficult to gain a given number of points for either team. Of course a team would need to win more games against weaker competition but it is easier to beat weaker competition.
I use a successive substitution convergence method to solve for the rating of every team. The second iteration uses the ratings from the first iteration to determine chance of victory and does the process over for every game again. It keeps resolving until the rating for all teams stops changing. I think this iterative process is the only possible way to solve for the ratings. The big question is exactly how to do you determine a teams chances of winning. The computer uses the current ratings and assumes that the chances of winning based on rating point differential is distributed normally (bell curve). There are two factors that must be set for the bell curve. These are the mean and standard deviation. The mean is easy. If two teams have the same rating then there point differential is zero. Two equally rated teams should have a 50/50 chance of beating each other. This means that half of the bell curve should be on each side of zero. Using simple logic the mean should be 0. The deviation is a bit more complicated. Probability of a team winning a game based on rating was studied using past data.
I have found that a win only system that makes sense under all extreme conditions is hard to write. I have had fun trying.
I think the key lies in keeping risk and reward balanced.
E-mail your questions or comments to firstname.lastname@example.org
Read Who's Got the Best System by Mark Hopkins and My reply.
Bihl Rankings Home