少女福利

Starting in 2024, the College Football Playoff (CFP) Committee was instructed to now rank the top 25 teams with the intent of determining who the best teams were for that season, and to have twelve such best teams invited to compete for the National Championship.

The Improved Linear Model (ILM) was originally trained to match the committee’s top four selections. A recent study was conducted into finding a possibly more accurate set of weights, and those results were presented at the 11th MathSport International Conference (June 4th-6th, 2025). My paper – “Evaluating the Improved Linear Model (and its successor?) with regards to the expanded College Football Playoff” (which was also published in the conference proceedings, and you can Google ISBN 9789083581408 to find the PDF which contains all of the papers for that conference) – that described the major results of that study was limited to 6 pages, which meant that almost a dozen additional tables in the paper’s Appendix had to be excluded. Therefore, I have posted an expanded version of the conference paper online, which includes all of those omitted tables.

The performance of the newer – and original – ILM models (each model having a different set of five weights), as outlined in that paper, for 2024, can now be found below. The first four models listed below are named after how well they performed during the 9 years of training: 2014-2019, 2021-2023 (excluding 2020 – due to COVID-19 based, conference scheduling restrictions). For instance, 38,99 had 38 exact matches of the top 12 CFP committee selections in those 9 years, and 99 of the 108 teams invited appeared in that model’s top 12 as well. Orig. stands for the model which is still using the original ILM weights that were determined using 2014-2017 as the training data and only tried to match the top four teams, which was the original mandate for that committee; its performance for those training years was 31,96.

Two new formulas were recently devised to provide two more objective, quantitative measures to maximize a weight set鈥檚 performance 鈥� besides the number of exact and overall matches in the top twelve CFP selections. These formulas assign a rewarded point value for each rank; the closer the prediction is to the CFP rank, the larger the portion of this point value that will be earned. With regards to these formulas, it seemed more important to match the higher ranked teams, and so exactly matching the CFP #1 team would be worth 100 points whereas exactly matching the #12 would only be worth 34 points. The values in the second row in the table below decrease in a linear fashion, starting with subtracting eleven and then ten 鈥� all the way down to a one point difference between the full reward for matching the teams ranked eleventh and twelfth (by the CFP committee).

The value earned per rank is reduced by the square of the difference between the weight set鈥檚 prediction and the actual CFP rank in the first formula and will be referred to now as F_Sqr. The other formula, F_*, will reduce the value earned as well 鈥� but in this case, the reduction is multiplicative in nature; for each position that the prediction is further away from the actual CFP rank, the point value reduction is by another 10%. So, for example, if the prediction for the team ranked as the fourth team is off by three, the value awarded for the prediction produces an award of 61 points (70 鈥� 9) when applying the F_Sqr approach, whereas F_* would reduce the award by 30% yielding 49 points (70 * 0.7). The bottom two rows in table illustrate the reduction that would occur for the differences appearing in the top row in said table.

These two measures can also be used as a criterion for choosing a weight set; therefore, F_Sqr and F_* below refers to the two models and their weight sets that maximized each respective formula’s value for all fifteen billion generated weight sets during the Monte Carlo simulation (using the training data set). (Both of these formulas will award a minimum of zero points if the difference between the prediction and the actual rank is large enough; for F_*, this difference would be 10 or more places 鈥� and for F_Sqr, the largest difference that still produces a positive point value depends upon the rank of the team in question.) F_* was (32,99), F_Sqr was (30,99) and SCC achieved (28,96) over the nine years of training data. The SCC model is the one whose weights maximized the Spearman Correlation Coefficient (SCC) for the 25 teams listed in each of the committee’s final rankings – which determined the teams playing in the CFP – in the nine years of training data (for the same fifteen billion weight sets that were generated).

Pre-Bowl ranking for these eight models:
2025: 38,99 || 41,96 || 40,98 || 33,100 || Orig. || F_Sqr || F_* || SCC
2024: 38,99 || 41,96 || 40,98 || 33,100 || Orig. || F_Sqr || F_* || SCC

Below are the results for all eight of these models (using the same performance notation as described above, which also appears in the model’s current name – for that new set of weights):

Year聽 聽 聽 聽 聽 38,99聽 聽 聽 聽 聽 聽41,96聽 聽 聽 聽 聽 40,98聽 聽 聽 聽 聽 33,100聽 聽 聽 聽 聽Orig.聽 聽 聽 聽 F_Sqr聽 聽 聽 聽 聽 F_*聽 聽 聽 聽 聽 SCC
2024聽 聽 聽 聽 聽 聽3,11聽 聽 聽 聽 聽 聽 1,10聽 聽 聽 聽 聽 聽 2,11聽 聽 聽 聽 聽 聽 1,10聽 聽 聽 聽 聽 聽 1,11聽 聽 聽 聽 聽 2,10聽 聽 聽 聽 聽 2,10聽 聽 聽 聽 聽 2,10