Final NCAA Men’s Basketball Poll Model Page
Welcome to the NCAA Final Coaches’ Poll Modeling/Prediction Page.
The first two models in the table below will add the specified weight (according to how many wins a team achieves in the NCAA tournament – not including ‘play-in’ games) to the coaches’ poll total (the poll before the NCAA tournament begins), once the latter has been normalized into the range from zero to one. For instance, the two teams who reach the Final Four, but lose their next game, will have 1.5 added to their normalized, penultimate poll total when using the LN2 model’s weights.
The last three models below will add the specified weight to the full Tournament Selection Ratio (TSR) that is computed for each team, and is comprised of objective and subjective measures: the TSR uses the normalized AP and ESPN/USA Today (penultimate) polls (25% each), and, a trimmed Borda mean, utilizing eight computer-based systems (four which incorporate the full margin of victory, and four employing no margin of victory, i.e. only wins and losses matter), and this makes up the other 50% of the TSR. (More details about the TSR can be found in following paper: “Evaluating Regional Balance in the NCAA Men’s Basketball Tournament using the Tournament Selection Ratio”, Proceedings of the Fourth International Conference on Mathematics in Sport, June 5-7, 2013, found here. Here is a PDF file which contains the tech report that provides more details about the origin of the models appearing on this page; this report was summarized at the 27th European Conference on Operational Research, which was held July 13th-15th, 2015.)
Starting at zero, LN2 adds increasing increments (0.1) to the preceding weight, to generate the next larger weight. ZPF and ZP2 rely on the Zipf distribution, where ZPF begins with 1/7, then adds 1/6, then 1/5, and so on, until adding in 1/1 for the tournament champion’s weight, whereas ZP2 begins with 1/8, and finally adds in 1/2 for the champion. PR2 is similar to the idea the Zipf distribution utilizes, but employs only prime numbers in the denominator, and 2 in the numerator. The first weight is 2/17, and then 2/13 is added to it, followed by 2/11, then 2/7, 2/5, 2/3 and finally 2/2 (like ZPF). Finally, 50T relies on the approach the next weight is roughly 50% larger than the previous one, beginning with 0.24.
# Wins 0 1 2 3 4 5 6
LN2 0.1000 0.3000 0.6000 1.0000 1.5000 2.1000 2.8000
ZP2 0.1250 0.2679 0.4345 0.6345 0.8845 1.2179 1.7179
ZPF 0.1429 0.3095 0.5095 0.7595 1.0929 1.5929 2.5929
PR2 0.1176 0.2715 0.4533 0.7390 1.1390 1.8057 2.8057
50T 0.2400 0.3600 0.5400 0.8100 1.2100 1.8100 2.7100
Average SCC values for the 26 years from 1993-2018.
Model SCC-15 SCC-25 SCC-35 Avg. Diff. (top 35)
ZP2 0.92997 0.95631 0.93903 2.1887
PR2 0.91144 0.94804 0.93603 2.2964
50T 0.91927 0.95091 0.93493 2.2192
LN2 0.92294 0.95031 0.94586 2.1107
ZPF 0.89550 0.94227 0.94531 2.2597
MCB 0.84777 0.85040 0.85481 3.4023
OCC 0.89858 0.93982 0.92142 2.7581
The article “How Predictable is the Overall Voting Pattern in the NCAA Men’s Basketball Post Tournament Poll?” appears in Chance (published by Springer-Verlag, under the supervision of the American Statistical Association), Volume 27, Issue 2, 2014, and describes more about how the MCB model was derived. (Here is a copy of that preprint for that article.)
The MCB model (Monte Carlo “Best”, for the best performing weights after running the simulation model with millions of random possible weight values) derived its coefficient values after evaluating a weighted, least squares regression model. The weights used to produce the predicted, final poll’s (vote) total are: 6.68507, for multiplying each team’s winning percentage (*100) by; 17.64763 was the factor associated with each team’s power rating; the number of NCAA tournament wins + 1 was multiplied by 88.24644; and (the number # of NIT tournament wins + 1) is divided by four before said multiplication (by 88.24644).
The OCC model was presented at the Sixth International Conference on Mathematics in Sport, June 26-28, 2017, and the paper entitled “Applying Occam’s Razor to the Prediction of the Final NCAA Men’s Basketball Poll” from that conference’s proceedings can be found here. Essentially, the OCC model will take each team’s rank (in the penultimate poll) and 1.05 will be added to that integer value, and then this will be divided by 2 raised to the number of NCAA tournament wins + 1. Finally, the teams will be sorted into ascending order, according to the values produced by the operation, and this will produce the predicted final poll after the tournament is done. (Teams that are not ranked before the tournament use a value of 67 before adding the 1.05, and NIT wins are essentially worth one fourth of an NCAA win.)