** footballcommentary.com **

A model-based approach to football strategy.

May 2, 2005 |

Below we present a Table of win probabilities for the two-minute drill. The probabilities are computed using the model described in our article A Model for the Two-Minute Drill. By interpolating within the Table, one can estimate the offense's probability of winning the game when they trail by one score in the last 2:00. The Table assumes that it's first down and ten yards to go for a first down.

There are three sections in the Table, corresponding to whether the offense trails by more than three points, exactly three points, or fewer than three points. In the first section the listed probabilities are the offense's probability of scoring a touchdown. In the other two sections the listed probabilities are their probability of winning the game.

Within each section there are four subsections, corresponding to the time remaining when the ball is snapped. Each subsection has four rows, corresponding to different lines of scrimmage. In each such row, the first entry is the line of scrimmage (70 means the defense's 30-yard line); and entries two through five are the offense's probability of winning (or of scoring a touchdown) if they have zero, one, two, or three timeouts remaining.

As an example, suppose the offense has 1st and 10, trails by 1 point with 1:00 left, is at their own 30-yard line, and has 2 timeouts. Then according to the model, the offense's probability of winning the game is 0.3042.

For another example, suppose the offense has 1st and 10, trails by 8 points with 1:30 left, is at their own 10-yard line, and has 3 timeouts. Then according to the model, the offense's probability of scoring a touchdown is 0.1268. Of course, to get their probability of winning the game we have to factor in the probability of making a two-point conversion, and the probability of winning in overtime. If these are 0.4 and 0.5 respectively, then the offense's probability of winning the game is

** Trailing by > 3 points. Probability of Scoring a Touchdown. **

2:00 left 10 0.1174 0.1308 0.1419 0.1503 30 0.2091 0.2218 0.2311 0.2372 50 0.3345 0.3414 0.3453 0.3472 70 0.4916 0.4929 0.4934 0.4935 1:30 left 10 0.0824 0.0989 0.1139 0.1268 30 0.1659 0.1881 0.2059 0.2189 50 0.2991 0.3192 0.3327 0.3404 70 0.4813 0.4881 0.4914 0.4929 1:00 left 10 0.0424 0.0562 0.0697 0.0778 30 0.1040 0.1293 0.1510 0.1631 50 0.2270 0.2612 0.2869 0.2985 70 0.4252 0.4592 0.4770 0.4821 0:30 left 10 0.0095 0.0148 0.0171 0.0174 30 0.0314 0.0474 0.0533 0.0537 50 0.1199 0.1450 0.1520 0.1526 70 0.2712 0.3201 0.3283 0.3293

** Trailing by 3 points. Probability of Winning the Game. **

2:00 left 10 0.1411 0.1527 0.1618 0.1684 30 0.2388 0.2484 0.2549 0.2590 50 0.3662 0.3705 0.3728 0.3741 70 0.5350 0.5355 0.5357 0.5357 1:30 left 10 0.1077 0.1244 0.1388 0.1501 30 0.2035 0.2227 0.2370 0.2468 50 0.3423 0.3565 0.3653 0.3702 70 0.5290 0.5330 0.5349 0.5355 1:00 left 10 0.0647 0.0815 0.0966 0.1068 30 0.1461 0.1723 0.1933 0.2059 50 0.2870 0.3147 0.3353 0.3457 70 0.4972 0.5175 0.5281 0.5318 0:30 left 10 0.0102 0.0209 0.0296 0.0308 30 0.0634 0.0853 0.0957 0.0975 50 0.1732 0.2115 0.2252 0.2273 70 0.3936 0.4341 0.4490 0.4514

** Trailing by < 3 points. Probability of Winning the Game. **

2:00 left 10 0.2130 0.2240 0.2314 0.2359 30 0.3418 0.3475 0.3505 0.3521 50 0.4992 0.5006 0.5012 0.5014 70 0.7261 0.7261 0.7261 0.7261 1:30 left 10 0.1748 0.1956 0.2113 0.2219 30 0.3131 0.3306 0.3411 0.3469 50 0.4898 0.4961 0.4992 0.5006 70 0.7255 0.7260 0.7261 0.7261 1:00 left 10 0.1144 0.1405 0.1613 0.1754 30 0.2465 0.2803 0.3042 0.3172 50 0.4507 0.4745 0.4884 0.4944 70 0.7203 0.7242 0.7255 0.7260 0:30 left 10 0.0130 0.0356 0.0543 0.0564 30 0.1228 0.1595 0.1752 0.1781 50 0.3013 0.3663 0.3844 0.3893 70 0.6839 0.7049 0.7161 0.7185

Copyright © 2005 by William S. Krasker