Win Probabilities for the Two-Minute Drill

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 0.1268 × 0.4 × 0.5 = 0.025.

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