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A model-based approach to football strategy.

May 29, 2004

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Two-Point Conversion Chart

The chart shown below, computed using the footballcommentary.com Dynamic Programming Model, is intended to provide guidance on when to attempt a two-point conversion.

The rows are labeled by the lead after scoring a touchdown, but prior to the attempt at an extra point or points. The columns are labeled by the amount of time remaining in the game.

As an example of how to use the chart, suppose that after scoring a touchdown you trail by 5 points, with 21:00 remaining in the game (i.e. 6:00 left in the 3rd quarter). In the row corresponding to minus 5, and the column corresponding to 21:00, the entry is 0.31. This means you should attempt a two-point conversion if your probability of making it exceeds 0.31. NFL teams make about 40% of their two-point conversions, or perhaps a bit more. So when trailing by 5 with 21:00 to play, going for two is the correct play.

For another example, suppose that after scoring a touchdown you lead by 4 points, with 5:00 remaining in the game. In the row corresponding to 4, we interpolate between the columns corresponding to 3:00 and 6:00, and find that the interpolated Chart entry is 0.47. This means you should attempt a two-point conversion if your probability of making it exceeds 0.47. For most if not all NFL teams, the correct choice is to kick.

Time Remaining In The Game
3:00 6:00 9:00 12:00 15:00 18:00 21:00 24:00 27:00 30:00
30 0.81 0.80 0.77 0.71 0.65 0.61 0.60 0.59 0.58 0.57
29 0.59 0.58 0.58 0.58 0.58 0.59 0.57 0.55 0.53 0.51
28 0.68 0.67 0.67 0.65 0.63 0.62 0.61 0.61 0.60 0.60
27 0.59 0.59 0.60 0.60 0.60 0.60 0.59 0.59 0.59 0.59
26 0.19 0.24 0.29 0.34 0.37 0.38 0.40 0.41 0.43 0.44
25 0.66 0.67 0.66 0.64 0.63 0.62 0.61 0.60 0.59 0.58
24 0.97 0.93 0.79 0.68 0.62 0.60 0.59 0.59 0.59 0.59
23 0.59 0.59 0.60 0.61 0.61 0.61 0.59 0.57 0.56 0.55
22 0.78 0.76 0.70 0.64 0.62 0.58 0.54 0.52 0.50 0.48
21 0.59 0.59 0.59 0.60 0.60 0.59 0.59 0.59 0.59 0.58
20 0.63 0.63 0.63 0.63 0.62 0.62 0.61 0.61 0.60 0.60
19 0.27 0.24 0.29 0.31 0.33 0.35 0.37 0.39 0.40 0.41
18 0.58 0.57 0.57 0.57 0.58 0.58 0.57 0.57 0.57 0.56
17 0.71 0.69 0.67 0.66 0.65 0.64 0.63 0.62 0.61 0.60
16 0.95 0.86 0.71 0.65 0.59 0.55 0.53 0.52 0.51 0.51
15 0.58 0.57 0.56 0.55 0.53 0.51 0.49 0.47 0.46 0.46
14 0.72 0.69 0.70 0.66 0.65 0.63 0.62 0.61 0.60 0.59
13 0.59 0.59 0.59 0.59 0.59 0.59 0.59 0.59 0.58 0.58
12 0.04 0.09 0.13 0.19 0.24 0.29 0.32 0.35 0.37 0.38
11 0.90 0.85 0.80 0.74 0.69 0.65 0.62 0.59 0.58 0.56
10 0.58 0.58 0.59 0.59 0.59 0.59 0.59 0.59 0.59 0.59
9 0.61 0.57 0.54 0.53 0.51 0.50 0.49 0.48 0.47 0.47
8 0.92 0.76 0.70 0.59 0.53 0.49 0.47 0.46 0.45 0.45
7 0.58 0.64 0.59 0.59 0.59 0.58 0.58 0.58 0.58 0.58
6 0.58 0.60 0.62 0.62 0.62 0.61 0.60 0.59 0.57 0.56
5 0.05 0.08 0.13 0.19 0.24 0.27 0.30 0.32 0.34 0.36
4 0.45 0.48 0.49 0.50 0.51 0.52 0.53 0.53 0.54 0.53
3 0.93 0.90 0.84 0.79 0.75 0.71 0.68 0.65 0.63 0.62
L 2 0.42 0.42 0.41 0.39 0.38 0.38 0.38 0.39 0.39 0.40
E 1 0.10 0.14 0.21 0.28 0.34 0.37 0.40 0.42 0.43 0.44
A 0 0.97 0.95 0.90 0.84 0.78 0.73 0.69 0.66 0.63 0.62
D -1 0.56 0.48 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49
-2 0.01 0.04 0.08 0.14 0.20 0.25 0.29 0.32 0.35 0.36
-3 0.86 0.77 0.73 0.67 0.63 0.60 0.57 0.56 0.55 0.54
-4 0.56 0.59 0.60 0.61 0.61 0.61 0.61 0.60 0.59 0.58
-5 0.05 0.12 0.17 0.21 0.25 0.28 0.31 0.33 0.35 0.37
-6 0.54 0.47 0.46 0.46 0.46 0.45 0.45 0.44 0.44 0.44
-7 0.95 0.88 0.84 0.78 0.74 0.70 0.67 0.65 0.63 0.62
-8 0.38 0.39 0.38 0.37 0.37 0.38 0.39 0.40 0.41 0.42
-9 0.40 0.40 0.38 0.39 0.39 0.40 0.40 0.40 0.40 0.40
-10 0.03 0.14 0.26 0.35 0.42 0.47 0.49 0.51 0.52 0.52
-11 0.38 0.41 0.45 0.47 0.48 0.49 0.50 0.51 0.52 0.52
-12 0.40 0.40 0.40 0.40 0.39 0.39 0.39 0.39 0.40 0.40
-13 0.10 0.14 0.19 0.24 0.29 0.33 0.36 0.38 0.40 0.41
-14 0.94 0.91 0.85 0.80 0.75 0.70 0.66 0.64 0.62 0.60
-15 0.40 0.40 0.39 0.39 0.39 0.39 0.40 0.40 0.40 0.41
-16 0.27 0.29 0.30 0.31 0.33 0.35 0.36 0.37 0.38 0.39
-17 0.41 0.41 0.42 0.43 0.44 0.46 0.48 0.50 0.51 0.52
-18 0.01 0.09 0.23 0.34 0.39 0.43 0.45 0.47 0.47 0.48
-19 0.30 0.30 0.31 0.32 0.33 0.34 0.36 0.37 0.38 0.38
-20 0.39 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.42 0.42
-21 0.82 0.76 0.71 0.67 0.65 0.63 0.61 0.60 0.59 0.58
-22 0.35 0.35 0.36 0.36 0.36 0.37 0.37 0.38 0.38 0.39
-23 0.40 0.40 0.40 0.39 0.39 0.39 0.39 0.40 0.40 0.40
-24 0.21 0.23 0.27 0.32 0.37 0.40 0.43 0.46 0.48 0.49
-25 0.40 0.40 0.39 0.38 0.38 0.38 0.40 0.41 0.43 0.44
-26 0.02 0.05 0.16 0.28 0.35 0.38 0.39 0.39 0.40 0.40
-27 0.35 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40
-28 0.79 0.76 0.70 0.66 0.62 0.60 0.59 0.57 0.56 0.55
-29 0.40 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.40 0.40
-30 0.31 0.31 0.32 0.33 0.35 0.36 0.37 0.38 0.38 0.39

Copyright © 2004 by William S. Krasker