Required Probability Of Making A First Down, To Justify Going For It On Fourth Down. (Ball at own 20 yard line; we will kick off to start the second half.) As computed by the footballcommentary.com Dynamic Programming Model. Time Remaining In First Half 3:00 6:00 9:00 12:00 15:00 18:00 21:00 24:00 27:00 30:00 ------------------------------------------------------------------------------------- 30 | 0.83 0.69 0.69 0.69 0.68 0.67 0.67 0.66 0.66 0.66 29 | 0.83 0.68 0.69 0.68 0.68 0.67 0.67 0.66 0.66 0.66 28 | 0.83 0.68 0.68 0.68 0.67 0.67 0.66 0.66 0.65 0.65 27 | 0.83 0.67 0.67 0.67 0.67 0.66 0.66 0.65 0.65 0.65 26 | 0.83 0.67 0.68 0.67 0.67 0.66 0.66 0.65 0.65 0.65 25 | 0.83 0.67 0.67 0.67 0.66 0.66 0.65 0.65 0.65 0.65 24 | 0.83 0.66 0.67 0.66 0.66 0.65 0.65 0.65 0.64 0.64 23 | 0.83 0.66 0.66 0.66 0.66 0.65 0.65 0.64 0.64 0.64 22 | 0.82 0.66 0.66 0.66 0.65 0.65 0.65 0.64 0.64 0.64 21 | 0.82 0.65 0.66 0.66 0.65 0.65 0.64 0.64 0.64 0.63 20 | 0.82 0.64 0.65 0.65 0.64 0.64 0.64 0.64 0.63 0.63 19 | 0.82 0.64 0.65 0.65 0.64 0.64 0.64 0.64 0.63 0.63 18 | 0.82 0.64 0.64 0.65 0.64 0.64 0.64 0.63 0.63 0.63 17 | 0.82 0.63 0.64 0.64 0.63 0.63 0.63 0.63 0.63 0.62 16 | 0.82 0.63 0.64 0.64 0.63 0.63 0.63 0.63 0.62 0.62 15 | 0.81 0.63 0.63 0.64 0.63 0.63 0.63 0.63 0.62 0.62 14 | 0.81 0.62 0.63 0.63 0.63 0.62 0.62 0.62 0.62 0.62 13 | 0.81 0.62 0.62 0.63 0.62 0.62 0.62 0.62 0.62 0.61 12 | 0.81 0.62 0.62 0.63 0.62 0.62 0.62 0.62 0.62 0.62 11 | 0.81 0.61 0.62 0.62 0.62 0.62 0.62 0.61 0.61 0.61 10 | 0.80 0.61 0.61 0.62 0.61 0.61 0.61 0.61 0.61 0.61 9 | 0.80 0.61 0.61 0.62 0.61 0.61 0.61 0.61 0.61 0.61 8 | 0.80 0.60 0.61 0.61 0.61 0.61 0.61 0.61 0.61 0.61 7 | 0.80 0.60 0.60 0.61 0.60 0.60 0.60 0.60 0.60 0.60 6 | 0.79 0.59 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 5 | 0.79 0.59 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 4 | 0.79 0.59 0.59 0.60 0.60 0.60 0.60 0.60 0.60 0.60 L 3 | 0.78 0.58 0.58 0.59 0.59 0.59 0.59 0.59 0.59 0.59 E 2 | 0.78 0.58 0.59 0.59 0.59 0.59 0.59 0.59 0.59 0.59 A 1 | 0.78 0.58 0.58 0.59 0.59 0.59 0.59 0.59 0.59 0.59 D 0 | 0.77 0.57 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 -1 | 0.77 0.57 0.57 0.58 0.58 0.58 0.58 0.58 0.58 0.58 -2 | 0.77 0.57 0.57 0.58 0.58 0.58 0.58 0.58 0.58 0.58 -3 | 0.77 0.56 0.57 0.58 0.58 0.58 0.58 0.58 0.58 0.58 -4 | 0.76 0.55 0.56 0.57 0.57 0.57 0.57 0.57 0.57 0.58 -5 | 0.76 0.56 0.56 0.57 0.57 0.57 0.57 0.57 0.57 0.58 -6 | 0.76 0.56 0.56 0.57 0.57 0.57 0.57 0.57 0.57 0.57 -7 | 0.75 0.54 0.55 0.56 0.56 0.56 0.56 0.57 0.57 0.57 -8 | 0.74 0.54 0.55 0.56 0.56 0.56 0.56 0.57 0.57 0.57 -9 | 0.74 0.54 0.55 0.56 0.56 0.56 0.56 0.57 0.57 0.57 -10 | 0.73 0.53 0.54 0.55 0.55 0.56 0.56 0.56 0.56 0.56 -11 | 0.73 0.53 0.54 0.55 0.55 0.55 0.55 0.56 0.56 0.56 -12 | 0.73 0.53 0.54 0.55 0.55 0.55 0.55 0.56 0.56 0.56 -13 | 0.72 0.53 0.54 0.55 0.55 0.55 0.55 0.56 0.56 0.56 -14 | 0.71 0.52 0.53 0.54 0.54 0.54 0.55 0.55 0.55 0.55 -15 | 0.71 0.51 0.53 0.54 0.54 0.54 0.55 0.55 0.55 0.55 -16 | 0.70 0.51 0.53 0.54 0.54 0.54 0.55 0.55 0.55 0.55 -17 | 0.69 0.51 0.52 0.53 0.53 0.54 0.54 0.54 0.55 0.55 -18 | 0.69 0.50 0.52 0.53 0.53 0.53 0.54 0.54 0.54 0.54 -19 | 0.69 0.50 0.52 0.53 0.53 0.53 0.54 0.54 0.54 0.55 -20 | 0.69 0.51 0.52 0.53 0.53 0.53 0.54 0.54 0.54 0.54 -21 | 0.67 0.49 0.51 0.52 0.52 0.53 0.53 0.53 0.54 0.54 -22 | 0.67 0.49 0.51 0.52 0.52 0.52 0.53 0.53 0.53 0.54 -23 | 0.66 0.49 0.51 0.52 0.52 0.52 0.53 0.53 0.53 0.54 -24 | 0.65 0.48 0.50 0.51 0.51 0.52 0.52 0.53 0.53 0.53 -25 | 0.65 0.48 0.50 0.51 0.51 0.52 0.52 0.52 0.53 0.53 -26 | 0.64 0.48 0.50 0.51 0.51 0.52 0.52 0.52 0.53 0.53 -27 | 0.64 0.48 0.50 0.51 0.51 0.51 0.52 0.52 0.53 0.53 -28 | 0.63 0.48 0.49 0.50 0.50 0.51 0.51 0.52 0.52 0.52 -29 | 0.62 0.47 0.49 0.50 0.50 0.51 0.51 0.52 0.52 0.52 -30 | 0.62 0.47 0.49 0.50 0.50 0.51 0.51 0.52 0.52 0.52 Copyright 2004 William S. Krasker