Required Probability Of Making A First Down, To Justify Going For It On Fourth Down. (Ball at own 5 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 | 0.80 0.77 0.78 0.77 0.77 0.76 0.76 0.76 0.76 0.75 29 | 0.80 0.77 0.77 0.77 0.77 0.76 0.76 0.76 0.75 0.75 28 | 0.80 0.77 0.77 0.77 0.77 0.76 0.76 0.76 0.76 0.75 27 | 0.80 0.77 0.77 0.77 0.76 0.76 0.76 0.76 0.75 0.75 26 | 0.80 0.76 0.77 0.76 0.76 0.76 0.75 0.75 0.75 0.75 25 | 0.79 0.76 0.77 0.76 0.76 0.76 0.75 0.75 0.75 0.75 24 | 0.79 0.76 0.77 0.76 0.76 0.76 0.75 0.75 0.75 0.75 23 | 0.79 0.75 0.76 0.76 0.75 0.75 0.75 0.75 0.75 0.74 22 | 0.79 0.75 0.76 0.75 0.75 0.75 0.75 0.74 0.74 0.74 21 | 0.79 0.75 0.76 0.75 0.75 0.75 0.75 0.75 0.74 0.74 20 | 0.79 0.74 0.76 0.75 0.75 0.75 0.75 0.74 0.74 0.74 19 | 0.78 0.74 0.75 0.75 0.74 0.74 0.74 0.74 0.74 0.74 18 | 0.78 0.74 0.75 0.75 0.74 0.74 0.74 0.74 0.74 0.74 17 | 0.78 0.73 0.75 0.75 0.74 0.74 0.74 0.74 0.74 0.74 16 | 0.78 0.72 0.74 0.74 0.74 0.74 0.74 0.73 0.73 0.73 15 | 0.78 0.72 0.74 0.74 0.74 0.73 0.73 0.73 0.73 0.73 14 | 0.78 0.72 0.74 0.74 0.74 0.74 0.74 0.73 0.73 0.73 13 | 0.78 0.72 0.74 0.74 0.73 0.73 0.73 0.73 0.73 0.73 12 | 0.77 0.71 0.73 0.73 0.73 0.73 0.73 0.73 0.73 0.73 11 | 0.77 0.71 0.73 0.73 0.73 0.73 0.73 0.73 0.73 0.73 10 | 0.77 0.71 0.73 0.73 0.73 0.73 0.73 0.73 0.73 0.73 9 | 0.77 0.70 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 8 | 0.77 0.70 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 7 | 0.77 0.71 0.72 0.73 0.72 0.72 0.72 0.72 0.72 0.72 6 | 0.77 0.70 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 5 | 0.76 0.69 0.71 0.72 0.71 0.72 0.72 0.72 0.72 0.72 L 4 | 0.76 0.70 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 E 3 | 0.76 0.70 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 A 2 | 0.76 0.69 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 D 1 | 0.76 0.68 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0 | 0.76 0.69 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 -1 | 0.75 0.68 0.70 0.71 0.71 0.71 0.71 0.71 0.71 0.71 -2 | 0.75 0.68 0.70 0.70 0.70 0.70 0.70 0.70 0.71 0.71 -3 | 0.75 0.68 0.70 0.71 0.70 0.71 0.71 0.71 0.71 0.71 -4 | 0.75 0.68 0.70 0.70 0.70 0.70 0.71 0.71 0.71 0.71 -5 | 0.75 0.67 0.69 0.70 0.70 0.70 0.70 0.70 0.70 0.70 -6 | 0.75 0.67 0.69 0.70 0.70 0.70 0.70 0.70 0.70 0.70 -7 | 0.75 0.67 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 -8 | 0.75 0.67 0.69 0.69 0.69 0.70 0.70 0.70 0.70 0.70 -9 | 0.74 0.66 0.69 0.69 0.69 0.69 0.69 0.69 0.70 0.70 -10 | 0.74 0.67 0.69 0.70 0.69 0.70 0.70 0.70 0.70 0.70 -11 | 0.74 0.66 0.69 0.69 0.69 0.69 0.69 0.70 0.70 0.70 -12 | 0.74 0.66 0.68 0.69 0.69 0.69 0.69 0.69 0.69 0.69 -13 | 0.74 0.66 0.68 0.69 0.69 0.69 0.69 0.69 0.69 0.69 -14 | 0.74 0.66 0.68 0.69 0.69 0.69 0.69 0.69 0.69 0.70 -15 | 0.73 0.66 0.68 0.68 0.68 0.69 0.69 0.69 0.69 0.69 -16 | 0.73 0.65 0.68 0.68 0.68 0.68 0.68 0.69 0.69 0.69 -17 | 0.73 0.66 0.68 0.69 0.69 0.69 0.69 0.69 0.69 0.69 -18 | 0.73 0.66 0.68 0.68 0.68 0.68 0.69 0.69 0.69 0.69 -19 | 0.73 0.65 0.67 0.68 0.68 0.68 0.68 0.68 0.68 0.69 -20 | 0.72 0.65 0.67 0.68 0.68 0.68 0.68 0.68 0.69 0.69 -21 | 0.72 0.65 0.67 0.68 0.68 0.68 0.68 0.69 0.69 0.69 -22 | 0.72 0.65 0.67 0.67 0.68 0.68 0.68 0.68 0.68 0.68 -23 | 0.72 0.65 0.67 0.67 0.67 0.67 0.68 0.68 0.68 0.68 -24 | 0.72 0.65 0.67 0.68 0.68 0.68 0.68 0.68 0.68 0.68 -25 | 0.72 0.65 0.67 0.67 0.67 0.68 0.68 0.68 0.68 0.68 -26 | 0.72 0.65 0.66 0.67 0.67 0.67 0.67 0.68 0.68 0.68 -27 | 0.71 0.64 0.66 0.67 0.67 0.67 0.67 0.68 0.68 0.68 -28 | 0.71 0.65 0.66 0.67 0.67 0.67 0.68 0.68 0.68 0.68 -29 | 0.71 0.65 0.66 0.67 0.67 0.67 0.67 0.67 0.68 0.68 -30 | 0.71 0.65 0.66 0.66 0.67 0.67 0.67 0.67 0.67 0.68 Copyright 2004 William S. Krasker