Required Probability Of Making A First Down, To Justify Going For It On Fourth Down. (Ball At Own 40 Yard Line.) As computed by the footballcommentary.com Dynamic Programming Model. Time Remaining In Second Half 3:00 6:00 9:00 12:00 15:00 18:00 21:00 24:00 27:00 30:00 ------------------------------------------------------------------------------------- 30 | 0.73 0.70 0.59 0.66 0.70 0.72 0.70 0.68 0.67 0.66 29 | 0.74 0.70 0.59 0.66 0.70 0.71 0.69 0.67 0.66 0.65 28 | 0.74 0.70 0.59 0.66 0.71 0.69 0.67 0.66 0.65 0.64 27 | 0.73 0.70 0.59 0.67 0.71 0.68 0.66 0.65 0.64 0.64 26 | 0.74 0.70 0.59 0.67 0.71 0.69 0.67 0.66 0.65 0.64 25 | 0.74 0.70 0.60 0.67 0.71 0.69 0.67 0.66 0.65 0.64 24 | 0.50 0.57 0.63 0.69 0.72 0.69 0.68 0.66 0.65 0.63 23 | 0.49 0.55 0.64 0.70 0.72 0.69 0.67 0.66 0.64 0.63 22 | 0.48 0.54 0.66 0.71 0.69 0.67 0.66 0.65 0.64 0.63 21 | 0.48 0.54 0.66 0.70 0.67 0.66 0.65 0.64 0.63 0.62 20 | 0.48 0.54 0.66 0.69 0.66 0.64 0.63 0.62 0.62 0.61 19 | 0.47 0.54 0.67 0.70 0.67 0.65 0.64 0.63 0.62 0.61 18 | 0.46 0.55 0.67 0.71 0.68 0.66 0.64 0.63 0.62 0.61 17 | 0.47 0.55 0.68 0.73 0.68 0.66 0.64 0.63 0.61 0.60 16 | 0.46 0.61 0.71 0.70 0.68 0.66 0.64 0.62 0.61 0.60 15 | 0.45 0.63 0.72 0.68 0.66 0.64 0.63 0.62 0.61 0.60 14 | 0.45 0.64 0.67 0.65 0.63 0.62 0.61 0.60 0.60 0.59 13 | 0.45 0.64 0.66 0.63 0.61 0.60 0.59 0.59 0.58 0.58 12 | 0.45 0.64 0.67 0.64 0.62 0.61 0.60 0.59 0.59 0.58 11 | 0.49 0.65 0.68 0.65 0.63 0.61 0.60 0.59 0.58 0.58 L 10 | 0.52 0.66 0.70 0.66 0.63 0.61 0.59 0.58 0.57 0.57 E 9 | 0.55 0.67 0.71 0.67 0.63 0.61 0.60 0.58 0.57 0.57 A 8 | 0.58 0.71 0.65 0.63 0.61 0.60 0.58 0.58 0.57 0.56 D 7 | 0.58 0.63 0.59 0.59 0.58 0.57 0.57 0.56 0.56 0.55 6 | 0.59 0.61 0.55 0.55 0.55 0.55 0.55 0.55 0.54 0.54 5 | 0.59 0.62 0.57 0.56 0.56 0.55 0.55 0.55 0.55 0.54 4 | 0.59 0.63 0.58 0.57 0.56 0.56 0.55 0.55 0.54 0.54 3 | 0.65 0.68 0.59 0.58 0.56 0.54 0.54 0.53 0.53 0.53 2 | 0.68 0.69 0.61 0.58 0.56 0.55 0.54 0.53 0.53 0.53 1 | 0.68 0.70 0.61 0.59 0.56 0.55 0.54 0.54 0.53 0.53 0 | 0.78 0.53 0.51 0.52 0.51 0.51 0.51 0.51 0.51 0.51 -1 | 0.21 0.33 0.38 0.44 0.47 0.48 0.49 0.50 0.50 0.51 -2 | 0.22 0.34 0.39 0.45 0.47 0.49 0.50 0.50 0.50 0.51 -3 | 0.20 0.32 0.37 0.43 0.46 0.47 0.48 0.49 0.50 0.50 -4 | 0.21 0.33 0.38 0.43 0.45 0.46 0.47 0.48 0.48 0.49 -5 | 0.23 0.36 0.41 0.45 0.47 0.47 0.48 0.48 0.49 0.49 -6 | 0.25 0.38 0.43 0.47 0.48 0.48 0.48 0.49 0.49 0.49 -7 | 0.23 0.38 0.41 0.43 0.44 0.45 0.46 0.46 0.47 0.47 -8 | 0.21 0.37 0.37 0.40 0.41 0.43 0.45 0.46 0.46 0.47 -9 | 0.19 0.26 0.34 0.36 0.39 0.42 0.44 0.45 0.46 0.47 -10 | 0.21 0.26 0.32 0.34 0.37 0.40 0.42 0.44 0.45 0.46 -11 | 0.24 0.28 0.33 0.35 0.38 0.41 0.42 0.44 0.45 0.45 -12 | 0.26 0.30 0.34 0.37 0.39 0.41 0.42 0.44 0.44 0.45 -13 | 0.26 0.31 0.35 0.38 0.40 0.42 0.43 0.44 0.45 0.45 -14 | 0.26 0.31 0.36 0.37 0.39 0.40 0.41 0.42 0.43 0.44 -15 | 0.26 0.31 0.34 0.35 0.37 0.39 0.40 0.41 0.42 0.43 -16 | 0.24 0.30 0.31 0.35 0.36 0.37 0.39 0.41 0.42 0.43 -17 | 0.08 0.30 0.29 0.32 0.34 0.36 0.38 0.39 0.41 0.42 -18 | 0.09 0.32 0.30 0.33 0.34 0.36 0.38 0.39 0.41 0.42 -19 | 0.10 0.32 0.31 0.34 0.35 0.37 0.39 0.40 0.41 0.42 -20 | 0.11 0.34 0.32 0.35 0.36 0.38 0.39 0.40 0.41 0.42 -21 | 0.11 0.34 0.32 0.34 0.35 0.37 0.38 0.39 0.40 0.41 -22 | 0.11 0.34 0.32 0.32 0.35 0.36 0.37 0.38 0.39 0.40 -23 | 0.11 0.34 0.32 0.31 0.33 0.35 0.36 0.38 0.39 0.40 -24 | 0.11 0.36 0.32 0.30 0.32 0.34 0.35 0.36 0.38 0.39 -25 | 0.10 0.45 0.33 0.31 0.31 0.34 0.35 0.37 0.38 0.39 -26 | 0.11 0.46 0.34 0.32 0.32 0.35 0.36 0.37 0.38 0.39 -27 | 0.11 0.46 0.35 0.32 0.33 0.35 0.36 0.37 0.38 0.39 -28 | 0.11 0.47 0.35 0.33 0.32 0.35 0.36 0.37 0.38 0.39 -29 | 0.11 0.46 0.35 0.33 0.32 0.34 0.35 0.36 0.37 0.38 -30 | 0.11 0.46 0.35 0.33 0.31 0.33 0.35 0.36 0.37 0.38 Copyright 2004 by William S. Krasker