Game theory football

[Tater10]

Yeah, your numbers match up with mine if the offense were to win with a 12 yd pass on 4th and 2. I found the game to be better with a loss for the offense. (actually, i got +.00003 EV for the Offense if you were to split on a 12 yard pass on 4th and 2, but thats no fun)

4th down numbers (the D_run% is the same as the O_pass%):
Yds / O_run / O_pass /O_EV
6 / .80 / .20 / (.73333)
5 / .667 / .333 / (.55556)
4 / .625 / .375 / (.37500)
3 / .556 / .444 / (.25926)
2 / .500 / .500 / (.16667)

My 3rd down numbers:
Yds / O_run / O_pass / D_Run / D_Pass /O_EV
10 .8108 / .1892 / .1892 / .8108 / (.81945)
9 .7780 / .2220 / .2220 / .7780 / (.73071)
8 .7264 / .2736 / .2736 / .7264 / (.64769)
7 .7351 / .2649 / .3930 / .6070 / (.39843)
6 .6640 / .3360 / .4261 / .5739 / (.17520)
5 .6447 / .3553 / .4418 / .5582 / +.03893
4 .5800 / .4200 / .4769 / .5231 / +.18798
3 .5643 / .4357 / .4772 / .5228 / +.34163

and 'yes' to the earlier post by AB that if 1 player plays according to the percentages above, the other "plays" optimal as well.

Typed this fast, so sorry about grammar & wording.

[AaronBrown]

My bad. I didn't read carefully enough. I assumed that a 12 yard pass from the 2 would still be in the endzone, although I didn't assume that from the 1. Of course, that doesn't matter, because you never pass from the 1.

I think most people would take the offense, not knowing the numbers, and would play this game very badly. I think most people would pass too much. Throwing away game theory, I bet you win against most first time offensive players by playing pass every down. Not many guys would run more than twice out of four downs, especially if he's got relatively long yardage, and two runs give him only 1/6 chance of winning if you play pass defense all the time.

On offense, I'm guessing most first time defenders would start with Pass defense, so I run. If I'm wrong, or get a low roll, I stick with the run. If I'm right, or get a high roll, I switch to pass.

[Tater10]

In the few times i have actually played this, i have done well because of what you said. People are pretty predictable.

[bobman0330]

Do you have a spreadsheet to do this for you?

If so, could you run 2nd and 1st downs and post the results?

[Tater10]

This is a copy and paste from my excel spreadsheet. I hope it's legible.

Here is what i have for each down. You would want to be defense, only by .0029

Down / yards / O_Run / O_Pass / D_Run / D_Pass / O_EV

1 10 68.6% 31.4% 39.8% 60.2% $(0.00290)
2 10 73.3% 26.7% 32.1% 67.9% $(0.42981)
2 9 69.5% 30.5% 35.2% 64.8% $(0.29851)
2 8 70.0% 30.0% 43.3% 56.7% $(0.07825)
2 7 66.3% 33.7% 46.8% 53.2% $0.13005
2 6 65.2% 34.8% 48.3% 51.7% $0.32656
2 5 60.0% 40.0% 50.5% 49.5% $0.46872
2 4 59.7% 40.3% 51.6% 48.4% $0.60710
2 2 100.0% 0.0% 0.0% 100.0% $1.00000
3 10 81.08% 18.92% 18.92% 81.08% $(0.81945)
3 9 77.80% 22.20% 22.20% 77.80% $(0.73071)
3 8 72.64% 27.36% 27.36% 72.64% $(0.64769)
3 7 73.51% 26.49% 39.30% 60.70% $(0.39843)
3 6 66.40% 33.60% 42.61% 57.39% $(0.17520)
3 5 64.47% 35.53% 44.18% 55.82% $0.03893
3 4 58.00% 42.00% 47.69% 52.31% $0.18798
3 3 56.43% 43.57% 47.72% 52.28% $0.34163
3 2 100.0% 0.0% 0.0% 100.0% $1.00000
3 1 100.0% 0.0% 0.0% 100.0% $1.00000
4 6 80.0% 20.0% 20.0% 80.0% $(0.73333)
4 5 66.7% 33.3% 33.3% 66.7% $(0.55556)
4 4 62.5% 37.5% 37.5% 62.5% $(0.37500)
4 3 55.6% 44.4% 44.4% 55.6% $(0.25926)
4 2 50.0% 50.0% 50.0% 50.0% $(0.16667)
4 1 100.0% 0.0% 0.0% 100.0% $1.00000


And, here is the strategy I have for 1st and 10 from the 20, with the offense getting 2:1 (still want to be defense by .0247)

Down YTG From O_Run O_Pass D_Run D_Pass Off EV
1 10 20 67.9% 32.1% 42.5% 57.5% $(0.0247)
1 GL 10 68.6% 31.4% 39.8% 60.2% $0.4957
1 GL 9 68.6% 31.4% 45.6% 54.4% $0.7804
1 GL 8 66.3% 33.7% 49.1% 50.9% $1.0455
1 GL 7 65.7% 34.3% 50.8% 49.2% $1.2904
1 GL 6 61.7% 38.3% 52.7% 47.3% $1.4706
1 GL 5 61.9% 38.1% 54.2% 45.8% $1.6354
2 10 20 71.9% 28.1% 34.2% 65.8% $(0.4521)
2 9 19 70.1% 29.9% 35.5% 64.5% $(0.2985)
2 8 18 69.6% 30.4% 42.1% 57.9% $(0.1042)
2 7 17 68.7% 31.3% 42.4% 57.6% $0.1121
2 6 16 71.9% 28.1% 41.0% 59.0% $0.2807
2 5 15 74.6% 25.4% 38.5% 61.5% $0.4522
2 4 14 76.9% 23.1% 38.0% 62.0% $0.6217
2 2 12 91.8% 8.2% 26.5% 73.5% $0.9873
2 GL 10 73.3% 26.7% 32.1% 67.9% $(0.1447)
2 GL 9 69.5% 30.5% 35.2% 64.8% $0.0522
2 GL 8 70.0% 30.0% 43.3% 56.7% $0.3826
2 GL 7 66.3% 33.7% 46.8% 53.2% $0.6951
2 GL 6 65.2% 34.8% 48.3% 51.7% $0.9898
2 GL 5 60.0% 40.0% 50.5% 49.5% $1.2031
2 GL 4 59.7% 40.3% 51.6% 48.4% $1.4106
3 10 20 81.2% 18.8% 18.8% 81.2% $(0.8327)
3 9 19 77.4% 22.6% 22.6% 77.4% $(0.7382)
3 8 18 72.3% 27.7% 27.7% 72.3% $(0.6395)
3 7 17 73.9% 26.1% 36.0% 64.0% $(0.4256)
3 6 16 72.7% 27.3% 36.4% 63.6% $(0.2214)
3 5 15 72.8% 27.2% 36.5% 63.5% $(0.0011)
3 4 14 70.0% 30.0% 38.1% 61.9% $0.2046
3 3 13 68.3% 31.7% 38.9% 61.1% $0.4174
3 2 12 84.2% 15.8% 54.5% 45.5% $0.8017
3 1 11 60.3% 39.7% 28.6% 71.4% $0.9413
3 GL 10 81.1% 18.9% 18.9% 81.1% $(0.7292)
3 GL 9 77.8% 22.2% 22.2% 77.8% $(0.5961)
3 GL 8 72.6% 27.4% 27.4% 72.6% $(0.4715)
3 GL 7 73.5% 26.5% 39.3% 60.7% $(0.0976)
3 GL 6 66.4% 33.6% 42.6% 57.4% $0.2372
3 GL 5 64.5% 35.5% 44.2% 55.8% $0.5584
3 GL 4 58.0% 42.0% 47.7% 52.3% $0.7820
3 GL 3 56.4% 43.6% 47.7% 52.3% $1.0124
4 6 16 85.8% 14.2% 14.2% 85.8% $(0.7862)
4 5 15 74.8% 25.2% 25.2% 74.8% $(0.5918)
4 4 14 69.3% 30.7% 30.7% 69.3% $(0.3854)
4 3 13 62.5% 37.5% 37.5% 62.5% $(0.2066)
4 2 12 57.3% 42.7% 42.7% 57.3% $(0.0375)
4 1 11 78.8% 21.2% 72.0% 28.0% $0.6705
4 GL 6 80.0% 20.0% 20.0% 80.0% $(0.6000)
4 GL 5 66.7% 33.3% 33.3% 66.7% $(0.3333)
4 GL 4 62.5% 37.5% 37.5% 62.5% $(0.0625)
4 GL 3 55.6% 44.4% 44.4% 55.6% $0.1111
4 GL 2 50.0% 50.0% 50.0% 50.0% $0.2500