Quote:
Originally Posted by madlex
After we've established that the second team is always going for 2 after scoring a TD in OT, I've been wondering about less obvious spots. Specifically how aggressive you're supposed to approach 4th down if the first team scored a FG.
Let's assume 4th & goal:
- From inside the 5 I'm pretty sure the answer is go
- From outside the 10 you probably have to kick
- What are you doing between the 5 and 10?
Let y equal the probability of a team scoring after receiving the kickoff when any score wins the game. If y is assumed to be equal for both teams, the probability then of a team kicking off and losing the game after 2 possessions is:
losing in next possession + opponent not scoring and team not scoring and then losing in subsequent possession +..., which is:
y + (1-y)^2 * y + (1-y)^4 * y + (1-y)^6 * y ...
This breaks down to a Maclaurin series whose sum equals 1/(1-x), or in this case:
y(1 + x + x^2 + x^3 + ...) where x = (1-y)^2.
So, below is a short table of the probability of the 2nd possession team tying game w/ 100% successful FG, then losing to 3rd possession team:
Code:
y lose prob
0.3 0.588
0.4 0.625
0.5 0.667
0.6 0.714
0.7 0.769
0.8 0.833
So if we assume both teams have about 50% chance of scoring, then KC should try to win the game outright when their 4th down conversion chance exceeds the FG win rate, or (1-0.667), or 0.333. If instead we assume 70% chance of both scoring, then the 4th down play only needs to exceed (1-0.769) or 0.231.
Below is a conversion of the above table for KC minimum win equity needed for 4th down conversion:
Code:
min win approx
y equity yd line*
0.3 0.412 3
0.4 0.375 3-4
0.5 0.333 4-5
0.6 0.286 6
0.7 0.231 8
0.8 0.167 10
*-my guess