Which is exactly the case. One starts on a 4th and 2. The other starts on a 1st and 10.
Tie probability = (.5*.2)+(.05*.1) = .105 = 10.5% chance of overtime by going for it.
.5 = Chance to convert 4th down
.2 = Chance to score a TD once the 4th down is successfully converted
Net chance to score a TD when starting on 4th and 2: 10%
.05 = Chance they go for it, fail, the ensuing FG attempt misses, Jets get the ball back
.1 = Chance to score TD after the missed FG
Net chance to score a TD when starting on 1st and 10: 10%
Huh?
You have a 20% chance to score a TD when starting with a 1st and 10 on around the 23 yard line.
In the same formula, you have a 10% chance to score a TD when starting with a 1st and 10 on around the 27 yard line.
The only difference is timeouts. Yet your cite completely ignores timeouts. Since your own formulas factor timeouts as being so incredibly important – altering the expected TD percent by 100% – you have to concede that your argument and your cite undermine each other, rendering one or both invalid.
Also, you have structured your formula in a suspect way. Because you are adding them, it is possible your formula would result in a greater than 100% chance if some of your individual terms were varied. For example:
If they go for it, 95% of the time they succeed, and they then go on to score a TD, say, 75% of the time. 5% of the time they fail – in this case, NE either scores or runs out the clock (100% NYJ lose) 25% of the time; the other 75%, the Jets get the ball back with a 50% chance to score a TD.
Tie probability = (.95*.75)+(.75*.50) = 1.0875 = 108.75% chance of overtime by going for it.
I question your cite, I question your argument, I question your logic, and I question your math. It’s all well and good to pick on my lack of higher education, but at least I don’t present probability formulas that can end up >100%.