Marshall 24, Ohio 23: Your [Insensitive Cardiac Arrest Joke] Finish Of The Day

you can’t draw a projected outcome from such a small sample. eventually your team will return to the mean. a 2PAT does not fundamentally change the advantages-disadvantages at any position vis-a-vis the opponent because there is a finite number of possible play choices from that position. .

but it doesn’t. .in the end, mattter what those averages are. because they are just going to be further diminished by the overall underdog disadvantage once the iteration begins round two, overtime. in other words, you are placed in the one position in a football game in which you get the “real odds” — success in a 2PAT isn’t really worth 2 but infinity, because you ended the game.

if you take the PAT you cede control of the topdog advantage back to the favorite — remember that just to be in the position of being able to be tied you overcame the odds against you. now you’re starting over with a new game with those same odds (divided by the as-yet-undecided percentage of a full game an overtime period constitutes) and added on. or, in the end, subtracted.

for the sake of simplicity, let’s take the AFL grand final friday night. I dont’ know that the real odds were. but collingswood was heavily favored. probably close to 2/3 probability. .meaning st kilda had a 2/3 probability of losing. they managed to tie, and in the grand final of the australian football league if there’s a draw the match is replayed a week later.

so by avoiding a loss, st kilda beat 2/3 odds of losing. now they play another game with identical rosters, no significant injuries, same coaches, same stadium. .the likelihood of collingswood winning is again 2/3 for this iteration and 2/3 that st kilda will lose.

but what are st kilda’s odds for not losing the AFL Championship? They’re actually 8/9. .(given the possibility of a draw, we can’t quite say their chances of winning the championship in this came are 1/9, but it’s very close.(

because they already beat significant odds to not lose the first game. .with each iteration of a game, the probabilities shrink (for the underdog) exponentially. .because you’ve managed to make the unlikely event happen each time. .

(the monte hall paradox works on the same principle.)

so say a st kilde player has the option to handpass a ball through the goal, which is a behind worth 1 point which would tie the game and force a draw. or he can try a risky maneuver to spin around and kick the ball through the goal, which is a 6-point championship winning goal. however, he has a 60% chance of being tackled and ending the game.in a loss. .he has a 100% chance of getting the draw with the hand pass. .what should he do?

he should go for the 40% chance of the goal every time. .because those are far better odds than 1/9. .in fact if he had a 20% chance of making the goal, he should still do it. the payoff is infinity. .

for our example, you would have to divide the second iteration probabilities by whatever divisor of a full game we decide an overtime period constitutes. .then add that to the probability of losing the game in its full time. .

by this same math, you can see that UAB’s coach erred in kicking a Field Goal at the end of OT 1 against Tennessee. I don’t know what the odds of UAB losing to tennessee was — probabily similar to ohio’s versus marshall. .by kicking a game-tying field goal to force an OT 2, they’ve managed to beat the odds AGAIN and force yet another exponential reduction in their odds to not lose the game.

(of course, we’d multiple the odds by the percentage of a game we deem an overtime to be for that, too. if st kilda manages to tie collingswood again this coming friday, they’ll have a lovely 88/89 chance of losing Championship (assuming rosters coaching etc stay the same)