Question 1204905: A football team has just scored a touchdown. If they go for the extra point kick there is a 94.4% chance
of success, a 5% chance of a miss and no points, and 0.6% chance of the opponent stopping the play and
running it back for 2 points (equivalent to losing two points). If they instead go for a two-point
conversion the chance of success is 47.9%, a 42.1% of missing and no points, and a 10% chance of the
opponent stopping the play and running it back for 2 points (equivalent to losing two points). What is
the expected number of points for each choice by the coach and which option should be picked based
upon the expected points?
Expected Points for Extra Point Kick: __________
Expected Points for Two Point Conversion: _________
The team should pick:
Cirlce one: Extra point Kick Two Point Conversio
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Expected value for Extra Point Kick = .932
Expected value for Two Point Conversion = .758
The team should pick extra point.
here's why:
extra point is 1 and opposite team running it back for 2 points is -2.
you get .944 * 1 + .05 * 0 + .006 * -2 = .932
2 point conversion is 2 and opposite team running it back for 2 points is -2.
you get .479 * 2 + .421 * 0 + .1 * -2 = .758
the expected value is the average number of points per play for each type of attempt.
assume 1000 attempts at each type of play.
for the extra point, you get (.944 * 1000 * 1) + (.05 * 1000 * 0) + (.006 * 1000 * -2) = (944 * 1) + (50 * 0) + (6 * -2) = 944 + 0 - 12 = 932 points / 1000 = an average of .932 points per attempt.
for the 2 point conversion, you get (.479 * 1000 * 2) + (.421 * 1000 * 0) + (.1 * 1000 * -2) = (479 * 2) + (421 * 0) + (100 * * -2) = 958 + 0 - 200 = 758 points / 1000 = an average of .758 points per attempt.
the decision based on the statistics favors going for the extra point.
the decision, however, is based on other considerations as well.
one consideration is:
if they go for the extra point and get it, but the other team is 2 points ahead and the game is over after the play, then going for the extra point is useless because they'll lose the game anyway.
they have to go for the 2 point conversion just to tie the score and force the game into overtime, even if the probability of success is less than going for the extra point.
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