should a football team go for it on fourth down?

Should a football team go for it on fourth down or punt?

Laura A. McLay, PhD(c) 2012

Based on Scorecasting by Tobias Moskowitz and Jon Werthem

Patriots vs. ColtsbNovember 2009

• Patriots were up by 6 points  near the end of the p y pgame.

• They faced fourth and two on their own 28 yard y yline.

• They had two choices:They had two choices:– Go for it on fourth down

– Punt to the ColtsPunt to the Colts

• There was one possession left. Whoever got the ball on the next play would finish the game.ball on the next play would finish the game.

Patriots vs. ColtsbNovember 2009

The Patriots were heading this way

The Colts would have to move the ball ~30 yards if the Patriots turned yover the ball on downs

Patriot OutcomesPatriot Outcomes

• If the Patriots went for it and made itt e at ots e t o t a d ade t– They would win with virtual certainty– They had a 60% chance of making 4th and two

• If the Patriots went for it and didn’t make it– The Colts could possibly win if they went 30 yards for 

hda touchdown– They had a 40% chance of not making 4th and two

• If the Patriots punted• If the Patriots punted– The Colts could possibly win if they scored a touchdown

Colts outcomesColts outcomes

• If the Patriots went for it and made itIf the Patriots went for it and made it– The Colts have a 0% chance of winning

• If the Patriots went for it and didn’t make itIf the Patriots went for it and didn t make it– The Colts have a 33% chance of winning 

• If the Patriots puntedIf the Patriots punted– The Colts would get the ball back on roughly their own 30 yard liney

– The Colts could win if they went ~70 yards for a touchdown, with probability 21%

Solve the Patriot’s problemSolve the Patriot s problem

• We can model this as a decision tree andWe can model this as a decision tree and compute the probability that the Patriots will win by using conditional probabilitywin by using conditional probability

Patriots decision treePatriots decision treeYes = 1Patriots 

win given successful?

Prob = 0.60Prob = 1

Y

Yes

NSuccessful?

YesNo = 0Prob = 0

Prob = 0 67No

Yes No

Go for it?

Patriots win given 

unsuccessful?

Yes = 1

No = 0

Prob = 0.40

Prob = 0 33

Prob = 0.67

Yes

No

Yes = 1

No = 0

NoProb = 0.79

Prob = 0.33

Patriots win?

No = 0Prob = 0.21

The Patriots’ best decisionThe Patriots  best decision

• If the Patriots go for it and made itg– They have a 100% chance of winning

• If the Patriots go for it and didn’t make it– They have a 67% chance of winning

• If the Patriots go for it:• If the Patriots go for it:– They have a 0.6(1.0) + 0.4(0.67) = 87% chance of winning

• If the Patriots punt:– They have a 79% chance of winning

The Patriots should go for it!The Patriots should go for it!

• The best decision is for the Patriots go for it.• This is counterintuitive.

Wh t if it f th d fi th P t i t ’ 20 d• What if it was fourth and five on the Patriots’ 20 yard line?– Update the probability that they would be successful (from 

)60%)– Update the probability that the Colts would win if the Patriots do not convert (increase from 33%)

– Update the probability that the Colts would win if the Patriots punt (from 21%) due to the Colts getting better field position

Were the Patriots right?Were the Patriots right?

• They did go for and lostThey did go for and lost.

• Did they make the right choice?Hi t ill b th j d– History will be the judge.

– The math says yes.

– Punting decreased the Colts’ chance of winning but they lost the possibility of not giving the Colts the ball to begin withthe ball to begin with.