With six minutes and 49 seconds remaining the fourth quarter, Jerry Kill faced a quandry. Down 38-22 and faced with a 4th and 15, he elected to kick a field goal instead of going for it. By kicking the field goal, Minnesota now only needed to score two touchdowns and make two extra points to win the game. If the Gophers went and scored and made the two point conversion, the team would only need one score to tie the game, or a touchdown and a field goal to win. Was kicking the field goal the right decision? I believe the answer is a resounding No.

Let's look at the math. Our first question is to see when a team would be indifferent between kicking the field goal and going for the conversion. For a team to be indifferent, the expected value of both would have to be equal or a bit more formally,

E(Convert) = E(FG)

### Skippable Section for Those Who Know How to Calculate Expected Value

For those who have never worked with expected values before, an expected value is the probability of an event multiplied by the payoff of the event. Consider rolling a dice where the payoff is the value of the roll. For example, if you roll a 6, the value is 6. Assuming the dice is fair, you have a 1/6 chance of rolling any number. To calculate the expected value of a single dice roll, we multiply:

E(V) = (1/6)(1+2+3+4+5+6)

E(V) = (1/6)(21)

E(V) = 3.5

There's a question about what this probability means, and whether it's an expectation or the likelihood of an infinite number of rolls. I'll put that aside, but note that when I think of probability, I think about it in terms of uncertainty.

### What's the Call in Isolation?

What are the numbers for our scenario? For the 4th down conversion, I'll use expected points (which I think is a poor model incidentally, but it's easy and available). 4th and 15 from the 20 is not a common play. I used Pro Football Reference's game finder to find all plays from 1994-2015 where a team faced at least 4th and 13 from the opponent's 21 yard line. My query returned three results, two incompletions and a sack. The expected points model for that situation is 1.99. Let's plug that in and do the math.

1.99 = E(FG Attempt)

1.99 = (Prob FG Make)(3)

1.99/3 = (Prob FG Make)

.66 = (Prob FG Make)

If our field goal kicker is better than 66% from 36 yards, we should kick the field goal. Ryan Santoso is 10/13 on the year or ~77%. With the note that some of his misses have been beyond 40 yards, this is a reasonable prior, and well above 66%. In isolation, the Gophers should take the field goal every time.

### Hold on. Wasn't there some other information?

There was! The Gophers are down 38-22--two possessions--before the play. After kicking the field goal, the Gophers are now down 38-25, which means they are down two possessions. The field goal did not alter the game at all!

Now the Gophers will have to successfully cover not one, but two onside kicks that Nebraska expects. What's the odds of recovering an onside kick? In the professional game, the odds are around 20% if the other team expects the kick. In college, some work by Football Outsiders from 2011 pegged the number at 25% for college. I find that number suspiciously high, so I will use the Pro Football number for college as well.

In probability there is a question about whether or not an event is independent. Two events are independent if the result of one event does not affect the result of the other. *The formal definition is P(A*B) = P(A)*P(B). *If the onside kicks are independent, Minnesota has a

P(Recover Two Onsides) = P(Recover) * P(Recover)

P(RTO) = (.2)(.2)

P(RTO) = .04

Only 4% chance of recovering both kicks?

This actually gets a bit worse because I don't believe that multiple onside kicks in a game have the same probability. I do not mean in the sense of a conditional probability because the kicks are separate. Instead, the second onside kick will be the second best onside play, and so the chances of recovery should be worse. How much is hard to say because this scenario does not come up very often, but for argument's sake let's say it is 18%. Now that same equation produces a success rate a little over 3.6%.

In the other scenario, Minnesota either converts--and likely scores because it would have been a shot to the end zone--or gives Nebraska the ball on the Cornhuskers' 21. If they convert and score, the team must go for two. Against Nebraska's horrific pass defense, this probability is likely rather high. Indeed, Minnesota has quite a few plays to get two yards in the playbook. If the Gophers do score and convert, it is now 38-30. They can now win with a combination of a field goal and touchdown, or a touchdown and a two point conversion. Crucially, they only need one stop on defense and have almost seven minutes to score 8 points or more.

If they fail to score the two point conversion, **then they enter the first scenario.**

If they fail to convert, Nebraska gets the ball deep in their own territory. The defense must get stops, and that may have been too much to ask yesterday. In general, and contrary to some commenters, Minnesota has a good defense. We should expect that they can get a stop if needed. In the event that they force a 3 and out, Minnesota will get the ball **in about the same area as a successful onside kick. **If the Gophers fail to get an initial stop, but force the punt, they will likely get the ball around the 20 yard line. The game clock will be disadvantageous, but that happens when a team lets its opponent score at will for three quarters.

### Conclusion

Jerry Kill made the wrong call. Minnesota should have gone for the conversion. The downside risk for missing the conversion was roughly identically to the upside in kicking the field goal. The upside of converting was much higher, and gave the Gophers many more options to score over the last seven minutes.

Further, this is not a normal situation because normally you do not give up 38 points to an opponent and expect to even have a slim chance to win.

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