By now we’ve seen plenty of numerical models attempt to quantify just how improbable the Aggies miraculous comeback over Northern Iowa was. The probabilities range as "high" as 0.03% (Kenpom) and bottom out at zero (Bill James Lead Calculator). Unless we're still dreaming, we know the odds of this comeback are in fact greater than zero, so now it’s time to grab our lunch pails, put on our hard hats, and do the math ourselves. (WARNING: TL;DR)

Let's start by making some assumptions. Here’s what we know happened:

• A&M's odds of winning reached their minimum after Caruso missed a 3 with 36 seconds left and the Aggies down 12 (#branding).
• A&M's comeback is completely unprecedented. No NCAA team has ever recovered from more than a 10 point deficit with under 1 minute remaining, and no team has ever recovered from more than an 8 point deficit with 35 seconds remaining (via FiveThirtyEight). Not just in the tournament. EVER. Therefore there is no historical data to compare this occurrence to.
• Every possible play during this 36 second stretch was a positive outcome for Texas A&M. This includes the UNI dunk, which we'll discuss later. If any of these plays had not worked in A&M's favor, they would have lost the game.
• During these final 36 seconds, Northern Iowa completely forgot how to play basketball.

With these assumptions in mind, the probability that Texas A&M competes this comeback can be approximated as:

P(comeback) = P(Every result favors Texas A&M given that UNI forgets how to play basketball) x P(UNI forgets how to play basketball) x P(Texas A&M wins in overtime).

Let’s dive into each component.

--

P(Every result favors Texas A&M given that UNI forgets how to play basketball)

The probability of this component is calculated by breaking down the play-by-play of the comeback.

35.8 Seconds remaining, 69-57: Admon Gilder rebounds Caruso’s missed 3 (80% chance)

The comeback begins when Caruso’s desperation heave bounces off the rim. A&M’s offensive rebound percentage on the season is 33.9% while UNI gives up 25.8% of rebounds on defense. If UNI had still remembered how to play basketball, you could take the average of these numbers to estimate that A&M had roughly a 30% chance of coming down with the ball (NOT WEIGHTED FOR STRENGTH OF SCHEDULE, PAWL). As previously noted however, UNI did not remember how to play basketball. Therefore, for the remainder of this section, we will mostly shy away from the average statistics of each team and instead use our own crudely estimated probabilities. Let's assume that A&M had an 80% chance of grabbing the rebound. It would be 100%, but a strange bounce would still have the chance to land into an unsuspecting UNI player’s hands.

34.5 Seconds remaining, 69-59: Admon Gilder makes putback layup (90% chance)

This basket was made pretty easy by UNI not knowing how to play defense, or basketball altogether, but the quick putback still takes an incredible amount of balance and precision from Gilder, and therefore the bucket was no guarantee.

30.0 Seconds remaining, 69-59: Admon Gilder steals inbound pass. (50% chance)

This guy was all over the place, and even though UNI forgot how to throw a good inbound pass, because that is part of basketball, this turnover also required players from our squad being in the right place at the right time.

28.2 Seconds remaining, 69-61: Danuel House makes layup (60% chance)

Even though UNI forgot how to play defense here, which is a very important component of basketball, the quick score from the turnover required great vision by Gilder to find House inside and a nice finesse move by House to put the ball in the hoop.

23.5 Seconds remaining, 69-61: Jalen Jones recovers UNI turnover (50% chance)

UNI forgot how to play basketball (we’ve already established this, dammit), which is why their guy threw the ball right to Jones. This play was set up by a perfectly executed trap however, and that ain’t easy to pull off.

22.0 Seconds remaining, 69-63: Jalen Jones makes dunk (100% chance)

Number 33 for UNI didn’t know how to play basketball, but he still knew to stay the fuck out of the way of the inbound train.

22.0 Seconds remaining, 69-63: UNI throws inbound pass out of bounds (25% chance)

Since UNI did not know how to play basketball here, we can assume that the ball was thrown at random. Had the ball stayed inbounds, there would be a 5/9 chance of A&M recovering the ball since they accounted for 5 of the 9 players not throwing the inbound pass. This number could actually be higher since 4 of the 9 players eligible to catch the inbound pass did not know how to play basketball at this time.

Even if A&M had recovered the inbound pass, this would still not be a favorable result for A&M compared to what actually happened, as Aggie players would not be set in good positions to score, and more time would run off the clock. Therefore, let’s assume that an out of bounds pass is the only favorable result, for which we will approximate had a 25% chance of occurring given that UNI did not know how to play basketball.

20.1 Seconds remaining, 69-66: Danuel House makes 3 point shot (31% chance)

A&M ran a beautiful set piece on the inbound pass because they remembered how to play basketball. We’ll say their odds of getting House an open look was 100% because UNI did not know how to defend this inbound pass at this time. Even with the perfect inbound, House shoots 31% from 3 on the season, so we’ll assume that was his odds of making this shot.

19.6 Seconds remaining, 71-66: UNI dunks inbound pass (100% chance)

Thank God for this quick play that only burned a half second. Had UNI remembered good clock management skills, which is part of playing basketball, they could have dribbled another 5 or so seconds off the clock before getting fouled and then potentially scoring 2 points anyway.

11.8 Seconds remaining, 71-69: Caruso makes and-1 layup and free throw (36% chance)

Although UNI made a poor attempt of playing defense here due to their deficient knowledge of basketball, A&M may have benefited from an iffy whistle. It looks like the UNI player got an arm on Caruso, but contact was minimal at best, and it’s a 50% chance the ref actually calls this foul. Since the contact did little to impact the shot, it made an easy layup for Caruso (let’s say 90% chance). His free throw percentage on the year is 79% so we’ll assume the odds of completing the 3 point play here are the multiple of these 3 percentages.

4.6 Seconds remaining, 71-69: Admon Gilder recovers UNI turnover (50% chance)

This play is almost identical to the trap and turnover recovery from Jones, so we’ll give it the same probability. Also, UNI didn’t know how to play basketball here.

1.9 Seconds remaining, 71-71: Admon Gilder makes layup (80% chance)

This shot also took incredible balance from Gilder, and it went so high off the glass that the bucket wasn’t a given. Holy hell though, that was some atrocious defense from number 4 on UNI. He literally moved out of Gilder's way, and that is not what you do if you know how to play basketball.

0.0 Seconds remaining, 71-71: UNI misses full-court buzzer beater (99.9% chance)

It appears that UNI had finally remembered how to play basketball at this point because that shot was way too close for comfort. Even with UNI’s storied history of sinking long-range buzzer beaters, the shot came in just a tad too hot, and the good-guys successfully forced the game to bonus periods, in which they completed their improbable comeback.

--

With the probabilities of each play in mind, we can estimate that

P(Every result favors Texas A&M given that UNI forgets how to play basketball) = 80% x 90% x 50% x 60% x 50% x 100% x 25% x 31% x 100% x 36% x 50% x 80% x 99.9% = 0.12%.

This is just a hair over a 1 in 1000 chance.

--

P(UNI forgets how to play basketball)

This is arguably the most intriguing part of this comeback. Just how on God’s green earth did Northern Iowa forget how to play basketball? Calculating the odds of this occurring is definitely the biggest wild-card, because it’s incredibly difficult to quantify the psychology of each player on that team.

We do know these factors however:

• UNI was in a situation where teams tend to play less focused.

• UNI became visibly flustered by A&M’s full-court press and momentum.

There are plenty of instances in which teams lose leads because of these factors, but UNI relinquishing a 12 point lead in just over 30 seconds is an unprecedented meltdown. They had simply checked out of the game. For each factor to infect UNI with Chuck Knoblauchesque severity (Gig ‘em, Chuck!), we’re looking at incredibly low probabilities. These factors are almost certainly correlated, so instead of guessing the probability of each factor occurring, let’s make a semi-educated guess and assume their overall mean meltdown probability in this situation is 5% with a variance factor of ¯\_(ツ)_/¯. Please let me know in the comments if you have a better way of estimating this because this is really bad.

--

P(Texas A&M wins in overtime)

Once the game reached overtime, UNI regained their basketball competency for the most part, so for this component, we’ll go ahead and use Kenpom’s OT win probability for A&M of 60%.

(Fun stats nugget sidebar: Kenpom’s win probability for A&M at the start of the game was 75%. Since overtime is a much smaller sample, there’s more room for variability thereby lessening the advantage of the favorite.)

--

Conclusion

Now that we have each component crudely estimated, we can even more crudely express the overall probability of Texas A&M's comeback as:

P(comeback) = 0.12% x 5% x 60% = 0.0036%, or roughly a 1 in 28,000 chance.

So there you have it. Given that there are 63 games played in the NCAA tournament, you can expect to see this type of comeback in March Madness roughly once every 450 years, which leads me to believe I'm woefully underestimating a team's likelihood of forgetting how to play basketball. Even so, these calculations show just how astonishingly rare the Aggies comeback was, and you may never see it happen again.

In the even rarer occasion that the team making this improbable reconciliation is a team that you root for, you may have already turned off the game out of frustration thereby missing the comeback altogether. I am speaking about a friend of course, and said friend is currently en route to the Association of Former Students office where their ring will be confiscated.