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Filling out brackets is an American tradition every March, with the draw of the NCAA Tournament pulling in even the most basketball-agnostic bystanders. But bracket pools are far from the only way to get in on the action during March Madness. Squares is another easy, entertaining game that keeps you involved through the entire tournament and doesn’t require any knowledge about the teams.

I’ve gotten into squares the last several years and have roped some friends into combining forces for a pool that is too rich for our blood individually. There is a distinct camaraderie in rooting for an otherwise meaningless free throw in the final seconds of a 12-point game just so we can get a win for our square. Plus, your entry is alive for the entire tournament, as opposed to a bracket pool where some people will realistically be out of the running after the first weekend.

After years of playing squares in March, I’ve looked for research on which numbers you want. I had some theories about which point differentials are more common, but didn’t have any data to back it up. So I decided to do the work myself.

Before getting too deep into the numbers, let’s give a primer on how squares works for college basketball. Just like Super Bowl squares, the game requires a 10-by-10 grid with digits 0-9 on both axes, forming 100 squares correlating to those digits. One axis is the winning team’s score; the other is the losing team’s score. You win by having a square that matches the end digits of the final score of a game. So if you are assigned a 0-3 square and a game finishes 70-63, you win, but if the game finishes 73-60, you don’t. (Although some pools give payouts for reverse scores for the Final Four or title game.) The difference between Super Bowl and March Madness squares is the Super Bowl is one game divided into quarters, while for the NCAA tournaments, it’s the final score of every game (and maybe halftime of the title game if your pool gets creative).

Typically, payouts increase for each round. So, for example, a first-round win could net $5, but a title-game win could be worth $50.

The squares should be assigned randomly, so this research isn’t actionable other than to find out if the square you drew is any good.

With the basics out of the way, let’s get into the nitty-gritty. Gathering the scores and point differentials for the last 10 men’s tournaments (2013-2023), we have data from 669 games that show several trends. One oddity in the numbers: There are 67 games in every tournament, but VCU had to forfeit in 2021 due to a COVID outbreak on the team, so we don’t have a round number of games. The 2021 tournament is weird in more ways than that, but more on that later.

As far as the likelihood of a square hitting, the biggest difference between playing squares for the Super Bowl and March Madness is that the digits should, in theory, be more random and balanced in basketball. Football is a lower-scoring game with a limited number of ways to score, which makes certain numbers come up more often. Having a seven in Super Bowl squares is great, but a five is basically dead on arrival. In basketball, you can score one, two or three points at a time, and scoring is high enough that the numbers themselves should be relatively random. Is that actually the case, though?

Most common March Madness square numbers

Winning team number

Losing team number

Looking at the tables above, which aggregates data from the last 10 years of men’s tournaments, not much of a pattern emerges. Winning-team digits had a smaller range of frequency, between 58 to 78 occurrences. But even with the losing-team digits, where the occurrences show more range (51-82), it’s hard to find a logical reason to explain that range. Why would a three come up more than a seven?

Let’s say the digits themselves don’t matter, but you probably would’ve guessed that.

What about point differentials, though? That’s next.

Most common margins of victory

March Madness is famous for close finishes. If you get stuck with 4-4 or 7-7, you need at least a 10-point spread to win. So those squares are bad, right? You would prefer to have something like 3-2 or 7-5. But is that how it has played out?

Here’s what the past 10 years say about that.

Margin of victory (MOV) frequency

Based on these numbers, there are a few visible trends that matter for squares.

• Four is the most frequent margin of victory, with a relatively high gap to the next highest margin of victory. There may be some basketball logic to this. If a team is playing defense down two or three in the last seconds of a game, that’s an automatic foul situation, bringing four into play from the free throw line. Down four with a few seconds left, a team might give up and let the clock run out, leaving the point differential at four.
• The seven most frequent margins of victory in the last 10 men’s tournaments are 1-7, and the 12 most frequent margins of victory are 1-12. Closer scores appear more often, but the gap isn’t drastic.
• After the margin of victory goes over 20, it drops off a cliff fairly quickly, other than a 23-point margin of victory happening 17 times. None of the other margins above 20 happened more than seven times.

In squares, though, the exact margin of victory isn’t the only value that affects your specific square. If you have a 9-6 square, a three-point win and a 13-point win are just as good, so both are part of a specific square’s value. Six-point victories have come in more often than one-point victories, but is six a better point-differential to have in a square than one when you factor in 16-point wins being less likely than 11-point wins?

Margin of victory (MOV) end-digit frequency

Here’s how the numbers look when you add up every circumstance when a point differential ends with a certain digit (i.e. 6 = 6, 16, 26, 36, 46).

This table tells the most complete picture of valuable squares. Four still comes out on top, but it’s a smaller margin between the top four numbers. Instead, three tiers emerge:

• Good point differential digits: 1, 2, 3, 4
• Decent point differential digits: 5, 6, 7
• Not-so-good point differential digits: 8, 9, 0

After all that number-crunching, the most logical conclusions were true. You want a square with a small point spread, but each number is not significantly different from the next.

Most and least frequent March Madness squares

If you don’t want to think that hard and just want the list of most and least frequent squares, here you go. The first number is the winning-team digit, and the second number is the losing-team digit.

Most frequent squares

Least frequent squares

Final takeaways

Through all this research, a few interesting facts showed up about margins of victory in the tournament. For example, would you have guessed that 52 percent of games finished with a double-digit margin of victory in the last 10 men’s tournaments? That’s partially due to all the lopsided opening matchups for top seeds, but a majority of games in the Round of 32 and Sweet 16 have also been decided by double figures.

It makes sense for the First Four and the title games to be the most evenly matched because those teams should generally be peers and not have a true favorite or underdog, unlike most of the rest of the tournament. The Final Four would also be in that category, but the average got thrown off thanks to Villanova’s 44-point shellacking of Oklahoma in 2016. Taking out that game drops the average margin of victory in Final Four games to 8.6, right in line with the First Four and the title games.

Remember when I said the 2021 tournament was weird in more ways than one? That tourney, which was played entirely in the state of Indiana and had limited crowds, also featured the lowest rate of single-digit margins of victory in the last 10 years. Over 60 percent of the games that year were decided by 10 points or more. You can take that little piece of trivia to your office squares pool.

(Photo credit: Tyler Schank / NCAA Photos via Getty Images)