March Madness Metrics: Measuring Madness in Men’s Basketball

It’s been nearly two full months since the 2021-2022 college basketball season ended with Kansas Jayhawks“Comes from behind the victory over North Carolina Tar Heels In the national championship match. But the data has no off-season.

So far this spring, we’ve been examining the resumes of the NCAA Tournament of the Best College Basketball Men’s Coaches over the past 40 years. We just found it Based on raw numbersAnd the Michigan State Coach Tom Izu is among the best. When it comes to Performance compared to expectationsCoach Izzo he is The best ever.

We also explored and measured The difficulty of both the drawing and the actual path From several notable teams over the past 20 tournaments. Interestingly, the data indicates that the 2022 Jayhawks have had the easiest path to a national title for any team since 2002. Ironically, 2021 Baylor Bears It was the hardest track in the same time frame.

Finally, it’s time to end this series with a deep dive into the overall odds of the NCAA Championship as well as the odds of picking the perfect chip in an office pool. As we shall see, it is possible to define March Madness.

Total tournament odds

Throughout this series, and in my NCAA Annual Tournament PreviewI have outlined a variety of tools that can be deployed in order to gain a deeper understanding of the way the tournament actually works. Almost all of them depend on using Kenpom’s efficiency data to display point margins and odds of winning for any random championship match.

With these tools, it is possible to calculate the odds of any team winning any of the NCAA tournaments going back to 2002 when Kenpom began tracking this data. When all this data is gathered together, a big picture emerges of the opportunities for any network cutting team. Figure 1 below summarizes this data.

Figure 1: Probabilities of each NCAA team winning the 2002-2022 National Championship using a linear scale (left) and a logarithmic scale (right).

As we can see, the best pre-tournament odds for any team in the past 20 years have been a little better than the 35 percent, which Gonzaga had before the 2021 championships. Other notable teams with odds above 25 percent include the 2002 Duke Team and Kentucky Team 2015 Team Kansas 2008 and Virginia Team 2019.

Note that the difference in odds shown in Figure 1 for teams with similar kinbaum proficiency before the tournament is entirely due to differences in the tournament draws for each team. This was the topic Covered in detail in the previous installment of this series.

Of the seven teams whose odds of entering the tournament were greater than 25 percent, only two of those teams (Kansas in 2008 and Virginia in 2019) actually won the national title, which is true to the expected value of 2.13, based on the calculated equation. Prospect. In other words, check #math.

The bottom line is that winning the NCAA Championship is tough. Even teams that finished the season with a Kenpom efficiency margin of +30.0 or more, average only a one-in-five chance of cutting the net. Historically, the first seed has an average of only 14 percent chance.

Teams ranked low have much worse odds. The right panel displays the same data, but listed on a logarithmic scale. Interestingly, the total range of tournament chances for the best and worst teams of the past 20 years extends to 14 places.

For those who scored on home soil, the team with the worst odds in the last 20 years was the 2005 No. 16 ranked Alabama A&M team, who lost to No. 16 Oakland in game play. My account gave the bulldog team a one in 97 trillion chance of winning the national title.

Perfect arc odds

Over the years, many people have dreamed of winning their “office” arc in the NCAA tournament by choosing the results of all 63 games correctly (not counting the playing round). Naturally, this has led to many people trying to calculate these probabilities. The Internet has a lot of articles trying to make this calculation. Most of them are wrong.

The most trivial way of doing this calculation is to assume that all 63 games are coins and that each team has a 50 percent chance of winning each game. If so, the odds of picking the perfect chip would be about one in 9.2 quintillion, a much-cited number. But it’s actually a form of an upper bound on real possibilities.

The reason is that not all games are omissions. #1 seed Kansas didn’t have a 50 percent chance of beating #16 seed Texans this spring. KS odds were closer to 97 percent. In other words, the currency we use to perform the calculation in the previous example is loaded. It will only be a “fair” currency in the extreme case.

As it turns out, the real odds of picking an ideal bracket are based on a given weighted average (technically a geometric mean) of the odds of the favorite team winning every game of the tournament. This weighted average is a function of each team’s specific strengths in any given tournament, which means that the odds of picking all games correctly vary from year to year.

The actual weighted average is about 58 percent (not 50 percent) based on data for the last 20 cycles. The value tells us that the true odds of choosing an ideal slice are closer to one in 540 trillion. That’s still a really big number, but it’s 17,000 times more than the value most people are referring to.

It is also possible to calculate the minimum possibilities for choosing an ideal slice. These odds occur in the scenario where the favorite teams win all 63 games of the NCAA Championship. Effectively, the tournament will continue according to “chalk”.

In this scenario, the weighted average of the virtual currency is close to 68 percent on average. Based on this value, the odds of picking the perfect class have averaged one in 49 billion over the past 20 cycles. True odds are about 11,000 times less likely than this minimum.

Perfect odds in parentheses over the years

Now that it’s clear that the odds of the perfect class have clear limits and vary from year to year, it’s time to visualize what those odds have looked like over the years. Figure 2 provides this summary.

Figure 2: Actual odds of a perfect arc compared to a ‘chalk’ arc where the favorite teams win each competition and average odds generated by a series of Monte Carlo simulations for each tournament.

As we can see from the orange bars, the weighted average “coin” is between 65 and 70 percent for the most likely “chalk” arcs. This translates to probabilities between one in 1 billion and one in 1 trillion. The best possible odds of getting a perfect chip in 2015 would have been using the strategy of picking all Kenpom’s favorite games to win all 63 games. In this scenario, the odds of being correct were one in 4.3 billion.

When each cycle was then simulated, the odds were significantly reduced, as indicated by the striped green bars. Over the past 20 cycles, the geometric mean of probabilities for a perfect simulated slice has ranged from a high of one in 60 trillion in 2015 to a low of one in 10 quadrillion in 2006. Note that the “chalk” data and the simulated data highly interconnected.

It is interesting to note that the odds of picking an ideal bracket were better in years like 2015, 2019 and 2021. The odds were worse in years like 2003 and 2006. In the earlier part of this series, I pointed out that the set of previous years was the one in which he was Sagittarius is particularly strong and subsequent years have been those in which Sagittarius has been particularly weak.

As a rule, the strongest chip should It leads to fewer perturbations and therefore will be more predictable with better odds of selecting the ideal class. While there is a relationship between the simulated probabilities and the actual probabilities of a perfect arc, this correction is very weak. As the green dotted bars show, the actual odds of correctly selecting the outcomes of all 63 games varied between one in 3.2 trillion (in 2019) and one in 350 quadrillion in 2022.

A comparison of simulated and actual odds essentially provides a way to estimate March Madness. In years where the actual odds were higher than the average of the simulations (such as 2007, 2008, 2019), the tournament tends to have fewer overall upsets and a greater number of higher seeded players advancing to the fourth final. For example, 2008 is the only year in history that all of the top four seeded women have advanced to the fourth final.

The opposite is true for years when the actual odds are much worse than the simulated odds. In those years, there was an above-average amount of madness due to a large number of disturbances, major disturbances (such as the 15th seed winning over the second seed) or both. These years also tend to advance lower seeds to the fourth turn.

To highlight some examples, in 2011 the No. 8 (Butler) and No. 11 (VCU) seed hit the Final Four. In 2018, the top seed Virginia lost to the 16th seed UMBC (University of Maryland, Baltimore County) and the 11th seed (Loyola Chicago) took the fourth final. In 2021, she ranked second Ohio State Lost in the first round and ranked No. 11 University of California Make the last four. In 2022, seed No. 15 St. Peter made it to the Elite Eight and North Carolina No. 8 reached the final.

When it comes to unexpected events in the NCAA Championship, losing the #1 seed Virginia in the first round to the #16 UMBC seed is usually the most “crazy” event. However, statistics (based on the prevalence of Vegas) indicate that this type of disruption should occur in about one percent of all games. In other words, we should expect to see the first seed drop about once every 25 years.

However, a No. 15 seed qualifying for the regional finals (as did St. Peter this year) has odds of close to 0.18 percent, or one in 550. This indicates that this type of event should only happen once every 140 tournaments. The mathematics suggests that it is likely that no one alive will ever witness such an unexpected NCAA championship again in their lifetime.

However, the magical race of St.

With that said, it’s time to finally lay the bow on the college basketball season. Until next time, have fun, and go green.