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March Madness Masters, Quantified: A Deep Dive Into Tournament Performance Metrics

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January, February, Izzo, April. You may own the t-shirt, but I have the mathematical proof

NCAA Basketball: Final Four-Practice Day Shanna Lockwood-USA TODAY Sports

Back in 2015, I went down a bit of a math rabbit hole based on a curiosity of mine. I wondered if it was possible to quantify the performance of coaches and teams in the NCAA tournament in ways other than simply wins and losses, Final Fours, and National Titles. In particular, I wanted to quantify under and overachieving in March. Along the way, I developed a few metrics that compared each coaches’ and team’s performance to the average performance of all other coaches / teams in similar tournament situations.

Somewhere along the way, I discovered that others had also formulated a similar metric called “PASE” (Performance Against Seed Expectation). My metrics were mathematically a bit different, and I settled onto two, one that I call PARIS (Performance Against Round Independent Seed) and PAD (Performance Against exact seed Differential). Three years ago, I gave a pretty detailed mathematical description of each metric and summarized notable coaches performance based on these metrics. That analysis can be found here. While the 2020 Tournament was sadly cancelled, I thought that is was a good time to revisit those metrics again.

For those that are not so interested in mathematical underpinnings of the PASE, PARIS, and PAD metric, the basic idea is as follows. PASE measures the number of games won by a specific coach or team per tournament relative to the average number of games won per tournament by all teams of that seed in tournament history. My PARIS metric essentially does the same thing, only it considers each game independently and not linked to other games played in the same tournament. The PAD metric uses a similar formula, but it instead considers each team’s performance relative to the specific seed of the opponent in each game, as opposed to just the performance per round.

The PAD metric essentially corrects for the fact that some teams benefit from easy draws. For example, MSU made the Final Four this year by beating a 15-seed, 10-seed, 3-seed, and 1-seed. But, back in 2001, MSU made the Final Four by beating a 16-, 9-, 12-, and 11-seed. Clearly, the 2019 path was much tougher than the 2001 path. My PAD metric takes this into account, while MSU would get the same “credit” for both paths using both the PASE and PARIS metrics.

Based on data through the 2019 Tournament, we can look at how various coaches stack up with each other. As we will see, in all three metrics Tom Izzo is currently at the top of all three charts. Let’s start with the PAD metric. The following chart shows the value of PAD over time for seven of the best tournament coaches in the last 40 years.

Not only in Izzo in first place, his current score in the PAD metric (8.41) is higher than any other coach at any other point in the history of the tournament (since seeding began in 1979). The only time any coach had a higher score was also Tom Izzo following the 2015 tournament. As for other coaches, Roy Williams is currently in second place, followed by John Beilein, John Calipari, Jim Boehiem (not shown), and Coach K. It is interesting to note that even though Coach K won titles in 2010 and 2015, his PAD score has taken a bit of a nosedive since 2001.

For reference, here is the same plot using the PASE metric:

In general, the story is the same here: Tom Izzo is awesome. However, in the case of the PASE metric, Izzo’s current score (15.13) is slightly below the PASE score achieved by Coach K is 2001 (15.81) and in 2004 (15.24). But, Izzo’s PASE following the 2015 tournament (16.32) remains the highest of any coach at any point in history. While MSU’s loss to Middle Tennessee State in 2016 put a dent in that score, another strong run or two in March will likely allow Izzo to soon break his own record.

As for the PARIS metric, it tracks very closely with the PASE metric. So, by itself, those values do not add a lot of additional insight. However, as I mentioned above, the difference between the PAD and PARIS metric has to do with the relative difficulty of a team’s NCAA tournament path. This difference in path “luck” can be quantified by subtracting a coach’s PAD score from his PARIS score. In this way, it is possible to visualize true tournament performance (based on PAD) in relationship to “luck” (PARIS minus PAD). The chart below compares these two parameters for all 632 coaches to participate in the Tournament since 1979.

This chart really allows us to differentiate the “good” coaches in March from the not-so-good ones and the lucky ones from the not-so-lucky ones. As the chart shows, Izzo is clearly very good, and he has been historically slightly lucky relative to the field, similar to Denny Crum, Rick Pitino and Calipari. But, other “good” coaches have been more lucky, notably Beilein, Calhoun, Boeheim, Coach K, and the king of all tournament luck: Billy Donovan.

A few good coaches are rather unlucky, notably Roy Williams and Rollie Massimino. Lute Olson was very unlucky (and right at zero in the PAD metric). Meanwhile despite some positive luck in their draws, Bill Self, Bob Huggins, and Tony Bennett (despite the 2019 Title) are all still solidly in the “under-achiever” category. But, they can all take solace in the fact that they aren’t Rick Barnes, the current champion of under-achievement in March (Gene Keady, Fran Dunphy, and Jamie Dixon are also thankful for Coach Barnes).

As for other data comparisons, there is one more metric that I developed that is interesting to examine and that is each coach’s tournament performance not in terms of seed, but instead relative to the Kenpom efficiency margin of each team. In effect, this is similar to a measure of a coach’s performance relative to the spread, although it only considers winning and losing, and not the final scores of the games. Another way to think about this is that this metric (which I dubbed “PRAKAEM” or Performance Relative to Average Kenpom Adjusted Efficiency Margin) is that is adjusts for teams actual strength as opposed to just their seed. One downside of this metric is that the data only goes back to 2002, but it is still useful. Below I plot each coach’s PAD vs, their PRAKAEM back to 2002.

There are a couple of take-aways from this data. First of all, the PRAKAEM metric is one of the few tournament metrics where Izzo is not in first place. He is actually only in 5th, behind Roy Williams, Boeheim, Beilein, and Calipari. But, also keep in mind that this set of data does not include Izzo’s Final Four runs of 1999-2001.

But, what I find interesting here is the coaches that deviate significantly from the best fit line with PAD. As I mentioned above, the difference between the PAD and PRAKAEM metrics is essentially a measure of the accuracy of seeding, at least in reference to Kenpom efficiency. Most coaches are very close to the line. However, some coaches (Roy Williams, Boeheim, Calhoun, and Bill Self) are notably below the line, which suggests that either their teams have on balance been seeded higher than they should or that they have on balance played teams that are seeded lower than they should have been. It seems like the odds of consistently drawing under-seeded opponents are extremely small, so I guess this has more to do with the over-seeding of those coaches.

In contrast, Tom Izzo is notably well above the trend line. Moreover, Izzo is a clear outlier on this graph in general. This suggests that Izzo’s teams, by far, have been seeded lower than their Kenpom efficiencies merit relative to literally every other team/coach since 2002. I don’t mean to contribute to any conspiracy theories out there, but this data is a pretty strong piece of evidence that the committee has done a poor job of seeding MSU over the past two decades.

So, when it comes to performance against expectation, Tom Izzo is clearly awesome and likely the best coach in the history of the tournament. But, there are other factors to consider as well. So with the remainder of my space here today, let’s just review Tom Izzo’s current standings in a wide variety of other tournament performance statistics.

Total Win Percentage:

Tom Izzo: 52-21 (71.2%)

Good for 9th place among all coaches with more than 4 appearances since 1979 and 4th place among active coaches (behind Coach K, 76.4%, Roy Williams, 75.2%, and Calipari, 74.7%)

Wins as the Lower Seed:

Tom Izzo: 15

Good for 1st place all-time. Jim Boeheim has 13, and Massimino and Lute Olson retired with 11. The next closest active coaches are Bruce Pearl, Beilein, Gregg Marshall, and Mark Few, all with seven. Also amazing is that Izzo actually has a winning record (15-13) as the lower seed.

Win Percentage as the Higher Seed:

Tom Izzo: 37-8 (82.2%)

Just because Izzo is great as the underdog doesn’t mean he struggles as the favorite. Izzo’s win percentage as the higher seed is good enough for 8th place all-time among coaches with greater than 10 appearances and 4th place among active coaches. The Top 3 are John Beilein (86.4%), Roy Williams (84.1%), and Calpari (83.3%). Denny Crum and Rich Majerus both retired at 87.5%.

Wins over No. 1 seeds:

Tom Izzo: 5

Good enough for a tie for 4th place all time behind Coach K (8), Lute Olson (7), and Roy Williams (6). Izzo is tied with Boeheim, Rick Pitino, and Dean Smith. Since 1998, Izzo’s five wins are more than any other coach. Izzo also has the most wins over No. 1 seeds and No. 2 seeds combined (9), the top three seeds combined (13), the top four seeds combined (17), and even the top five seeds combined (18) since 1998.

Two-Day Prep Record:

Tom Izzo: 23-6 (79.3%)

Izzo is legendary for his 2-day preps and his record on the 2nd game of the weekend bears this out. This winning percentage is 2nd all-time (behind Denny Crum at 82%) and 1st among active coaches with at least 10 tournament appearances. There are a handful of coaches with higher percentages (like Steve Lavin, Tom Crean, and Jim Larranaga) but these records are all based on less than 10 total games. I will also note here that Izzo’s record on the 1st day of a weekend is “only” 29-15 (66%) which is one of those rare stats where Izzo is pretty average.

Sweet Sixteens:

Tom Izzo: 14

Good for 6th place behind Coach K (25), Roy Williams (19), Boeheim (18), Dean Smith and Calpari (15). Also, Tom Izzo has made the Sweet 16 in 63.6% of his tournament appearances, which is also tied for 6th place all-time. Since 1998, only Coach K has more Sweet 16s (17).

Elite Eights:

Tom Izzo: 10

Good for a tie for 5th place behind Coach K (16), Roy Williams (13), Calipari and Pitino (12). Izzo is tied with Dean Smith and Bill Self. Izzo has made the Elite 8 in 45.5% of his tournament appearances, which is 7th place all-time. Since 1998, Izzo is tied for first place with Self, Roy Williams, and Calipari.

Final Fours:

Tom Izzo: 8

Since 1979, Izzo has now moved into 3rd place behind only Coach K (12), and Roy Williams (9). Tom Izzo has made the Final Four in 36.4% of his tournament appearances, which is the best rate in history among coaches with more than 8 appearances. Larry Brown (37.5% in 8 years) and Brad Stevens (40% in 5 years) have slightly better rates, but with far fewer attempts. Also, since 1998, Izzo is alone in 1st place in this category.

As we all know, Izzo has struggled a bit once he gets to the Final Four. His record in National Semifinal games (2-6, 25%) is the lowest of any coach with more than 2 appearances in the Final Four. Izzo has only won a Championship in ~5% of his tournament appearances, while the other coaches in his peer group typically have a rate between 10 and 15%.

But, by all indications, Tom is going to be hanging around in East Lansing for a while now, and the future looks very bright. More than one of Izzo’s Final Four runs has been submarined by injuries, 2019 included. In 2020, well, we all know what happened. But, Coach Izzo and MSU’s luck is bound to turn around at some point. Hopefully Coach Izzo can add to his amazing stats in the years to come.