2015 Luck of the Draw, NCAA Tournament Analysis

(This was originally posted to various internet sources in March, 2015)

As we await MSU's 13th appearance in the Sweet 16 in 18 years, I thought that I would once again dive into some NCAA tournament data, this time with an eye on how easy or difficult a path teams tend to take to advance in the NCAA tournament. In my analysis a few weeks ago, I outlined different coaches performance in the tournament based on seed expectations and I used (I believe) a unique metric based on seed differentials to try to normalize for "ease of draw" factors. At some point last weekend after MSU's exciting and decisive victory over Virginia, I caught wind on the Twitterverse that some people (who may or may not have Ann Arbor zip codes) were grumbling that Izzo's amazing performance in the tournament is largely due to getting an easy draw. My seed differential analysis suggests that Izzo has benefited a bit from good draws (notably in 2001 and 2010), but I was curious if I could look at this idea in a bit more detail. Fortunately, my database of NCAA tournament games and Excel were more than willing to help.

The premise of this analysis is that in any given tournament run, there is always going to be a path of greatest resistance, based on seeding. For example, if your team is a 1-seed, the toughest bath would be to play a 16-seed (which is fixed), followed by an 8-seed, 4-seed, and 2-seed in the Regional Final. Then, once this team reaches the Final Four, the toughest path would be to play two consecutive 1-seeds en route to a National Title. If your team is a 2-seed, the most challenging path would be a 15-seed (fixed), 7-seed, 3-seed, 1-seed, 1-seed, and a 1-seed, and so on. Now, we all know that upsets happen, for example, on rare occasions a 15-seed beats a 2-seed, and suddenly the 3-, 7-, and 10-seeds in the bottom half of the bracket have a much easier path to advance. If the 7-seed gets to face a 15-seed instead of a 2-seed, this is a whooping +13 seed advantage / variance from the expected path based on chalk. This variance in opponent's seeds can be calculated for each team in each round from the round of 32 all the way to the title game.

In compiling this data from each coach in NCAA tournament history, I considered two factor. First, how often did a coach get an "easy draw," i.e. how many of their opponents were not the highest possible seed that that could have faced? As you might expect, the farther a team advances in the tournament, the more chaos accumulates and the more likely a team is to draw a lower seed. Second, I also wanted to measure the "intensity" of the easy draw, which is simply the seed variance from the chalk / most difficult seed. In other words, getting a 15-seed instead of a 2-seed (+13) is a major advantage, while drawing a 5-seed instead of a 4-seed (+1) is not. With the right collection of data, it is fairly simple to calculate the sum of seed variance from chalk for each coach in each round since 1979. I then attempted the normalize the data by dividing the sum of seed variance by both the total number of "easy" games as well as the total number of all games played, excluding 1st round games in all cases, since the seeds are fixed. The average seed variance per game played seems to me to be the best way to rank coach's "luck of the draw" as it captures both the frequency and intensity of the "easy draw."

As you can imagine, there are quite a few games worth of data since 1979 (over 2000 games form the 2nd round on), so I limited the analysis only to coaches who have played in 10 or more NCAA tournament games past the 2nd round (plus Tom Crean, who has 9), which gets the number down to a manageable 43 coaches. Here is the summary for these 43 coaches including all games from the 2nd Round on:

As you can see, Izzo ranks 10th of all 43 coaches in terms of seed variance ("ease of draw") per game after the 2nd round, which about 0.5 seed advantage/game higher than the average of all games (row in yellow). But, I think that it is also interesting to see where some other notable coaches lie on this table. As we perhaps suspected, the kings of the good draw seem to be Billy Donovan and Bo Ryan, with Bill Self and two guys named Steve Fisher and John Beilein also near the top. Donovan and John Chaney have the distinguished honor of being the only two coaches in history who have benefits TWICE each in their careers from a 15-2 upset in the first round. That is just crazy lucky. Donovan also has a whopping 67% rate at a easy draw which is also a clear outlier. As for Izzo's neighborhood, his number are comparable to Brad Stevens, Jim Calhoun, and Jim Boeheim. Also on the "lucky" side of the board are Coach K, and Rick Pitino. As for the "not so lucky" crowd, most notably are Calipari, Thad Matta, Lute Olson, and surprisingly to me, Roy Williams.

The table above summarizes all games from the Round of 32 thought the Title game. I thought that it would be interesting to see how the data would be affected by looking at each round individually, at least until the Final Four, which is a bit of a different animal. So, the following tables show the results of the same analysis in the Round of 32:

The Sweet 16:

and the Regional Final / Elite Eight Round:

The trends for the Round of 32 are essentially the same for the overall trends, which a few minor exceptions (all of Lute Olson's luck seems to have occurred in this round, for example) with Izzo dropping to 14th "most lucky") still behind Fisher, Donovan, Bielein, and Self. In the Sweet 16 Round, again the trends are stable, with Izzo dropping here to 18th. It appears that Calipari and Coach K are a little luckier in this round, while Calhoun was less lucky. Finally, in the Regional Final round, Izzo is 16th. Here, Calhoun jumps to 5th, while Boeheim plummets to the "unlucky" area.

The data presented above takes into account the entire tournament resume of a given coach. I order to complete this analysis, I thought that it would only be fair to take a look at the "luck of the draw" for each Final Four and National Champion individually, to see if anything interesting pops out of the data. Since 1979, there have been 144 Final Four participants, and if you sum the seed variance for each team up until the Final Four, you can generate the following histogram, where the vertical red line indicates the median of the data:

I honestly expected this to look like a bell curve, but it is actually heavily front loaded to the "not so lucky" side. A full quarter of all Final Four participants made it with a seed variance of less than 2. However, when you consider the teams that actually won the national title, the histogram looks like this:

Now, this is much more like what I expected, with a bell curve-like shape and the median right in the middle at 10. A striking feature of this data is that not a single team in the history of the tournament has won the title using the most difficult possible path. I sifted through the data a little more and found seven teams that made it to the Final Four using the most difficult path and faced a 1-seed in the National Semifinal. All 7 teams lost. The team that did win the National Title with the lowest seed variance was Dean Smith's 1993 UNC squad with a variance of 1. Rollie Massimino also brought Villanova a title as an 8-seed in 1985 with a total variance of 2. I tip my hat to those gentlemen.

So, where does Izzo fit into all of this? Again, he fits into the "a little bit lucky" category. Izzo's six Final Fours have variances of 0 (2000, toughest quartile), 3 (2009. 2nd quartile), 9 (2005, 3rd quartile), 11 (1999), 12 (2010), and 18 (2001, all in the" easiest" 4th quartile). For the 2000 title squad, the road to the Final Four was as tough as it gets, but the Final Four opponents were an 8 and 5 seed, which results in an overall variance of 11 (right at the median). Looking through the data, my general impression is that for coaches that have multiple Final Fours, there is usually a distribution of lucky and unlucky paths that generally mirrors the overall variance summarized in the first table above. The luckier Final Four coaches are: Jim Boehiem with variances of 6,8,8, and 14; Jim Calhoun with variances of 3,4,10, and 10; Steve Fisher at Michigan (9,11,14); and Bill Self (11,16). Billy Donovan is a mixed bag (1,3,10,10); as is Coach K with multiple paths in each quartile (0,1,3,5,5,6,8,8,11,13, and 13); and Dean Smith (0,2,3,6,10,17). Lute Olson was not very lucky (0,1,1,3) until he finally won the title in 1997 (with a variance of 15 prior to the Final Four); Rick Pitino tends to be unlucky (0,1,2,5,5,8); as is Roy Williams (0,0,0,2,3,3,6); and John Calipari's road has generally been tough (0,0,1,1 with Kentucky and Memphis and 9 with UMass).

Add it all up and I guess we can say that yes, Izzo has gotten some good draws in his career, but he is certainly not an outlier in this area (that would be Billy Donovan).

For those interested in the raw data, here are four tables with the 4th (easiest) quartile through the 1st (toughest) quartile of Final Four data, followed by the table of Champions. Enjoy!

4th quartile (easiest path)

3rd Quartile

2nd Quartile

1st Quartile (toughest)

National Champions