A Statistical Analysis of Bracket Strength
Twitter erupted last night with scores of fans from a variety of conferences and teams complained about their seeds, pods and brackets. In this diary, we look at the hardest bracket to the weakest bracket using overall seeds.
To calculate the overall strength I added the overall seed number for each team in a given region. For example, Duke was the No. 1 overall seed and MSU was No. 6, adding those brings us to seven (or so I'm told), then we add all the other teams to get to a final number. For teams in the play-in game, the overall seed list number is added and divided by two. For example, Arizona State and St. Johns are 45th and 47 respectively so we average their total at 46. Some regions end up with half points due to this average.
Region Rankings (Fewest points = hardest region)
1. South 508 points
2. West 520.5 points
3. East and Midwest 532 points
Of course these power rankings assume that the committee ranked every team appropriately and while I'm sure they are off here or there, it is pretty fairly balanced. One could immediately argue that the South is the hardest, but upon further review the region is one of two region's without three top 10 teams (Virginia and Tennessee). The South does have four of the top 16 teams with Purdue and Kansas State - which on it's surface looks weak. A strength for the south is the six team, Villanova checking in at 21, and the 10th team, Iowa, checking in at 37th.
The second strongest region is actually the West, which I'm sure many of us did not expect to be the case. With three top 10 teams, four in the top 16 and Marquette giving them five teams in the top 17, the region appears more mid-heavy than most which is clearly the region's strength. One weakness: only nine teams in the top 40 with the ninth team being Florida. Still the distance between the South's ninth team (Oklahoma at 36, is relatively small and probably not worth fussing over).
Next come the East and Midwest, tied for the weakest region which would be a surprise to certain Green fan bases who think they got jobbed. First the East: two top 10 teams with both coming no lower than 6 making this region the most top heavy - but it would always be that way with Duke. Like others, it has four teams in the top 16, but only seven in the top 25 and ten in the top 40. The mid level rankings are similar to other regions, with the weaknesses coming in the higher seeds. Coupled with two of the top six teams, this region seems the most unlikely for a big upset.
Finally, there is the Midwest with three top ten teams, four top 16 teams with the lowest ranked checking in at 13 overall making it strong at the top. Six teams are in the top 25 in this region and ten in the top 40 which is very similar to other regions.
Overall, the East is the most top heavy due to Duke, but Damn if the Midwest isn't close and maybe deeper in the top 20. The West may be strongest with five in the top 17 - or maybe I am just biased. The South has a similarly strong composition between 10th and 20th ranked teams but as a whole all four regions are very balanced through the top 20 and 40.
I'm sure everyone has a different opinion individual teams and relative strengths, but overall with the S-Curve or not - this is not, arguing over lopsided brackets is not the hill to die on - at least not this year.
And typo in the first sentence. Anyway, hope there aren't too many glaring errors in my first diary on the new site. Please don't throw too many tomatoes at me.
Thanks for doing this. I found it interesting and decided to take a look at doing the same analysis but using Kenpom Adjusted Efficiency Margin rather than overall seed. I was surprised that the results were similar.
Simply aggregating AdjEM for each region yields (higher is better):
South: 266.45
West 258.26
Midwest 250.5
East 250.39
For the play-ins I only selected the team with the higher Adjusted EM so each region was based on 16 teams.
That didn't match my expectation, and I thought maybe regions I thought should be higher (like the East) were being weighed down by dregs in the bottom half, so I tried looking at just the top 8 teams in each region. That did produce some change:
West: 187.54
South: 186.12
East 186.11
Midwest: 182.25
Having done that, it was natural to also slice it down to top 4, 2, and 1 teams to get:
South: 112.37 / 62.64 / 35.66
West: 111.54 / 62.23 / 32.79
East: 108.79 / 63.35 / 31.99
Midwest: 102.35 / 56.59 / 29.17
I based top x on Kenpom rating rather than seed, so, for example, despite being the 3 seed in the East, LSU was not included in that region's top 4 (because Kenpom says they're the #5 team in the region).
No matter how you slice it, the Midwest is weak. I laughed at MSU's draw, but the numbers say it's only the top 2 in the East that are really daunting (and I think Kenpom undervalues Duke with a fully weaponized Zion back). Michigan's draw in the West seems favorable to me (and others), but I think that's because I don't believe Gonzaga is as good as Kenpom says, and Michigan seems like they should be able to beat the rest of the region because Michigan is really good and would seem likely to beat seeds 3 through 16 in any region. And the South, well, it's just strong.
Thanks for the additional effort. The 15s and 16s just have too much influence in this kind of analysis.
March 21st, 2019 at 10:25 AM ^
MSU has an easier road than Michigan to the elite eight but a harder hurdle to final four. Given the way march madness works I'd much rather take spartys draw and deal with duke in the elight 8 than much harder matchups we have in the round of 32 and sweet 16
Your findings are interesting. I suspected that the MSU/sportswriter complaints of unfairness were exaggerated. My reason was because people tend overweight the chances of events that are not probable but are easily imagined---like a 1-2 Duke-MSU matchup. Sportswriters claiming "unfairness" tend to ignore all the other ways that MSU could lose. Based on the 538.com analysis linked below, the chances of a Duke MSU matchup is only 40%. And, if we gave Duke a 55% chance of winning that, the chance that MSU would reach that game AND lose would be only 22%.
Granted, that is greater than the chance of being called to "come on down" on The Price is Right (1/36) or having a nonfatal injury from a toilet (1/10,000). But it's still not terribly likely.
https://projects.fivethirtyeight.com/2019-march-madness-predictions/
http://cognitiveconsonance.info/category/psychology-2/heuristics-and-biases/
https://www.sheknows.com/living/articles/1023453/what-are-the-odds-21-statistics-that-will-surprise-you/
Lies,
Damned Lies,
and Brackets.
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