# The Incongruity {REDACTED} of the Two Seed

Submitted by saveferris on March 19th, 2014 at 1:25 PM

My excuse to post the Trey Burke GIF

Last season, as the Michigan basketball team entered the NCAA Tourney as a four seed, we took a look at historically how the fours have fared in tournaments past. The analysis produced this incredibly scientific chart (since adjusted to include 2013 tourney results).

1 Seed 2 Seed 3 Seed 4 Seed Other
Final Four Appearances 47 25 14 13 17
Percentage 41% 22% 12% 11% 14%*
Championships Won 18 4 4 1 2
Percentage 62% 14% 14% 3% 7%*

* - this 14% represents all Seeds higher than 4 that have made it to the Final Four, so while this number appears high, it's coming out of a much larger pool of participants.  When you factor in the total pool, only about 1% of Seeds higher than 5 make it to the final weekend, with only about 0.1% of those teams winning it all (1985 Villanova, 1988 Kansas)

Yes, the answer was discouraging and as it turned out, almost irrelevant as Michigan proceeded to go on an epic run that saw them become just the 3rd four seed ever to make it to the Finals and then came damn close to winning the whole shebang. Through that assessment though, we came across a strange statistical anomaly that this season proves presciently relevant.

2 Seed
Final Four Appearances 25
Percentage 22%
Championships Won 4
Percentage 14%

What’s up with that? While 2 seeds make the Final Four at about half the rate of the one seeds, they win titles at less than a quarter of the rate as the ones. If you like nice, statistical symmetry, you’re probably experiencing one of those involuntary facial tics right about now. Why have 2 seeds historically fallen flat in the Final Four? Let’s have a look.

Diving deeper into the numbers the winning percentage for the Top 4 Seeds in the past 29 tournaments since 1985 for the Semi-Finals and Finals break down like this.

Semi-Finals
W L Pct.
1 Seed 27 20 57.4%
2 Seed 12 13 48.0%
3 Seed 9 5 64.3%
4 Seed 3 10 23.1%

Finals
W L Pct
1 Seed 18 9 66.7%
2 Seed 4 8 33.3%
3 Seed 4 5 44.4%
4 Seed 1 2 33.3%

So in the Semi-Finals, the 2 Seeds don’t do too poorly; batting around .500. Plus, of the thirteen 2 Seeds that didn’t advance to the Finals, 10 of them lost to a 3 seed or higher, so it’s not like there are upsets galore grinding them up. Still, when we look at their winning percentage in the Finals? Woof. 2 Seeds have not fared well in the title game of years past. The big reason for this seems obvious, 6 of those 8 losses came against a 1 Seed. The other two losses were delivered by a 3 Seed, which judging by the numbers we’re showing, the discrimination between 2 and 3 seems to be much finer than 1 and 2.

As for those lucky four winners, 3 of those wins all were earned by defeating a 3 Seed. Only one 2 Seed since 1985 has taken home the Championship by defeating a 1 Seed (1986 Louisville over Duke)

So the math here draws some pretty reasonable conclusions. First, the Final Four is averaging just under a 2 Seed per season, so that’s nice. Year-to-year, you can expect at least one 2 Seed to advance to the final weekend. Second, if you are a 2 Seed, hope that the tournament gods deliver you from the evil of the 1 Seed, because you just don’t beat them much. The good news for Michigan this year is that there seems to more parity amongst the Top 16, which means 1 Seeds could be ripe for falling. Of course, that parity affects the entire Top 16 equally, and Michigan’s path seems particularly difficult with Duke sitting out there at the 3 Seed.

Still, compared to last season, the data delivers better news. It’s much better to be a 2 Seed than a 4 Seed (LOLSparty), so here’s to hoping we get to enjoy another deep and entertaining tourney run.

Win the Game!

Anachronism: "something or someone that is not in its correct historical or chronological time, especially a thing or person that belongs to an earlier time: The sword is an anachronism in modern warfare."

Did you mean mystery? Enigma? Riddle? Conundrum?

Touche'

Took a little too much liberty in looking for a big word for "something out of place".

Word police appeased.

It's really interesting to see those numbers--thanks for putting that all together. I'm not too surprised by the championship numbers of the 2 and 3 seeds--we're talking about so few games, that I wouldn't give a lot of credance to specifics, though I think it's enough to support your conclusion that the difference between 1 and 2 seeds is bigger than between 2 and 3 seeds.

One hypothesis is that, most years, there are 1-2 really, really good teams. Those are almost always 1 seeds, and they have a much larger chance of winning the whole thing than any other team. The gap between the last 1 seed and the first 2 seed might not really be that big--which would also explain why 2 seeds can get into the Final Four pretty well (there are 2-3 paths to the FF that don't involve knocking off the great 1 seed), but don't win it that well (you have to go through the great team unless they stumbled).

Unfortunately, in a quick Google search, I didn't find the odds for the overall #1 seed, but they may account for a fairly large chunk (at least well over 1/4) of the championships for 1 seeds.

If you take the final game records of the 2 and 3 seeds and adjust them by just one game, you'd get a totally different result....i.e., this is a very small sample size.

2 seed:  4-8 record becomes 5-7

3 seed:  4-5 record becomes 3-6

(I would figure out the winning percentages if I could find the calculator on my new Windows 8 laptop)

So, good analysis by you.  I just wouldn't put too much stock in the final game win percentages...given that one game would swing the percentages dramatically.

I think what these statistics mean is that a 2-seed is "due."  At least, that's what they would mean if only the concept of being due wasn't a statistical fallacy.

Yeah, I like that interpretation. Let's go with that.

It's only a statistical fallacy because there is no evidence that being "due" changes the probabilities. But that just means the evidence is "due." It'll stop being a fallacy any day now.

Given that one-seeds often enough play other one-seeds in the final, is perhaps the likeilihood of  of a one-seed winning understated?  If East 1-seed plays West 1-seed, the winning percentage for a given one-seed team is 50%, although there is a 100% chance of one-seed winning the game.