Some Math Principles for NCAA Basketball Fans to Think About

I've watched the NCAA tournament for longer than I'd care to admit, and I want to share some principles with you that I at least find interesting.  My hope is that, if you read this, you are a math guy or know some math guys who want to do the research to prove or disprove what I suggest.  If they disprove it, then perhaps they'll uncover trends of their own that they can share with us.  So, without further adieu, and in no particular order, here are my thoughts:

1.  Coaches of elite teams hate the rounds leading to the Sweet 16.  They do so because everyone gets up to play the chalk, and everyone has one game in them to beat a chalk team.  It doesn't usually happen, but the fact that it can with some frequency has every elite coach worrying that some smaller engine that definitely can will upend it, particularly in the first (okay, they call it second now) round.  There is, admittedly, less room for surprise in the next round, but there also is less time to prepare.  Witness, for example, Dayton's upset of Syracuse in the Round of 32.  True, Dayton upset Ohio State two days before, but it's probably also true that Syracuse didn't have enough time to prepare for a team on a mission.  While the same could be said for Dayton, it's typically the "overdog" that plays tight in that situation, not the underdog.

2.  With TV timeouts every four minutes, challengers need to cut the game into four-minute increments.  Stay close after four and eight, keep it close within the half, summon a run at some point.  While strength, flexibility and conditioning come into play, the timeouts also do.  They can kill an elite team's fast-breaking momentum and give an underdog a much-needed rest without compelling that team's coach to burn timeouts.

3.  Mostly any team in the tournament can stay with another team for 30 minutes.  Then, in the next two to five minutes, fascinating things can happen.  Single data points do not make a trend, but I recall having attended the early rounds in Philadelphia a couple of years back.  Albany, the 16th seed, led #1 (in the country) UConn by 12 with ten minutes to go.  The whole arena was buzzing, all but family, friends and sorted alums of UConn were in Albany's camp.  I remarked to my friend that either UConn was going to demonstrate its ability or perhaps they just weren't able, on that night, to summon that extra gear.  I joked that they would go on a 30-3 run or something and win it; the actual run was 28-5 and they did just that.  Instead of letting Rocky knock them out of the ring, they resorted to their sticking, moving, jabbing and occasional right crosses to systematically dismantle Albany.

That said, it seems to me that there is interesting psychology that goes on at that inflection point.  It happened last night in a different way, after Harvard trailed Michigan State by 16 and rallied to tie.  Michigan State was looking into its own abyss, and answered with a physicality and sense of purpose that the Crimson could not meet.  Harvard stayed in the Spartans' grille, but the Spartans shook them off and determined that they were going to win.

But at that inflection point is when interesting things happen.  Does the favorite kick into a higher gear, ramping its energy on defense, running faster and with more body work on offense, as if to say, get out of the way, the ball is ours, and we're going to take control of this game?  Or, is the favorite ambivalent, does the favorite start to doubt its ability, do a few players on the underdog step up, and does the underdog sense a lack of confidence and fear of failure in the favorite, feed upon it and push themselves to victory?  All sorts of things happen, and it would be interesting to see a study of upsets and close calls with the top four seeds in the first two rounds to see what happens at certain inflection points -- does the favorite step it up, or does the favorite just not have it?

My experience has been that after 32 or 35 minutes, the chalk seems to summon the extra gear and separate themselves from the challengers.  Call it talent, call it killer instinct, call it the benefit of having played against tougher opponents in louder, more packed arena, chalk it up to a deep-seated psychology within both teams that tells one they are supposed to win and the other that after having given it a good try, well, they're cooked, I don't know and cannot begin to tell you.  But the observation is that something does happen that determines the game.  It could be the play of a few individuals, or of the entire unit on the floor.