Metaprimer: Bracketology

Ah, March.  Among the shortest of all months, and yet the month in or near which virtually all of our great nation's most significant events have transpired.  From our victories in the Revolution, Civil War, World War I and World War II, to the birth of some of our country's greatest heroes, like George Washington, Mel Ott and Richard Chamberlain, to the very founding of the United States itself, all have taken place in March (or in months in its general vicinity).  And, in the modern age, mid-late March is known of course for Men's and Soldiers' Day (Mongolia) and the NCAA Men's Basketball Tournament.

One of the innumerable benefits afforded you, as a Premium Gold Subscriber* to South Side Sox, is our series of "Metaprimers", offering detailed insights into some of the most advanced methods for measuring athletic achievement and predicting future performance.  As Colin's essays** on wOBA and UZR have ably demonstrated, it is now possible to develop metrics which predict future results with absolutely guaranteed, 100% certainty, which are incapable of even the most minor error.  It is posts like those which have helped this publication attain its current lofty levels of readership, with an audience literally in the tens of dozens.  And it was, no doubt, with this in mind that our reclusive, mysterious proprietor, The South Side Cheat, requested that I, your humble Author Dipshit, pen this article last night:

2:14 a.m., March 17.  TAEG’s bedroom.  A shambling, shadowy figure clad in black robes appears from thin air with a loud cracking noise in a wisp of blue-ish grey smoke.  The figure is human-shaped, but has the head of a wolf and hooves where its feet should be.  It is holding a 20-sided die in one hand, and a jar containing a very large, very dead rodent of some kind in the other.

Apparition (in a booming voice):  WHO DISTURBS MY SLUMBER.

TAEG (waking up, completely out of sorts):  Uhhhh, it’s me, The Actual El Guapo.   (rubs eyes, exhausted, squints into the darkness)  Jesus … what time is it … Cheat is that you?  Hey, I didn’t “disturb” you, I was laying here asleep and you ca-

Apparition of Cheat (interrupting):  I SHALL EAT YOUR SOUL.

TAEG:  Ah … I see.  (pause)  Uh, don’t I need that?  I mean … that is … if it’s all the same to y—

Apparition of Cheat:  I SHALL REQUIRE YOU TO PERFORM FOR ME A WORK.

TAEG:  Oh.  A "work”? … what, you mean for your website thing?  Seriously?  I mean-

Apparition of Cheat:  I SHALL EAT YOUR SOUL.  (Vanishes)

TAEG (to Mrs. TAEG, still sleeping):  Honey, wake up!  Jesus, did you see that?

Mrs. TAEG (waking up, looking at TAEG for a long, silent moment):  God, I fucking hate you.  (goes back to sleep)

In satisfaction of what I interpret to be our proprietor’s requirements of evening last, I have elected to address the NCAA Tournament, that most topical of … uhhh … topics.  No doubt many of you have, since this past Sunday, been busily completing your “brackets”, studying the field of teams, calling to memory your recollection of games played over the season, and even perhaps perusing analyses written by our competitors.  We at SSS are certainly not so vainglorious as to believe that only we are capable of providing value in the arena of statistical analysis.  We acknowledge and in fact, applaud, the contributions of those such as KevPel (adjusted offensive and defensive efficiency), KenPom (tempo-free analysis) and KenWo (disturbing rants about little league trophies and mediocre, bespectacled White Sox outfielders of the mid-1980’s).  However, as befits our rigorous, disciplined nature, we do seek a greater degree of exactitude and certainty than afforded by our able peers.

Taking a step back from usual practice of minutely and closely scrutinizing each team and game for hours upon hours, only to be left when all is said and done in the realm of contingency, human error and random chance, it occurred to me that there might be some mathematical method for achieving more definitive predictive results.  As I mused, inspiration hit, gentle but firm, as though I had been touched on the cheek by the hand of Truth*** itself.  For it occurred to me that 100% accuracy in predicting the tournament is indeed possible:  Because the tournament involves a finite number of teams and a finite number of games between those teams, one could account for all of the possible results of those games between those teams, and conclude to a mathematical certainty that one of those results will be the correct result.  Therefore, in order to be assured of submitting a winning bracket entry, one must simply fill out a sufficient number of brackets to account for all possible outcomes of each game in the Tournament.  Due to its importance to the remainder of what follows of this analysis, I refer to the number of bracket entries necessary to be assured of achieving this result as the “Magic Number”.

Ah (the more skeptical of you may now be thinking), but might it not be inefficient to submit that number of bracket entries -- for if the cost of entering the requisite number of brackets exceeds the possible winnings from the pool, would it not be unwise to proceed notwithstanding the satisfaction gained from having submitted the winning entry?  What is this "Magic Number", anyway?  Let's take these two questions one at a time, starting with the second.

The Magic Number can be derived from the following formula:  X to the power of Y, where X=the number of possible results of each game of the Tournament, and Y=the total number of games in the Tournament.  Because we know both variables, determining the Magic Number is a matter of simple math.   X, the number of possible results of each game, will always be equal to 1 (i.e., there can be only one winner of each game, since both teams obviously can't win).  Y, we know, is 63 -- there are 63 total games in the Tournament, from the first round to the National Championship.  Therefore, 1 to the 63rd power is our Magic Number.  Doing the math**** (1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1* 1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1) results in 1, which is therefore our Magic Number.  In order to be assured of winning any NCAA Basketball pool, one must therefore fill out and submit exactly 1 brackets (1 being the aggregate number of brackets necessary to guarantee the accurate result, as demonstrated above).

Finally, to address the first question of our doubting friend, if the entry fee for the tournament pool (let's call this number "A") multiplied by our Magic Number above (1) is less than the winnings to be paid to the first place winner in the pool (let's call this "B"), then it is worth your while to fill out the Magic Number (1) of brackets and be assured of victory.  Using real numbers, if A, the tournament entry fee is $20, and the winner of first prize in the pool will be awarded B, $1,000, it is worthwhile to submit the Magic Number of brackets, since $20*1 (A times the Magic Number) is less than $1,000 (B).  If, on the other hand, the expected winnings for first place would be less than $20 (e.g., if B were $5), then one should not submit the Magic Number of brackets.  In that case, one could certainly submit fewer than the Magic Number of brackets, but one should realize that victory is no longer mathematically certain (I leave it to future authors, who are welcome to stand on the shoulders of this article in order that they may see more clearly, to determine the best method for "beating" this type of pool).

Please tune in for our next episode of Metaprimers, in which Winning Ugly and Marketmaker will tackle the stock market, attempting to prove the old saw, "past performance may not guarantee future results, but Bangkok-style auto-erotic asphyxiation and freshly dug basement graves certainly do ... in our pants!"

* - If you are not a Premium Gold Subscriber to South Side Sox (and have not fully paid all required fees) you are not permitted to read this article.  In fact, by reading this far (including that last sentence), you have already subjected yourself to severe penalties including, but not limited to, fines of up to 500,000 units of SBNMoney™ and up to 5 units of SBNTime™ of SBNConfinement™.  Every word you continue to read just makes this worse.  And yet you continue to read … just incredible.  OK, stand up immediately, slowly place your hands on your head, and remain entirely motionless.  SBN Security Officers have been summoned and will be arriving at your place of work/school/residence/worship shortly.  I SAID DON’T MOVE, MICHAEL J. ADAIR, OF 653 N. SUMMIT AVE., OAK LAWN, IL.  YOU ARE RESISTING SBNARREST™.

** - Bronze(ish) medal, Fist of Mathematical Accuracy Awards™, 2010.

***  i.e., larry.  That reminds me: larry, please stop touching my cheek.

**** - I know some of you will question the results of multiplying all these numbers since it is doubtful you have access to computers as advanced as those here at SBN CompuTechInternetLandWorld™.  You'll just have to trust me; I checked the results several times, and they are correct.