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March Madness and the Math behind this crazy tournament
How many ways are there for the tournament committee to match up 64 teams?
What are your chances of selecting the correct results on the bracket?
How many games are actually played in the tournament?
How many final four combinations?
What is the probability that a 1st seed makes it to the Sweet 16?
“Amateurs practice, professionals train”
Socrates
You are more likley to be hit by lightening!
Want a million dollars for life? Warren Buffet even offered $1 Billion in 2014 for a perfect macth on the bracket
Want a million dollars for life? Warren Buffet even offered $1 Billion in 2014 for a perfect macth on the bracket
Here we go again with March Madness. Remember in 2014 Warren Buffet offered 2014 for predicting the exact results in the tournament
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The complexity task The Selection Committee has creating a bracket
And the reason why there is a huge amount of human bias
112,275,575,285,571,389,562,324,404,930,670,903,477,890,625 possible combinations
The complex task the NCAA Selection Committee has creating the Bracket
It’s here again , the March Madness NCAA basketball tournament. After all stress of the normal college basketball seasons, we enter the conference division I championship games. A lot can happen during this period. Then we have the “Selection Sunday” where the nation awaits the Selection Committee announces the playoff bracket for the 64 final teams. The tournament teams include champions from 32 Division I conferences (which receive automatic bids), and 36 teams which are awarded at-large berths. The NCAA men’s basketball tournament has 64 teams, paired off to play in 32 first round games. But here is the big question, ever considered how many possible ways there are to pair up the 64 teams?
Simple case, look at all possible combinations (ignore seeding)
The above bracket shows the far left and far right columns that the Selection Committee must complete on Selection Sunday. There are 32 games and 64 teams. The question then is how to pair up in the first round the 64 teams. This is a counting question from Discrete Mathematics taught in most Algebra 2 classes.Game by game combinations 1st round, 32 games. We will look at it by considering each game individual with selection two teams one we will call “A” and the other “B”
And the counting continues to create each individual 1st round game…(next game)
And third 1st round game
And so the process continues
And game 32 of the 1st round game
If you follow the pattern of choices it goes 63 choices (game 1), 61 choices (game 2), 59 choices (game 3) ,….1 choice (game 32. The math is now simple as it is 63 times 61 times 59 times 57…3 times 1
THIS EQUALS =
112,275,575,285,571,389,562,324,404,930,670,903,477,890,625 Possible Combinations!!!
That’s over one hundred tredecillion possible ways, or roughly the number 1 with 44 zeros after it.
Clearly to make this manageable the Selection Committee has to put lots of other factors into the bracket includng the seeding combinations and of cource lots of human bias to teams. It is sim
There is a similiar reference showing the theory behind the calculation
Next scenario calculation (include seeding effect for matches)
Let’s now consider what happens if we consider a simple effect of seed positions of rankings of the teams. Each team is “seeded”, or ranked, within its region from 1 to 16. A more realistic approach is the Selection Committee (this is more common) will match high seeds to low seeds. So you will see a 1st or 2nd seed against a lower 14th, 15th or 16th seed. Certainly not fair to the lower seeds, but it makes the possible combinations drop dramatically. So consider this situation with 1 to 8 seeded teams in one group versus 9 to 16 seed teams in the other group.
We will do similar game by game combinations 1st round, 32 games. We will look at it by considering each game individual with selection two teams one we will call “A” and the other “B” but in this case A will be from the top seeds while B will be from the lower seeds. This we have 2 groups of 32 teams to figure out all the combinations.
It should be clear this cannot be handled easily to produce the tournament bracket .It is simply impossible to remove human bias from the bracket creation if you consider the above number of possible combinations of brackets. Unless they use a random process of pairing teams in the tournament, we can be certain the bracket will have bias. So despite all our passion and belief in the true randomness and fairness in the bracket creation, both the above calculations of the unavoidable human subjective conscious bias suggest we might need a better method to create a bracket.
Sports Illustrated has looked into this issue in 2010
Study: Subconscious human bias exists in tournament selection
http://www.si.com/more-sports/2010/03/15/selection-bias
And here is a Fox Sports Article
11 things that may surprise you about the NCAA selection process
http://www.foxsports.com/college-basketball/story/ncaa-tournament-committee-selection-sunday-process-bubble-teams-021616
Political Correctness, Selection Bias, and the NCAA Basketball Tournament
Rodney J. Paul, Mark Wilson
http://journals.sagepub.com/doi/abs/10.1177/1527002512465413
So despite all our passion and belief in the true randomness and fairness in the bracket creation, both the above calculations of the unavoidable human subjective conscious bias suggest we might need a better method to create a bracket.
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