The time has come for NCAA basketball tournament brackets. People across the country are devoting untold hours researching and discussing basketball this week. Hundreds of millions of dollars will exchange hands. But I have a nerdier question that simply who will win basketball games. I want to know what the best way is to determine who wins the brackets.
Now, "best" is a subjective term here. So my idea here is that a non-zero number of you will submit a scoring system for dealing with bracket picks, along with an argument as to why that scoring system for brackets is superior to all others. Some definition of what your overall purpose is may be necessary in your justification. I present below a few common scoring systems, along with a brief discussion of some pros and cons.
Note: For all discussion here, the "first four" games are ignored and the 32 Thursday/Friday games are considered Round 1. (This is not a requirement for your comments, but simply what I'll be doing.)
System #1: 2^(Rd#-1)
This is the most common scoring system. Each game within a round is worth the same number of points, and each round is worth the same total number of points (32). This system is simple, easy to implement, and widely accepted. But if the best argument for something is simply that doing it differently is hard, that's not very convincing. In general, games in the later rounds do need to be worth more than games in the earlier rounds; at the time of picking, we don't even know who will be in the championship game, let alone who will win, so picking the winner is fairly difficult. However, this system awards the same number of points for getting the winner correct as for getting all 32 games correct in the first round. Which is harder? I suspect that any given year a non-trivial percentage of brackets get the winner right, perhaps varying from 5-20%. However, how many get the entire first round correct? Out of the millions of brackets entered on ESPN.com, only a very small handful. So, what is more deserving of 32 points last year, picking UConn to win it all, or picking Butler, VCU, Gonzaga, Richmond, Florida State, Morehead St and Marquette to win, while at the same time not picking Princeton, Michigan St, Memphis or Missouri to win? The tougher task should be rewarded accordingly.
System #2: Rd#
The next most common and simple system is increase the value of each game by one point in each round. Rather than increase geometrically (1, 2, 4, 8, 16, 32), they increase arithmetically (1, 2, 3, 4, 5, 6) which serves to over-emphasize the opening rounds. Again, I think the important question is to ask which is harder: guessing the champion, or getting an additional 6 games right in the opening round? A further downside to this scoring technique is that is allows some people to build large advantages early on, which become almost insurmountable later; the contest isn't too exciting if the championship game isn't enough to bring you back significantly. System #1 has the opposite problem, of course, where there is almost no lead that is safe: the final 2 victories of by the champion are worth 25% of the total points available, which generally corresponds to well over 1/3 of any individual score. It doesn't seem right that such a huge percentage of your points hinge on the final 2 games in a 63 game tournament.
System #3a: Seeds
System #3b: Difference in Seeds
The idea behind these systems are to award risks by offering bounties for picking upsets. A point value of a victory by a given team is equal to that team's seed, i.e. a 12/5 upset is worth 12 points. (Or, in system 3b, it would be worth 7 points.) Victories by favored (or evenly seeded) teams are worth a single point. These systems risk over-valuing upsets to the point that bracket pickers are encouraged to simply pick every upset. Statistically, a few will hit, and if the bonus is big enough, it doesn't matter that you missed on the majority of them. A scoring system shouldn't favor mindless picking of lower seeded teams any more than it should favor mindless pick of higher seeded teams.
So where does that leave us? Its time to start combining the best aspects of the various systems. Pay attention here, because the math gets slightly trickier.
System #4: 2^(Rd#-1)+(Seeding Difference)*Rd#
This is just system #1 with an added bonus for getting upsets, which scales through the rounds. Picking 11-seeded VCU to win in the first round last year would have required guts (and luck) so we want to reward that with more than a single wimpy point. So you get 1 point, plus the difference between their seed (11) and their opponents seed (6), for a total of 6 points. But to pick them to win a second game? Even less likely. So, their victory over the 3 seed was worth 2^(2-1)+(11-3)*2 = 2+16 = 18 points. But here is where the quirk of this method kicks in. In VCUs next game, they played 10th-seeded Florida State (having just knocked off the 2-seed (ND)). VCU was (by seed) basically a coin flip to win the game, so that victory was worth only 2^(3-1)+(11-10)*3 = 4 + 3 = 7 points. Perhaps the craziest thing about a system like this is that going into the tournament, it is impossible to know how many total points there are going to be, and that victories in different rounds can be worth very different amounts. The most valuable win last year would have been VCU's next game where they beat 1-seed Kansas for a 48 point victory. (That's 2^(4-1)+(11-1)*4 = 8 + 40 = 48 points, if you didn't want to work that out in your head.) The final game, as it wasn't an upset, was worth 32 points, which tied with Butler's upset of Florida. The next most valuable games were 3 2nd round upsets at 18 each. This system certainly gets hard to track in your head, because so many different things can happen, and opponents affect point values. A weakness is that the 8/9 games become fairly mindless. 9-seeds actually have a slight advantage historically, and a victory over a 9 seed is worth 2 points, whereas the 8 seed winning is only worth 1. You really should just pick all the 9s. However, this is only going to net a few points, which probably won't be too consequential. (A perfect bracket in last year's tournament would have been worth 410 points, though, if Butler had won the final, it would have been worth 30 more points than the UConn win.)
So, what have I missed? What crazy idea do you like? (And yes, I know the tournament starts in earnest in about 36 hours.)
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