HSAC Blog

Here’s an article written by a couple of our members, Haibo Lu ‘08 and Alex Ahmed ‘10, for our biweekly column in the Harvard weekly paper, The Harvard Independent (www.harvardindependent.com).  The type of prediction probability scoring that is discussed in the article is not limited to the NCAA basketball tournament - it has a lot of interesting applications.  Look for more on this topic in the months to come. 

 I can’t help but think about the words of Edgar Allen Poe as I watched the waning seconds of the UCLA-Memphis game in the Final Four. “TRUE! –nervous –very, very dreadfully nervous I had been and am; but why will you say that I am mad?” Well, I’ll tell you why I’m mad. I’m mad because I picked 56 of the 63 total games correctly (a slight exaggeration) and now some random person who just happened to advance all the number one seeds and then pick Memphis and Kansas to tango will end up destroying my chances of winning the pool. Alas, so is the format and scoring of the NCAA bracket.

            This is a statement of bitterness. Yes, I am bitter: bitter that my knowledge of college basketball has blinded me and luck takes on a huge factor in the craziness that is March. No upsets of the number one seeds?? Really? Come on now, I thought parity had come to stay in the NCAA yet not one single team can take down the 1 seeds? Georgetown? Tennessee? Grrr… It gets me mad just thinking about it. So what do I propose? Well, I propose a new system of scoring the NCAA brackets so that knowledgeable folks can get their props during March instead of some lucky upstart stealing the spotlight (how’s that for bitterness?) Also, I’m a second semester senior with nothing better to do with my time so I’m just going to complain.

            The problem with the current way of scoring the brackets is that you don’t get rewarded for any of the real upset picks that usually occur in the 1^st or 2^nd rounds. The big points are only awarded down the line, basically from the elite 8 onwards. Let’s imagine a crazy scenario where a number 10 seed makes it all the way to the elite 8. That’s great! You score a couple of points on the upset but the way current brackets are usually scored, all the points that you would have gained from picking Davidson are completely negated by someone who picked Kansas to go to the Final Four. The last couple of games are weighted so heavily that the first several rounds just don’t count for anything. But the problem is that the first rounds are where all the fun match-ups are and where upsets occur the most. Did you have a 15 seed beating a 2 seed? That’s great, but you only get 1 or 2 points for it and if you didn’t get the elite 8 or final 4 pick, then it counts for essentially nothing. What we need is a new way of scoring to really reward the people who can pick the upsets and best predict the true outcomes.

            I have two suggestions of alternate scoring strategies that will make things more even. The first is a multiplicative scoring system. Basically, you take the seed number of the team that wins and multiply it by the round and then add up all the points. So in the first round, if you pick a number 1 seed to beat a number 16 and you get it right, you get 1 x 1 = 1 point but if you pick the number 16 seed to upset the number 1 seed, you get 16 x 1 = 16 points. That way, if you pick an upset, you get much more points than if you just stayed with the safer picks. But would that mean everyone would just pick upsets all the time in hopes of cashing in on a lucky game? Not necessarily. In the Sweet 16, for example, if you have a 1 seed playing a 5 seed, the points are worth 15 if the 5 seed wins (seed 5 x round 3 = 15) and 3 if the 1 seed wins, but you need to make sure that the 5 seed gets there, so it wouldn’t help you if you had the 12^th seed upsetting the 5^th seed in the first round and then not have it happen. Basically in this system, it awards people for being able to predict upsets and also rewards them if they have the best foresight about who is going to win what paths. It is basically what the current bracket scoring system aims to have, but is slightly more fair to everyone involved. So next year, why not do traditional scoring and also this round multiplication scoring system? It’ll make things much more exciting and entertaining while keeping the scoring system still relatively simple.

            Now if you really want to get into it, I have another suggestion: the probability scoring system. This might be a little too much for your average fans, but if you are passionate about your bracket (and know a little bit of math), this is the way to go. In a probability bracket, you don’t pick the winner. You state the probability that you think a team is going to win and then you score points off of a certain function that deals with those probabilities, most likely some sort of logarithmic function. So for example, let’s take the 2 versus 15 seed match up in the West region of this year’s tournament. Ahh….a little Duke bashing. No article about March Madness is complete without some Duke bashing. Anyways, the match up is Duke versus Belmont. Instead of just picking who you think will win, you assign probabilities to the match up. So for example, I say that I think Duke will win 70% of the time and Belmont will win 30% of the time. After the game is over, you tabulate your score using a scoring function that could be something like s = -100ln(1-p), where p is the probability you gave to the team that actually wins the game and s is the score you get for this game.  So if Duke wins, you get 120 points and if Belmont wins you get 36 points. But wait a minute, you say, I don’t really understand. Don’t you still get more points for predicting the winner? Yes you do, but what this system of scoring does is that it punished you for being arrogant. If you are really sure of something, for example that Duke will definitely win against Belmont and you do something like 99.99% / 0.01%, then if Belmont pulls the upset, you will be severely punished, and receive no points. For example, if you actually think Belmont is going to win this game, and you give them a probability of 51%, you will be rewarded with 71 points, while the sorry loser who gave them only 0.01% is left feeling empty with a 0 for that game. 

In rounds after the first round, there are different ways to continue this scoring system.  One would be to give each team a conditional probability of winning in each successive round, so you would give the a percentage of winning the second game assuming they had already won one game.  The second way of continuing would be to allow participants to list as many teams as they want so they could be ensured of getting at least some points.  To go back to our previous example, we would now include the rest of that group of four, the 7 seed West Virginia and the 10 seed Arizona.  To pick the second round game in this scenario, you could give Duke a 35% chance, West Virginia a 30% chance, Arizona a 25% chance, and Belmont a 10% chance.  This way, you would have gotten 36 points for correctly picking West Virginia to win, but wouldn’t have lost out completely if someone else had won, like you do in the current popular scoring system.

So if you are sick of finishing in the lower half of your pool every single year, even though you seem to be the only one who’s not picking based on team colors and mascots, try switching your brackets over to a system like one of these, that rewards more on skill than on luck.  That way you’ll be able to watch the elite 8 and final 4 in peace, knowing that you have it wrapped up already because of your 31 for 32 first round, and the impressive call you made on giving Belmont a 40% chance to beat Duke, when everyone else only gave them 1%.

Alex is a sophomore Applied Mathematics and Biology concentrator in Winthrop House. His main interests with the club are improving baseball strategy, including pitch counts and ideal use of players. He is also interested in doing research on college sports, mainly basketball and baseball. This semester, he is working on research projects with the Arizona Diamondbacks.