Thursday, March 21, 2013

NCAA Tournament Survivor Pool

NCAA tournament time, fill out your brackets, blah blah blah. I love the tournament, but in some respects, the whole filling-out-your-bracket thing gets kind of repetitive year after year.

So how about something different? Hat tip to Adam M. for pointing me to an "NCAA Tournament Survivor Pool". It's kind of like an NFL Survivor Pool; in those, you pick one team to win each week throughout the season, and you're only allowed to use a team once. Once your pick for the week loses, you're out of the pool; last man standing wins.

The NCAA tournament version of the Survivor Pool works like this:
- Pick three teams to win in the Round of 64 (or whatever the NCAA is calling it these days).
- Pick two teams to win in the Round of 32.
- Pick one team to win in every subsequent round, through the Championship game.
- You may only use a team once throughout the tournament.
- If one of your picks for a given round loses in that round, or you don't have any teams left to pick (i.e. you use every eventual Final Four team prior to the Final Four), you're out. Last man standing wins.
- The tiebreaker - and ties are pretty likely here depending on the size of the pool - is higher "seed total"; i.e. the sum of the seeds each person successfully picked throughout the tournament. This is an incentive to make more risky picks.

I didn't enter, mostly because the entry fee is $25 (or, about $24 more than I'd be willing to spend on it). But, I am going to play along at home and see how I do, because I'm fascinated by it.

So...what's the strategy? Before we get into that, let's look ahead to the end, because you really have to think ahead here.

Let's say the Final Four is Louisville v. Ohio State, and Florida v. Indiana. You've already used both Florida and Indiana, but not Louisville or Ohio State. Therefore, you have only one choice: whoever you think will win Louisville v. Ohio State must be your National Semifinal pick. (For the purposes of this exercise, let's pick Louisville.) After that, one of two things will happen: 1) Ohio State wins. You lose! 2) Louisville wins, then giving you a championship game between two teams that you've already picked, and thus can't pick again. You lose! So, basically, it's in your best interest to hold off on the best teams as long as possible.

You only have to pick 9 teams throughout the tournament, so you could get away with only taking teams seeded 3 or better. But that wouldn't set you up very well for tie-breakers. Instead, here's my strategy:

Round of 64: There is (normally) a big drop-off between the 12 seeds (usually the last at-larges) and 13 seeds (usually automatic qualifiers). Everyone who follows the tournament knows the history of 5/12 upsets. With that in mind, I think taking any team seeded 5 or worse in the Round of 64 is an unnecessary risk, and besides, you're better off saving those guys for the Round of 32 anyway (as I'll explain below). Therefore, I think the thing to do in the Round of 64 is to pick the #3 and #4 seeds with the best odds of advancing to the Round of 32, excluding teams that have a solid chance of going deep in the tournament. I consider #3 Florida to be a team with a solid chance of going deep, and so my Round of 64 selections are #4 Syracuse, #4 Michigan, and #3 New Mexico.

Round of 32: I'm lazy and don't feel like crunching the numbers on this, but there is a good chance that at least one team seeded 13-15 pulls a Round of 64 upset. If that happens, then that makes that team's Round of 32 opponent a virtual no-brainer. That opponent will be a) a solid favorite, b) seeded no better than 5, which is good for tiebreaking purposes, and c) unlikely to advance particularly deep in the tournament. This is another reason why I think it's best to save all teams seeded 5 or worse for the Round of 32, in case they get an easy Round of 32 matchup.

Of course, the fallacy with that argument is that a 13-15 seed upset could screw you over completely if you pick 3s and 4s in the Round of 64. Guess who those 13 and 14 seeds are matched up against? But that's why you take the 3/4 seeds with the highest chance of victory, as opposed to, say, Marquette. (For simplicity's sake, I've been using the Nate Silver numbers to gauge relative chances of victory.) If everything lines up right - the 3/4 seeds you picked all win, and at least one of the 3/4 seeds you didn't pick lose - then you're looking great at this point.

But if all 1-4 seeds win their first game, then this won't be easy. Then, you have to look for teams that have a good chance of victory, but not a good chance of advancing deep. I'm thinking 2 and 3 seeds will be the best choices in that case. Right now, I think #2 Georgetown is a good pick here, unless #3 Florida (their would-be Sweet Sixteen opponent, at which point we would certainly not want to pick Georgetown) somehow loses their opener, in which case Georgetown would have a relatively easy Sweet Sixteen matchup, meaning you'd want to save them for the following round. #2 Duke and #3 Michigan State might also be good options here. But it all depends on the upsets that happen in the Round of 64.

Sweet Sixteen: Now, it's time to start thinking about who you want to save for the end. Between the first Sunday and second Thursday, I'm sure TV pundits and online columnists will anoint one team as "the hottest team in the tournament". My advice is to ignore all of that completely, because playing well the first weekend is often just 1) noise, and/or 2) the result of drawing weak opponents. (Exhibit A: Florida last year.)

Instead, this will again be dictated by upsets in the first two rounds. If there is a #2 versus a #6 matchup in this round, and you don't think the #2 seed is one of the favorites to win the title, perfect! That's your pick. A #3 v. #7 game is also one to look at. Or, you could get really lucky and get something like a #1 v. #13 game, like last year with #1 North Carolina and #13 Ohio. But again, you might want to save that #1 seed for later depending on how good they are. Ideally, you want a team that is a solid favorite here, but that will be a solid underdog in the next round, but that might be hard to find. So much can happen in the first two rounds, it's hard to know where we'll stand at this point.

Elite Eight: Now you must have the following to consider. If one of the Final Four matchups features two teams that you have both picked previously, it will not be possible for you to make it all the way to the end. (See my example above.) If you've already used both East Region finalists, for example, then do not pick either of the South Region teams to win in this round (the East and South are on the same side of the bracket), or else you're setting yourself up for failure.

That's one restriction on your pick this round; the other is, as usual, to pick the team with the best odds of winning, but the worst odds of winning once they get to the Final Four. For example, if you have a regional final that's a #5 versus a #3, or something like that, that's a perfect time to use the #3. (If they're still available, which they may not be if you followed my advice in the first two rounds.)

Really, I think it will mostly come down to luck at this point anyway. All the games from here onward are likely to be competitive and come down to the end. So, maybe your best bet in this round, if you think you can predict how the other people in your pool will lean, is to go contrarian and hope things fall your way.

Final Four and Championship: Congratulations on making it this far! But now, it really comes down to luck, because you may not have much of a choice in who you pick. If you played your cards right, you'll have one of two scenarios:
- You've used two Final Four teams, one in each Final Four game. Then, the strategy is simple: take the team least likely to win the title first, and take the other team in the Championship game. This is assuming the goal is to make it to the end; if you could win the pool without going all the way to the end, then take the biggest favorite here and now.
- The only Final Four team you've used is the one you picked to win in the Elite Eight. In that case, and provided the the Final Four teams are all relative equals (which they may or may not be), the optimal strategy is to take the team playing against the team that you've already picked, right now. (Let's call this Team X.) This way, you only need two games (one Final Four game + the Championship) to go your way instead of three (both Final Four games and the Championship), and regardless you need Team X to win here to have a chance anyway, so you may as well make them your official pick. If Team X is a heavy favorite to win the title, though, and are reasonably confident about the outcome of the opposite Final Four game, then maybe you could justify taking the winner of the opposite Final Four game first followed by Team X in the Championship. But again, under that scenario you need all three Final Four games to go your way.

How would this strategy have panned out in last year's tournament? Let's go back and look:

Round of 64: Among 3/4 seeds, the heaviest Round of 64 favorites according to KenPom were #4 Wisconsin, #4 Indiana, #3 Baylor, and #4 Louisville. Wisconsin was a decent relative favorite to go all the way, though (4.2%), so I would have saved them, and instead used the other three. All three won. Next! Hey, good thing I didn't take #4 Michigan, amirite?

Round of 32: Any big upsets? Yes - in fact, TWO #15 seeds won! That makes their second round opponents - #7 Florida and #10 Xavier - virtual no-brainers. Both won. Next! (#13 Ohio also won, but they drew #12 South Florida instead of #5 Temple, so Ohio's opponent wouldn't have been a good pick.)

Sweet Sixteen: We have three double-digit seeds still alive: #10 Xavier (versus #3 Baylor), #11 NC State (versus #2 Kansas), and #13 Ohio (versus #1 North Carolina). I've already used Baylor, so that leaves UNC and Kansas. KenPom had UNC as the weaker of the two (making them a better pick in this round), but taking Kansas is more beneficial for tie-breakers, so I'm not sure what I would have done. In hindsight, UNC would have ultimately been the better pick here, because Kansas ended up beating them in the Elite Eight. But to make this exercise a little more difficult, let's use up #2 Kansas here and see what happens.

Elite Eight: Of the eight teams remaining, I've used four: #4 Lousville, #7 Florida, #3 Baylor, and #2 Kansas. And, Louisville and Florida play each other. Uh oh. That means I don't have much of a choice here. The Louisville/Florida winner plays the Kentucky/Baylor winner next, so I can't take Kentucky yet, or else I'm automatically screwed. So, I must take either North Carolina (v. Kansas), or Syracuse/Ohio State (v. each other). Based on the logic I outlined in the "Final Four" section above, the correct pick is to not depend on the outcome of the Syracuse/Ohio State game, and instead pick North Carolina.

North Carolina loses. Game over! Note that had I picked Ohio State (who beat Syracuse) instead of UNC, I still would have been screwed, because then Kentucky would have been my only unused Final Four team. The key selection was the Sweet Sixteen selection, in which I should have chosen UNC instead of Kansas. Then, I would have taken Kansas in the Elite Eight, and Ohio State in the Final Four (saving Kentucky for the end)...and still lost, because Kansas ended up beating Ohio State. In hindsight, the correct order for my last four picks would have been UNC, then Ohio State, then Kansas, and finally Kentucky. But the only way to know that would have been to know the outcomes of the games in advance, which of course we don't. See what I mean when I say it comes down to luck towards the end?

I can think of two lessons learned here:
- Don't worry about the "seed sum" tiebreaker at all from the Sweet Sixteen onward; just take the team that makes the most sense, independent of their seed. (Unless there are two equally optimal options, in which case, take the lower seed.)
- It is VITALLY important that you save the best teams for the end. If you use a team early and they end up advancing to the Final Four, or farther, it can really mess you up.

I'll update this post once throughout the tournament with my Survivor picks in each round. Enjoy the games!

Round of 64 (conservative): #4 Syracuse, #4 Michigan, #3 New Mexico
Round of 64 (aggressive*): #8 North Carolina, #8 NC State, #4 Michigan

(* - UPDATE: I did a quick Twitter search and found that the winner of last year's pool had a seed sum of 43. Even if I had gotten UNC/Ohio St/Kansas/Kentucky in the correct order, my seed sum would have only been 34. Based on that, maybe the optimal strategy is to go higher risk in the Round of 64 and shoot for a seed sum of 20+ with your first three picks, and hope for the best? By the way, according to Nate Silver's probabilities, the most likely seed sum of 20+ to verify in the first round is #8 North Carolina + #8 NC State + #4 Michigan, at 42.4%. Another decent option, at 40.0%, would have been #11 Minnesota + #6 Arizona + #4 Michigan, but I like the NC State option better because it doesn't use any potential Round of 32 opponents for 13-15 seeds.)

UPDATE Friday 3/22: New Mexico loses to Harvard! See why I didn't pay the entry fee? :) If UNC and NC State both win then I'll keep the "aggressive" picks going, otherwise, well, that was fun.

UPDATE Saturday 3/23: NC State loses to Temple, which isn't all that surprising, really. But hey, that Minnesota/Arizona/Michigan parlay I considered would have worked out okay, so let's see if I can keep that thread going. By the way, 78% of pool entrants are already eliminated.

Round of 64 (revisionist history): #11 Minnesota, #6 Arizona, #4 Michigan
Round of 32: #7 San Diego State (v. #15 FGCU), #4 Syracuse (v. #12 California)

UPDATE Monday 3/25: Well, that was fun.

No comments: