
 14 June 27, f: 3:25p It has come to my attention that all the analysis below is no good. The theory behind the method which converts the betting line into a probability was correct, but the execution was wrong: I was actually equating expected profit, and not expected value like I was supposed to. This is fixed, and with it all the numbers below have changed. I've decided that it's easiest to just replace the numbers as they are, but I'll note what's been updated in this dark green. Sorry about this; hopefully my work didn't get into any academic journals. Basically, the perfect bracket odds didn't change that much, only by a factor of 200 or so. But most of the ancillary predictions improved, or became sane when they were once insane. Really the middle line for the first round should be around 2210, not 248, for instance. And I now get that about 1 in 243 people should have picked Connecticut to win, instead of 1 in 1848 (the actual number was around 1 in 333). And so on. If you scratched your head before at my figures, have another look. If you've never seen this thread before, then you won't have your mind poisoned with incorrect information.
As penance, here's what the moneyline method predicts the likelihood is that the favorites will advance to the quarterfinals of the World Cup.
14 April 07, m: 11.20p Perfect bracket statistics, through day ten. (For the first update in the college basketball thread, use keyword: bracket.)
Fittingly Kentucky, the small favorite, loses the championship game. Round by round, favorites went 257, 115, 53, 22, 11, 01. The control bracket went 248, 106, 44, 13, 02, 01.
About 1 in 1,618,695,535,357,751 brackets should have been perfect. If you got a billion dollars for a perfect bracket, you were severely underpaid. Among Sweet 16 brackets, 1 in 34,784 brackets should have survived the chaos. The odds would suggest that about 1 in 243 people would pick Connecticut, which is in line with the data, since about 0.3% of brackets on ESPN picked Connecticut as the winner, so somewhere around 1 in 333.
Here's a link to the winning bracket.
14 April 05, sa: 11.35p Perfect bracket statistics, through day nine.
Favorites are 11 today: Connecticut (+260) wins again, busting everybody's brackets. On a personal note, go Huskies!
I'm 248, 97, 35, 22, 02. I got my finalists to the Final Four, so I can't be too upset that I was washed away tonight.
About 1 in 724,214,090,069,627 brackets should be perfect to this point, though I think I'm probably testing the limits of Google Drive's precision. I'll doublecheck the final answer. Among Sweet 16 brackets, roughly 1 in 15,562 are still unblemished.
That UConn win came to pass, and the two top brackets have been brushed aside. Two people are now tied at the top with identical lines: 257, 124, 71, 40, 20. Each has Connecticut winning the title, one by the score of 6556 and the other by 7165. The bracket in fourth place is the heir to the throne if Kentucky wins the title.
Not shockingly, having either finalist this year was a great accomplishment. There are at least 96 brackets that had both finalists on ESPN, which is reasonable (my numbers predict around 2739 of them, but since I only have access to the top 100, who knows how many of them were out there?). (Update 4/7: I can up that 96 number to 134.)
Compare this to how it would have looked if Florida played Wisconsin, where the percentages were 2.170% for both (1 in 46), 31.534% for one (1 in 3.2), and 66.296% for neither (1 in 1.5). So don't take the table above as being typical of the final: this was quite unexpected. Incidentally, my calculations suggest that somewhere around 239,000 people had a FloridaWisconsin final on ESPN (myself included), all of whom went from healthy to busted in the span of just a few hours.
14 March 30, su: 4.20p Perfect bracket statistics, through day eight.
Favorites are 11 today. Who saw Connecticut (+235) coming? They continued their surprising run today by upsetting Michigan State.
I'm 248, 97, 44, 13, 1/2, continuing a personal trend of flaming out in the Elite Eight. Actually, that means that my "B" bracket, left for dead a few rounds ago with Virginia and Wichita State in the Final Four, has jumped back in front at 257, 97, 35, 22, with both Florida and Wisconsin alive.
About 1 in 100,952,511,725,603 brackets should be perfect at this point. Among Sweet 16 brackets, roughly 1 in 2,169 should be perfect.
The overnight leader had Michigan State and falls out of the top spot. A pair of brackets are now tied at the top, one with a 248, 142, 71, 40 line, and the other 284, 124, 71, 40. Their two predictions are Florida over Kentucky and Florida over Wisconsin, so a second UConn win over Florida would wipe them off the board.
Connecticut has been the surprise of the tournament, for sure. Of the Final Four, they were by far the most difficult to predict: one in 29 brackets should have had them. Compare to one in 2.6 brackets for Florida, one in 6.2 brackets for Wisconsin, and one in 19.25 for Kentucky. (That gives like 38.44% that you had Florida in the Final Four, which accounts for most of the people who had one of the four teams here.) Here's the full breakdown by number of teams. The people who had the Final Four correct have floated to the top of the leaderboard since the penalty for getting a game wrong at this point in the tournament is very high. There's 69 people who have them all right among the top 100, which is on the right order of magnitude again (the numbers below predict around 121 of them).
14 March 29, sa: 8.00p Perfect bracket statistics, through day seven.
Favorites were 11 today, as Wisconsin (+130) snuck by Arizona.
I'm 248, 97, 44, 11, 1/2.
About 1 in 16,414,580,386,020 brackets should be perfect at this point. Among Sweet 16 brackets, roughly 1 in 353 should be perfect.
The leader at the end of yesterday's games had Florida and Wisconsin in today's two games, and so has survived the evening. The lead is sizeable (the equivalent of six firstround games), but every game from here on out is worth so much that he'll have to run the rest of the table to secure the crown.
14 March 28, f: 11:55p Perfect bracket statistics, through day six.
Favorites went 22 today, though Iowa State and Connecticut was a pick'em. (Other books had Iowa State as a tiny favorite.) Kentucky +160 was definitely an underdog.
I'm 248, 97, 44, 3/4.
About 1 in 5,654,200,980,876 brackets should be perfect at this point. Among Sweet 16 brackets (i.e., one filled out after the first weekend), roughly 1 in 122 should be perfect.
Our leader who was perfect in the second round had his bracket shredded by Iowa State's loss to Connecticut. The new leader stands alone at 293, 151, 62. (Somehow that doesn't sound as good to me as some of the other bylines, but that is pretty good.) There is only one perfect Elite 8s near the top of the leaderboard, but my model predicts that there should have been a handful more. (As many as 47 or so, actually. Were people just unlucky?) We've reached the point where there's a real chance that you've got nobody left standing.
14 March 27, th: 11;45p Perfect bracket statistics, through day five.
Favorites went 31 today, as Dayton (+140) stayed alive.
I'm 248, 97, 31, 3/4.
About 1 in 370,132,041,778 brackets should be perfect at this point.
We started the day with two people at 293, 151, 7/8, but both of them had already lost the StanfordDayton game before it started. So a sea change is assured. Of the three brackets which had a perfect second round, only one had Dayton, and he assumes the lead at 266, 160, 40. The leader's bracket has Dayton in the Final Four, where they're supposed to lose to Iowa State. Obviously the injury to Niang was not part of his prognostications.
14 March 26, w: 10.30a Giddy with the knowledge that I can compute these things so readily, here's the likelihood of getting a given number of teams correct in the Sweet 16. I thought 248 was pretty good in the first round, and indeed it's better than three in four brackets. But I was bracing myself to discover that 97 in the second round was woeful, and in fact it's still at about the same level: only one in three brackets manages to put nine or more teams into the Sweet Sixteen.
14 March 25, tu: 3.55p Here's a sanity check on my method. Since we have the odds for any individual game, it's easy to determine the odds of an event like going 311 in the first round. To that end, I predict that about 1 in 117,933 brackets would be 311 in the first round. In the pool of roughly eleven million brackets on ESPN, this would predict roughly ninetythree 311 brackets. There were thirtyfive, so I'm off by a factor of about 2.6 here. As a second sanity check, I get that roughly 1 in 2,883,667 brackets should have gotten the entire Sweet 16 correct. This would correspond to about 3.8 brackets on ESPN. I don't have full access to everyone's results, but from the top hundred brackets there are three people who managed 266, 160. I can rule out from what I can see that anyone went 160 in the second round who was 275 or better in the first round, or 257 either. It's possible that some people who were 248 or worse in the first round went 160 in the second round, but this seems like a pretty remote possibility. In any case, it seems to have been a good prediction for this.
With a suggestion from George I was able to calculate the probability of coming up with any given record in the first round. The 50% line fell somewhere between 239 and 2210: about 40% of brackets were 239 or better this year, while about 58% of brackets were at least 2210. About one in two hundred had 29 wins, while about 199 in two hundred managed to go at least 1616. The number 3,332,316 should look familiar from my update a few days ago. I'll include percentages unless they look like all zeros, and I'll group numbers in batches of six to try to make them legible.
14 March 23, su: 11.00p Perfect bracket statistics, including day four.
Favorites are 53 today, with Stanford (+280), Kentucky (+175), and Baylor (+145) pulling upsets. The control bracket took some hits this round; it's now 248, 106, 5/8, 3/4. Favorites were 115 in the second round. (Is it possible to come up with a "favorites bracket"? You'd need to be able to predict what the linesmakers are going to think.)
My "B" bracket was busted with Wichita State, but the "A" bracket is 248, 97, 6/8.
About 1 in 46,535,957,021 brackets should be perfect to this point. (Still fifteen games to go, too! Where will the final number wind up?)
We started the day with a fourperson pack at 302, 80, 8/8, but Stanford wiped them all out. The next set of leaders all were washed away by Kentucky, and so on; nobody has held the top spot longer than one game today. The current leaders are 293, 151, 7/8, but there are some unblemished brackets lurking one game behind. We'll get some guess as to the number of people who picked the entire Sweet 16 correct in the morning. Also on the docket for this week: what is the probability distribution for wins in the first round, and what are the odds of having the Sweet 16 correct? These are questions I should be able to answer.
14 March 23, su: 12.15a Perfect bracket statistics, through day three.
Favorites went 62 today, with Dayton (+300) and Connecticut (+165) the surprises. Those were the two lower seeds to advance.
I'm 257, 62, 6/8, 6/8.
About 1 in 280,005,568 brackets should be perfect to this point.
Dayton finished off the three remaining 311, unblemished brackets, and almost washed all of the people who went 311 off the leaderboard altogether. The last two went out with Wisconsin. Now there are four people at 302, 80, 8/8 yet to default on a future game.
14 March 22, sa: 11.45a Perfect bracket statistics through day two.
Favorites were 124 today. The underdogs to win were Mercer (+850!), Stanford (+190), Gonzaga (+170), and Stephen F. Austin (+205). So the favorites went 257 in the first round. Three lower seeds were underdogs, and so the "control bracket" is 248, 15/16 with Duke the blemish.
About 1 in 3,332,313 brackets should be perfect to this point. (There's no point in giving the percentage, as it has a bunch of zeros.)
I'm 257, 14/16, 7/8.
The number of perfect brackets on ESPN became countable after Stanford beat New Mexico, getting us down to 58. Stephen F. Austin put down the last three undefeated brackets. After that there were 53 brackets at 271, but only 11 of them don't have further blemishes. The day ended with eight brackets tied at 311, 16/16. Thirtyfive entries wound up with a 311 record.
14 March 21, f: 12.15p Perfect bracket statistics, through day one (16 games).
Favorites are 133: Dayton (+260), North Dakota State (+150), and Harvard (+145) pulled upsets.
The percentage of brackets that should be perfect so far is 0.1607898%; that's about 1 in 622 brackets.
I'm 133, 16/16.
There are still too many perfect brackets on ESPN to count.
14 March 21, f: 11.40a keyword: bracket With the heightened awareness of the unlikelihood of a perfect bracket this year, in the airport yesterday I wondered how to measure exactly what the odds are of picking every game correctly, after the fact. If you pretend that every game is a coin flip, then there's
2^{63} = 9 223372 036854 775808, or about 10^{19}, different brackets, and of course only one of them will actually be the correct one. But every game is not a coin flip. A 1seed has never lost to a 16seed, for instance, and some of the other games are also very lopsided. When you sit down to fill out a bracket you don't spend a second mentally flipping a coin to see if Villanova will beat WisconsinMilwaukee. That's a free pick. The cool thing for us in this pursuit is that there are sites that (to a first approximation) measure what the likelihood is that a bracketmaker will pick any given team. The betting moneyline is set up to entice equal action on both sides of the game, which means that the line matches the aggregate public perception of the probability that either team will win. There's two details here: "in aggregate", since of course any individual person could look at the line and say it's way off, and bet accordinglybut this is no problem for us, since the idea is to estimate the likelihood that an average bracket will be perfect, so the public's average is what we need to assess. The second detail is more nettlesome, namely that the betting line is designed to get an equal amount of money to fall on both sides, and not necessarily an equal number of people. We'll make an assumption here that this won't affect things too much, and ignore this problem. (Probably the amount of money bet on each game is large enough that the number of people betting on each side roughly matches the amount of money put on each side, anyway.)
It's important to realize that I'm not claiming that the moneyline can tell you the probability that either team will actually win. That would be sorcery. We just need to know what people think is the likelihood that either team will win, because that's the quantity that is relevant for who picks what in their brackets.
How do you get from the moneyline to these implied percentages? With the assumption that the expected value has to be balanced. Take the morning's first upset, #11 Dayton defeating #6 Ohio State. The moneyline was Ohio State 320, Dayton +260. This means a bet of $1 on Ohio State returns 100/320 = $0.3125 (hence has a value of $1.3125 when Ohio State wins), while a bet of $1 on Dayton returns 260/100 = $2.60. What probability would make these two outcomes seem equal? If the probability of Ohio State winning is p, then the expected value of a $1 bet on Ohio State is 1.3125 × p, while the expected value of a bet on Dayton is 3.6 × (1p). Set these two equal to each other and solve for p, and you get p = 0.7328. So the implied probability of Ohio State winning was about 73.25%, and only about one in fourish brackets should have had Dayton.
There are of course problems with this: the moneyline reflects current information, as of the day of the game, while our perfect bracketeer would have to have anticipated matchups in later rounds weeks in advance. An injury to a key player on a highlyranked team, for instance, would cause a big rift between the expected bracket behavior and the betting public's behavior. I hope that these errors don't contribute too much to the overall picture. In the updates above I'll keep track of the moneyline predictions of how many perfect brackets are still out there, along with some information about how the ESPN leaderboard is doing and how my own bracket is holding up.
13 December 31, tu: 7.20p keyword: horizon 3a The Horizon
13.12.26, th: 11.10p Ever since I realized I was underwater
I've been pushing up,
Swimming up toward the depths
To which the sunlight can penetrate.
So far it's been nothing but darkness,
Inky brine unwelcomed pressing against my eyes.
The horizon? Don't talk of the horizon—
Not until I've fulfilled a hunger for the vacuum of air
Pushing at my gills after I've broken the surface.
13 July 08, m: 7.55p keyword: wedding 1a words of congratulation at a wedding
13.06.22, sa: 11.25p i'm sorry i came.
my role was to delay the best part,
the moment when i leave
then the apartment will grow silent
and you will
exhale, and sit down on the couch
by yourselves. the only vestiges of the party
are two broad smiles on your faces,
telling the nobody left to see you
this marriage is more than a wedding.
rather it is a series of private glances
and hands interlocked
and evening hours looking at the moonlight.
it's really happening. it starts tonight.
