The NCAA Tournament as Metaphor

[sagegrouse]

Satan vs. Beelzebub vs. Snoopy vs. BoPeep
Who's in the Final Four? Uh, that would be UConn, Kentucky, Butler, and VCU.

Pizza and Cartoon Network in the Athletic Center
What did the VCU players do during the NCAA Selection Show? No one was predicting the Rams as a tourney team, so they blew it off.

Four for fricking twenty-one?
What did Arizona shoot from three against UConn after going 9-15 against Duke? Teams can have bad games or they can face incredibly hot teams. For Duke it was the latter.

Eleven wins, ten losses
What's the record in the tournament so far of the best conference in the history of the universe -- the only conference to ever get eleven bids to the NCAAs? UConn can drive the percentage up to 56.5% by winning its next two games. The ACC finishes at 66.7% with eight wins and four losses. Anyone else believe the Big East was overrated?

"Houston, escape velocity has been reached"
How good are the offers being prepared for Brad Stevens and Shaka Smart by desperate colleges tired of missing the tournament?

Ten percent
How many NCAA brackets have even one team in the Final Four? And is every one of those a Kentucky or UConn fan?

Surely, each of you can do better than these.

sagegrouse

[uh_no]

Four for fricking twenty-one?
What did Arizona shoot from three against UConn after going 9-15 against Duke? Teams can have bad games or they can face incredibly hot teams. For Duke it was the latter.


Take away 5 3 pointers and Arizona still wins....There were issues other than them being a 'hot team,' most notably the rebounding.

[sporthenry]

Take away 5 3 pointers and Arizona still wins....There were issues other than them being a 'hot team,' most notably the rebounding.

Well I find that by going only on the box score never does near enough justice. Lets say Williams shoots 1-6 from 3 instead of 5-6 (which is what he shot vs UCONN as opposed to vs Duke and his shots vs UCONN appeared to be rather open just as vs Duke). Not only did he hit the one at the end of the half but he hit 3 in the last 4 minutes. So lets say he shoots 2-6, you really don't think it is a different ball game if Duke is up 15 at half?

[uh_no]

Well I find that by going only on the box score never does near enough justice. Lets say Williams shoots 1-6 from 3 instead of 5-6 (which is what he shot vs UCONN as opposed to vs Duke and his shots vs UCONN appeared to be rather open just as vs Duke). Not only did he hit the one at the end of the half but he hit 3 in the last 4 minutes. So lets say he shoots 2-6, you really don't think it is a different ball game if Duke is up 15 at half?

No doubt...I was simply pointing out that there were numerous other issues in the game, among which arizona's 3 point shooting was one, and it is wrong to sit here and say 'duke only lost because arizona was hot and Uconn only won because arizona was cold,' since neither is the truth

[sporthenry]

No doubt...I was simply pointing out that there were numerous other issues in the game, among which arizona's 3 point shooting was one, and it is wrong to sit here and say 'duke only lost because arizona was hot and Uconn only won because arizona was cold,' since neither is the truth

Well obviously any time a better/equal team gets blown out there are some other issues. But this Duke team got rattled and I wouldn't say they quit but they just got down and seemed to have little answers when things kept going wrong. So sure, you can cite the terrible defense where the lane just opened up and couldn't get a rebound (although a few were just unlucky) but had Williams not hit his 3's, Duke wins. Had Duke rebounded better in the 2nd half, Duke still might not have won since their offense was atrocious.

[sagegrouse]

It's all Rick Barnes's fault
Twelve seconds left, leading by two points, Arizona misses, and Texas's star, Jordan Hamilton, grabs the rebound. "Time out," Hamilton calls. Time out? Time out!!!!!!????? No, give the ball to J'Covan Brown and head for your front court. Zona will foul, and the Longhorns get a chance to ice the game. J'Covan was 13-13 at that point. At worst, the Wildcats have to go the length of the court to score against a set defense, as opposed to running a play for a layup under its own basket. It's coaching, Texas. It's coaching.

On the conversation above, even though Uh Oh is my man, I'm with Sport Henry that the dynamics of the game matter a lot. Arizona made two ridiculous threes against perfect defense in the latter moments of the first half. A 12-point lead at halftime could have made a huge difference and created some doubt in the "can't-miss" Wildcats.

sagegrouse
'Postscript: After I posted the message, I got a pop-up ad for vacations in Texas. Nice. I spent five years after Duke in Texas, and I like parts of it. Austin is a lot of fun, as is San Antonio. I got into the Gulf Coast, esp. the Laguna Madre and Matagorda Bay. I always wanted to go to Big Bend country, where the town of Alpine at 4,500 feet is supposed to offer some non-Texas climate in the sumer months'

[Faison1]

It's all Rick Barnes's fault
Twelve seconds left, leading by two points, Arizona misses, and Texas's star, Jordan Hamilton, grabs the rebound. "Time out," Hamilton calls. Time out? Time out!!!!!!????? No, give the ball to J'Covan Brown and head for your front court. Zona will foul, and the Longhorns get a chance to ice the game. J'Covan was 13-13 at that point. At worst, the Wildcats have to go the length of the court to score against a set defense, as opposed to running a play for a layup under its own basket. It's coaching, Texas. It's coaching.

The funny thing is, I was pretty thankful Arizona took out Texas. At the time, I would have much rather faced Arizona.

We can also take it one step further:

It's All Memphis' Fault!
I watched the first half of the Memphis/Arizona game and thought, "that's good....one less high-seed that Duke needs to worry about." But when Arizona pulled off the comeback, I figured it didn't really matter, because Duke had other teams it needed to be concerned with.

[Greg_Newton]

No doubt...I was simply pointing out that there were numerous other issues in the game, among which arizona's 3 point shooting was one, and it is wrong to sit here and say 'duke only lost because arizona was hot and Uconn only won because arizona was cold,' since neither is the truth

Well, it's not wrong to say that Arizona was only in the game at halftime because they were hot. Everything that happened afterwards was a consequence of that, and the circumstances it produced.

Saw somewhere that only 2 people had correctly predicted the final four in their ESPN brackets. Honestly, I'm surprised anyone got it at all (side note, how mad would you be if you had picked VCU, Butler, UK and Arizona?)

[uh_no]

Saw somewhere that only 2 people had correctly predicted the final four in their ESPN brackets. Honestly, I'm surprised anyone got it at all (side note, how mad would you be if you had picked VCU, Butler, UK and Arizona?)

You should not be suprised. There are only 65536 possible combinations of final four teams. Out of 6,000,000 brackets, about 100 should have gotten it correct. This is of course assuming independent picks, which obviously does not happen...either way, though, i was suprised at the low number

[Greg_Newton]

You should not be suprised. There are only 65536 possible combinations of final four teams. Out of 6,000,000 brackets, about 100 should have gotten it correct. This is of course assuming independent picks, which obviously does not happen...either way, though, i was suprised at the low number

Umm... this is not a minor distinction. The number of people who use a coin flip to decide every pick is miniscule.

I mean, the fact that someone picked not just UConn, but ALSO UK over the overall #1 seed, and ALSO Butler, despite being an 8-seed, and ALSO VCU, the consensus (at the time) worst at-large team in the tournament who wasn't even favored to make the round of 64 is mind boggling to me.

I assume it had to have been a Slumdog Millionaire-type scenario. You know, someone that grew up in Lexington, went to undergrad at VCU, went to grad school at UConn, and currently resides in Indianapolis... there's just no way you could have made those picks based on basketball knowledge and intuition.

[SuperTurkey]

I assume it had to have been a Slumdog Millionaire-type scenario. You know, someone that grew up in Lexington, went to undergrad at VCU, went to grad school at UConn, and currently resides in Indianapolis... there's just no way you could have made those picks based on basketball knowledge and intuition.

Nope, I just listened to an interview with the guy who won ESPN's bracket challenge -- he picked all 4 and is a grad of none of them. He lives in NJ and seemed to have no rational explanation for why he picked the teams he picked.

[Newton_14]

Umm... this is not a minor distinction. The number of people who use a coin flip to decide every pick is miniscule.

I mean, the fact that someone picked not just UConn, but ALSO UK over the overall #1 seed, and ALSO Butler, despite being an 8-seed, and ALSO VCU, the consensus (at the time) worst at-large team in the tournament who wasn't even favored to make the round of 64 is mind boggling to me.

I assume it had to have been a Slumdog Millionaire-type scenario. You know, someone that grew up in Lexington, went to undergrad at VCU, went to grad school at UConn, and currently resides in Indianapolis... there's just no way you could have made those picks based on basketball knowledge and intuition.

I would love to know how many brackets those 2 people filled out. There is just no way on earth anyone who filled out only 1 bracket would have gotten all 4 of those teams correct. Not any knowledgeable basketball fan anyway. I would bet many people had both UK and Uconn in their bracket, and likely a few that had Butler, given how weak that region was. No rational fan would have picked VCU to go from a play-in game all the way to the Final Four under any circumstance.

[SuperTurkey]

I would love to know how many brackets those 2 people filled out. There is just no way on earth anyone who filled out only 1 bracket would have gotten all 4 of those teams correct. Not any knowledgeable basketball fan anyway. I would bet many people had both UK and Uconn in their bracket, and likely a few that had Butler, given how weak that region was. No rational fan would have picked VCU to go from a play-in game all the way to the Final Four under any circumstance.

The guy interviewed on ESPN sounded far from knowledgeable. His son created the pool on ESPN when he should have been doing his homework, so the ESPN winner asked to be part of the pool as a way of shaming his son for mucking around with brackets when he should have been studying. Seems like the guy knew nothing about the schools aside from some vague references to them 'having good coaches.'

[cspan37421]

You should not be suprised. There are only 65536 possible combinations of final four teams. Out of 6,000,000 brackets, about 100 should have gotten it correct. This is of course assuming independent picks, which obviously does not happen...either way, though, i was suprised at the low number

About 100 turns out to be 91.55 ... but even then:

I think you are mistaken. The 65536 figure you gave is 64 choose 4 [hold on- I had that and now I don't - I get 636,376 - how did you get 65536? Isn't 64 choose 4 64!/(60!)(4!) = 64*63*62*61*60!/60!*4!= 64*63*62*61/24 = 636376?]; this tournament - especially evidenced by VCU's presence in the Final Four - is 68 choose 4, which is 814,685 possible combos. If there was a random distribution of choices (which of course there is not) one would expect 7 correct brackets. So 2 is low, but not so low at all under that assumption.

Another way to look at it, though, is let's say for argument's sake that 12 through 16 seeds have zero chance. Historically, that's more realistic. So that leaves 44 teams. Now it's 44 choose 4, though I forget how the extra 4 play-in teams are figured. Maybe it's more like 46 choose 4 - weren't there extra 12 and 16 seeds? So let's count a couple extra 12 seeds. For that, 46 choose 4, or 163,185, and out of 6 million brackets, you'd expect about 37 correct under the random choice assumption (again, suspect, but less so than under 64 choose 4 or 68 choose 4). So 2 now appears pretty low again, but still not so bad as when you expect 92.

If your 65536 should be 636376, then instead of 100 or 92, you should be comparing to 9. So my correction makes it compared to 7, but slightly more realistically, it should be compared to 37.

Still pretty rare.

[Duke: A Dynasty]

I would love to know how many brackets those 2 people filled out. There is just no way on earth anyone who filled out only 1 bracket would have gotten all 4 of those teams correct. Not any knowledgeable basketball fan anyway. I would bet many people had both UK and Uconn in their bracket, and likely a few that had Butler, given how weak that region was. No rational fan would have picked VCU to go from a play-in game all the way to the Final Four under any circumstance.

Well for ESPN you can only do 10.

[uh_no]

About 100 turns out to be 91.55 ... but even then:

I think you are mistaken. The 65536 figure you gave is 64 choose 4; this tournament - especially evidenced by VCU's presence in the Final Four - is 68 choose 4, which is 814,685 possible combos.

the 65536 is NOT 64 choose 4....not even close in fact (off by an order of magnitude in fact). 65536 is 16^4. You would use the first figure if any of the 64 teams could end up in any of the 4 slots, but they cannot. Since each of the four slots is limited to a set of 16 teams, it is effectively (16 choose 1)^4, or simply 16^4, which is 65536. The figure you quoted of 91.5 is, in fact, correct though.

The figure should NOT include the extra 4 teams since brackets are not due until after the first 4 are played.

[cspan37421]

the 65536 is NOT 64 choose 4....not even close in fact (off by an order of magnitude in fact). 65536 is 16^4. You would use the first figure if any of the 64 teams could end up in any of the 4 slots, but they cannot. Since each of the four slots is limited to a set of 16 teams, it is effectively (16 choose 1)^4, or simply 16^4, which is 65536. The figure you quoted of 91.5 is, in fact, correct though.

The figure should NOT include the extra 4 teams since brackets are not due until after the first 4 are played.

Oh of course, so the choose business would only work if any 4 could be final four - but in reality, only one from each region. Gotcha.

And you only ruled out 17^4 because brackets weren't due (to ESPN I guess) until after the so-called first round was done?

[uh_no]

And you only ruled out 17^4 because brackets weren't due (to ESPN I guess) until after the so-called first round was done?

Yeah, pretty much. If you include the play in games, the number expected number of random brackets to correctly guess the final four significantly decreases. In the 16 team instance, out of 16 brackets, the expected number of brackets that have each team winning is 1. For the 17 team instance, the expected number is 1 for all teams but the 2, for whom it is .5. Therefore the expression to determine the number of brackets becomes 6000000/(16*16*16*32). The 32 represents VCU, who came out of the play in game. The resulting value is 45 correct brackets.

What would be a more interesting exercise is to take the kenpom or some other predictor % chance of a team making the final four at the start of the tourney and using THAT information to figure out (if people were rational) how many people should have picket that bracket

[4decadedukie]

Satan vs. Beelzebub vs. Snoopy vs. BoPeep
Who's in the Final Four? Uh, that would be UConn, Kentucky, Butler, and VCU.

Pizza and Cartoon Network in the Athletic Center
What did the VCU players do during the NCAA Selection Show? No one was predicting the Rams as a tourney team, so they blew it off.

Four for fricking twenty-one?
What did Arizona shoot from three against UConn after going 9-15 against Duke? Teams can have bad games or they can face incredibly hot teams. For Duke it was the latter.

Eleven wins, ten losses
What's the record in the tournament so far of the best conference in the history of the universe -- the only conference to ever get eleven bids to the NCAAs? UConn can drive the percentage up to 56.5% by winning its next two games. The ACC finishes at 66.7% with eight wins and four losses. Anyone else believe the Big East was overrated?

"Houston, escape velocity has been reached"
How good are the offers being prepared for Brad Stevens and Shaka Smart by desperate colleges tired of missing the tournament?

Ten percent
How many NCAA brackets have even one team in the Final Four? And is every one of those a Kentucky or UConn fan?

Surely, each of you can do better than these.

sagegrouse


Great post, my friend. Please let me know when you return . . . the Silver Diner awaits.

[sagegrouse]

Yeah, pretty much. If you include the play in games, the number expected number of random brackets to correctly guess the final four significantly decreases. In the 16 team instance, out of 16 brackets, the expected number of brackets that have each team winning is 1. For the 17 team instance, the expected number is 1 for all teams but the 2, for whom it is .5. Therefore the expression to determine the number of brackets becomes 6000000/(16*16*16*32). The 32 represents VCU, who came out of the play in game. The resulting value is 45 correct brackets.

What would be a more interesting exercise is to take the kenpom or some other predictor % chance of a team making the final four at the start of the tourney and using THAT information to figure out (if people were rational) how many people should have picket that bracket

Uh Oh, the reasoning for 68 teams is not as complicated as you propose. IMHO (where the H is characteristically silent) it is as simple as throwing darts at a board. If there are 16 teams, the chance is 1/16. If there are 17 (like two regions) or 18 teams (like one region), it is 1/17 or 1/18. I did the math on the whole field, and there were 83,000 possibilities, such that if everyone had selected teams randomly before the First Four, there would be 70 correct answers out of 5.8 million. If there are 16 teams, I believe you pointed out that there would be 100 correct entries by chance. Instead, there were TWO.

I think we can all agree it is a surpassingly strange tournament, when the number of correct FF entries is one-fiftieth of what one would expect from picking teams randomly. I know "a little learning is a dangerous thing," but in this case, "knowing everything about college basketball" was utterly useless in the NCAA tournament pool.

sagegrouse

[uh_no]

IMHO (where the H is characteristically silent) it is as simple as throwing darts at a board. If there are 16 teams, the chance is 1/16. If there are 17 (like two regions) or 18 teams (like one region), it is 1/17 or 1/18.

Unfortunately the analogy does not hold since 2 of the teams play one more game. From their perspective, getting to the final 4 will only happen with a probability 1/2^5 since to them, the bracket might as well be a 32 team bracket. Since they play 1 extra game, it is in effect, half as likely for one of them individually to be in the final four, but just as likely that one of the two teams from that play in game make the final four as it would be for any other individual team. If you could develop a bracket where each of the 17 teams played an equal number of games, then you would, in fact be correct, bus since we can't run a round robin tournament here, that's the way it has to be.

take the big east tournamnet for example. by your logic, each team, regardless of bye status would have a 1/16 chance to win. This is untrue. The double by teams would have a 1/8 chance, the bye teams would have a 1/16 chance, and the last 8 would have a 1/32 chance.

[Indoor66]

You math types make this ole country lawyer's head explode.

[sagegrouse]

Unfortunately the analogy does not hold since 2 of the teams play one more game. From their perspective, getting to the final 4 will only happen with a probability 1/2^5 since to them, the bracket might as well be a 32 team bracket. Since they play 1 extra game, it is in effect, half as likely for one of them individually to be in the final four, but just as likely that one of the two teams from that play in game make the final four as it would be for any other individual team. If you could develop a bracket where each of the 17 teams played an equal number of games, then you would, in fact be correct, bus since we can't run a round robin tournament here, that's the way it has to be.

take the big east tournamnet for example. by your logic, each team, regardless of bye status would have a 1/16 chance to win. This is untrue. The double by teams would have a 1/8 chance, the bye teams would have a 1/16 chance, and the last 8 would have a 1/32 chance.

We are working different problems. The problem I am attacking is how well an utterly random pick of teams compares with actual result. In that case, every team has the same weight, and therefore, it is a matter of combinations.

Your argument seems to go on who has the best chance to win. Uhhh,... that isn't what we are trying to decide. We are talking about throwing a dart blindly at a board with equal spaces for 16, 17 or 18 teams, depending on the region. Who has the best chance -- or longest road -- doesn't enter the consideration because we are trying to establish that utterly blind and stupid picks are 50 times more accurate than the informed picks supposedly represented by 5.8 million entries in the ESPN contest.

sagegrouse