March Madness Champion
by wtfitzhomie on Mar 26, 2008 1:10 AM CDT
24 comments
I just started doing a project today for one of my classes regarding correlations, and I just wanted to share my initial research regarding March Madness:
I've researched from the present all the way up till the 1997-1998 year, and I would appreciate it if one of you statistical gurus could look deeper into this. Those Kentucky Wildcats finished the year with a 13 game winning streak. Since 2000 however, I think the highest was 12 (please correct me if I'm wrong).
It's common knowledge, for a variety of reasons, that winning the next game during a winning streak become harder than the previous one, up till the point where the odds make it close to impossible to keep the streak going.
Here are the current streaks of the Sweet 16 teams and what the streak would be if they won the whole Tournament in parenthesis:
NC - 13 (17)
UCLA - 12 (16)
Memphis - 9 (13)
Kansas - 9 (13)
Wisconsin - 12 (16)
Tenn - 2 (6)
Texas - 2 (6)
WSU - 2 (6)
Louisville - 2 (6)
Vill - 2 (6)
Davidson - 25 (29)
Stanford - 2 (6)
Mich State - 2 (6)
Western Kentucky - 8 (12)
Xavier - 2 (6)
WVU - 2 (6)
Kentucky had the 13 game winning streak back in a time where it was still possible for teams to stockpile talent for a whole variety of a reasons (less competition for recruits, lesser technology, etc.) so we will make the 12 game winning streak as the highest in the "Modern Era" and set it as a base. There are obvious flaws in this, but there has to be a max point in the data set. The minimum point is 6 (which has occurred 3 times out of the last ten years, so it isn't exactly an outlier).
I know this is selective data, but even without doing a basic probability distribution, it cames as a great surprise that all four number one seeds have the odds stacked against them when it comes to winning the championship. This is not to say they will not make the Final Four or the championship game; just that the actual probability of them winning the Championship game is extremely low. We can thus also eliminate Wisconsin, Davidson (who ironically will play each other), Villanova, and Western Kentucky (highest seed to win, #8 Villanova in 1985).
Somebody correct me if I'm wrong, but no coach has ever won the Championship in their first appearance in the Final Four. We can thus also eliminate Tenn, Stanford, WSU, & Xavier.
This leaves us with the teams most likely to win it all this year:
Texas, Louisville, Michigan State, & WVU.
Once again, this is selective data, but your opinions/bashings are appreciated.
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It's common knowledge, for a variety of reasons, that winning the next game during a winning streak become harder than the previous one, up till the point where the odds make it close to impossible to keep the streak going.
Common knowledge to who? Intuitively that's an incorrect statement. Statistically it is impossible to keep an infinite winning streak, because in each game there is a chance of losing. But this chance does not increase by the size of winning streak.
the actual probability of them [4 #1 seeds] winning the Championship game is extremely low
Just because they are on a roll? Vegas for sure disagrees with you, and Vegas is rarely wrong. "the actual probability" does not come from your so-called correlations.
no coach has ever won the Championship in their first appearance in the Final Four. We can thus also eliminate Tenn, Stanford, WSU, & Xavier.
Tubby Smith did it with Kentucky. Also, you can't say Texas has never won a championship, so they will never win one!!
by Cyrus on Mar 26, 2008 1:40 AM CDT reply actions 0 recs
well
Vegas doesn't set their odds based on any objective mathematical probability, they set it based on what gives them the best chance to make money. The only thing that strong Vegas odds on all four #1 seeds reaching the final four means is that Vegas believes public opinion and betting trends strongly back those four teams above all others; therefore those teams should have the highest odds to limit bettor payout and potential casino losses(i.e. $100 bet on UNC at 2/1 odds pays out $200 while $100 bet on UNC at 5/1 pays out $500. If tons of money is going to a team you could lose a lot if they have big odds). Unless there's a compelling reason not to, Vegas probably picks the four 1 seeds EVERY year.
Mathematically speaking the odds of all four #1 seeds making it is in fact quite low. The odds of any specific 4 team combo making it are I think 1/256. Is a UNC-UCLA-Kansas-Memphis final 4 a lot closer to reality than a WSU-Davidson-WKU-MSU final 4? Probably so; but the fact that four 1-seeds have never done it should tell you something.
by the chairman211 on Mar 26, 2008 8:30 AM CDT up reply actions 0 recs
From my math
The odds that 4 specific teams out of the 64-team field , without regard to ranking and all the other factors that come into play, are 1/4096. But at this point it is 1/256.
As far as the winning streak goes, it's only statistically harder when projecting more than one game into the future. It really has no bearing on the very next game in the streak, because you still have as great a chance to win or lose that game as you did in the previous games of said streak.
Hope that makes sense.
by orangeblood1 on Mar 26, 2008 9:20 AM CDT up reply actions 0 recs
statistics
binomial probability theorem states for any of these teams to win exactly 4 of their next 4 games (with a 50/50 shot at winning/losing), the odds of that happening is 6.25%
on average each team has a 1/16 chance of winning (some might have a better chance, but for them to have a better chance someone else has a worse chance, but it still averages to 1/16).
1 / 16 = .0625 btw.
"Common knowledge to who? Intuitively that's an incorrect statement. Statistically it is impossible to keep an infinite winning streak, because in each game there is a chance of losing. But this chance does not increase by the size of winning streak."
The probability of success (or conversely, failure) does factor into the probability of the length of the winning streak.
by UTFan85 on Mar 26, 2008 12:43 PM CDT up reply actions 0 recs
no
Read Meekrob response for a better explanation.
by Cyrus on Mar 26, 2008 4:24 PM CDT up reply actions 0 recs
no?
not sure if you're talking to me or not (your message is in reply to mine), but if that was to me, then my response is "yes".
by UTFan85 on Mar 26, 2008 4:53 PM CDT up reply actions 0 recs
again, read meekrob's response
If you don't understand what he says (and I was trying to say in my response as well), take an undergrad statistics course.
by Cyrus on Mar 26, 2008 6:00 PM CDT up reply actions 0 recs
hm
i was looking at his post saying
"If it has to happen. It'd be harder to believe if it didn't happen."
not the one that agrees with what i'm saying 100%
"However, from this point forward, the past doesn't matter in probability. Everyone needs a 4 game winning streak from here on out.
Think of it this way. If I flipped a normal, non-weighted coin ten times, and it came up heads 10 times, the chances of the next flip being heads are still 50%, even though the chances of getting 11 heads in a row, at the outset, is 1 / (2 ^ 11). I think."
this is exactly what i was saying... the future still matters, and using the same math he did (which i mentioned in my post). 1/2^4 = .0625. just like 1 / (2 ^ 11) =~ 0.0004882
i fail to see where you find a difference between what the two of us are talking about? respectfully, you need to re-read whats been posted. and perhaps you should re-take an undergrad stats course, because i'm currently ace'n mine. . .
by UTFan85 on Mar 26, 2008 10:52 PM CDT up reply actions 0 recs
You may be ace'n your stats course...
... but you would both fail any kind of communications seminar.
Don't be jerks. UTFan85, Cyrus is saying you're right about a winning streak having a probability of 1/2^n, where n is the number of games won (considering every game is against an equal opponent, and we're not talking about the "pressure" of keeping a long streak going getting into the players' heads or anything dorky like that - those two factors are unquantifiable from the information we are given, so we assume a simplified model). So, yes, when the Rockets lost their last game before their streak started, the odds that they would win 22 in a row were 1/2^22, or 0.0000238% - the same as if they had flipped coins to decide the games.
The thing, I think, that is causing this misunderstanding is that UTFan85 said:
The probability of success (or conversely, failure) does factor into the probability of the length of the winning streak.
I'm not really sure what this means. Did you mean the probability of success of the winning streak? Like, success if you win 10 games in a row but failure if you only get 9? That's not right, so I think you mean the probability of success in a given game, which is 50% under the assumptions we have to make. So, that's basically just a restatement of P(Winning streak of length n)=p(winning a game)^n where p(winning a game) is 50%. By that rule, then, the limit of P as n goes to infinity is zero, so Cyrus' statement that
Statistically it is impossible to keep an infinite winning streak, because in each game there is a chance of losing. But this chance does not increase by the size of winning streak.
was correct. I think Cyrus just misunderstood that enigmatic statement and took it to mean the inverse - The probability of the length of the streak factors into the probability of success (of winning the next game) - because you'd already discussed the whole P=p^n thing and that was old news, he thought you were talking about something else. If I am wrong in trying to interpret that statement, I apologize.
Basically, solve this problem by untangling that riddle you replied to Cyrus' statement with. Then quit telling each other to go take stats courses.
by Horn Brain on Mar 27, 2008 8:39 AM CDT up reply actions 0 recs
Although
this is the same thing as saying the probability of my dying today would be 50%, because either I would die or I wouldn't (and then ignoring my health or other factors). If people want to get into a stats discussion, then that's up to them, but figuring out a probability based on the binomial theorem for winning and losing is extremely oversimplified. The binomial theorem only applies when the events are independent of each other.
A Trojan can only be used once. A Bruin is forever.
by uclawarren on Mar 27, 2008 10:01 AM CDT up reply actions 0 recs
That's why people die eventually
A living streak of over 100 years is damn near impossible!
by Meekrob on Mar 27, 2008 10:24 AM CDT up reply actions 0 recs
Partially...
... why it's not worth yelling at each other about.
by Horn Brain on Mar 27, 2008 11:44 AM CDT up reply actions 0 recs
perhaps i should have clarified
The probability of success (or conversely, failure) does factor into the probability of the length of the winning streak.
i felt like that reply was already too long, so i didn't feel like explaining it before.
Basically, solve this problem by untangling that riddle you replied to Cyrus' statement with.
let me see if this is better, the actual probability of the success or failure of the coin flip does not change with the total number of trials. i agree with his statement of this (i was not arguing it).
the probability of having a streak of all heads / tails does change (it decreases) as the number of trials increases.
i believe the confusion comes from myself first, i think i missed the keyword
But this chance does not increase by the size of winning streak.
which lead me to interpret it as the chance of winning / losing does not having a bearing on the length of the streak and he was only looking at singular trials (each game is a trial and should not be seen as a set).
my statement merely says that the probability of a result in a trial does affect the probability of a streak of results (ie. if i have a 50% chance of flipping heads, then i have a .09% chance to get exactly 10 heads in a row. but if i have a 90% chance of flipping heads, then i have a 34.8% chance to get exactly 10 heads in a row.)
he looks at each game on a singular trial basis, whereas i think you should look at it as a set where talking about high level theory (which is all we're talking about since no one has the actual % chances of teams winning, and they fluctuate game by game. and yes, because they fluctuate game by game you might want to look at it as a single trial basis, but we're trying to extrapolate 4 games/trials from now).
it also doesn't help that neither of us really knows what he found fault with... since the entirety of his response was "no".
by UTFan85 on Mar 27, 2008 10:37 AM CDT up reply actions 0 recs
The odds of a winning streak of X games
Go down only from the start of the streak. So, before the streak begins, it is harder to get a 10 game winning streak than a 9 game winning streak (obviously, since you can't have a 10 without a 9).
However, from this point forward, the past doesn't matter in probability. Everyone needs a 4 game winning streak from here on out.
Think of it this way. If I flipped a normal, non-weighted coin ten times, and it came up heads 10 times, the chances of the next flip being heads are still 50%, even though the chances of getting 11 heads in a row, at the outset, is 1 / (2 ^ 11). I think.
by Meekrob on Mar 26, 2008 8:00 AM CDT reply actions 0 recs
However
what is discounted is that each of these coin-flips is independent of each other. While I don't necessarily believe that at this point of the (post-) season the psychology of winning streaks comes into play, but during many long winning streaks during the season (like maybe 15 or more), players start to think about continuing that streak and start pressing a little bit more, perhaps gambling or doing things they wouldn't normally do if they had only won 2 or 3 in a row. This is why a lot of coaches talk about how it's good to have a loss here and there during the regular season, because that pressure builds up. I believe that since 1976 (when Indiana went undefeated), no team has entered the NCAA tournament undefeated and won it all. Obviously, none of these teams was undefeated coming into the tournament, but I think the same might hold up for a winning streak of a certain length.
Having said all that, I think what is more important is the winning streak prior to the tournament. If a team has won 15 or 20 games going into the tournament, it might be more difficult with that pressure building up than for a team which has won 5 or 6 games entering the tournament. But if it is 11 games (which appears to be the maximum on this list, held by UNC), I don't think players are thinking about winning streaks, and they are just focused on each game at this point.
Also, I don't think you can eliminate #1 seeds, as #1 seeds have won the tournament 6 of the last 10 years.
A Trojan can only be used once. A Bruin is forever.
by uclawarren on Mar 26, 2008 12:09 PM CDT up reply actions 0 recs
Exactly, it's more about a unified mindset
All stats aside, the winner every year has one thing in common. Every starter and bench player on that team wants to win it more than any other team in the tournament.
To win six games in-a-row against the toughest competition in the country is an unbelievable achievement in any team sport, if you think about it. Physical ability plays a big part in achieving that goal, of course, but just like any other sport, half of the battle is convincing your mind that it's possible.
by UTAth on Mar 26, 2008 12:29 PM CDT up reply actions 0 recs
Unbelievable?
It has to happen. How can it be unbelievable?
I know what you mean, I just think people overuse that word.
by Meekrob on Mar 26, 2008 1:40 PM CDT up reply actions 0 recs
nitpicking and using in correct context
I don't know why you chose to target that one word, but I did use it in the correct context according to the definition below.
of such a superlative degree as to be hard to believe
If something is unbelievable, it doesn't mean it isn't possible. Merriam-Webster Online Dictionary uses this example..."made an unbelievable catch in center field". I think the word can be used in a somewhat slang form and that is how I was using it.
I don't know if the word is overused or not. I haven't really noticed. That was fun though. I enjoy looking things up on Google.
by UTAth on Mar 26, 2008 1:59 PM CDT up reply actions 0 recs
But it's not hard to believe
If it has to happen. It'd be harder to believe if it didn't happen.
by Meekrob on Mar 26, 2008 2:14 PM CDT up reply actions 0 recs
Agree to disagree
This is a childish conversation. Let's stick to talking about sports instead of grammar usage.
by UTAth on Mar 26, 2008 2:24 PM CDT up reply actions 0 recs
good answer!!
... especially since you're wrong!!! : )
nitpicky to be sure, but one team does it every single year, and I guarantee you one team will do it again this year, so...
well, I believe it!!
It is, however, like you were talking about there, an outstanding achievement, and one that certainly takes as much mental strength and heart as physical ability.
by agent orange on Mar 26, 2008 2:33 PM CDT up reply actions 0 recs
This site is replete
with gramatical misuses. I find it unbelievable that you chose to focus on this minutia.
by Brandon 97 on Mar 26, 2008 3:10 PM CDT up reply actions 0 recs
But
I believe that since 1976 (when Indiana went undefeated), no team has entered the NCAA tournament undefeated and won it all.
I don't think this proves or disproves that pressure build up actually hurts your chances of winning.
Because teams so seldom go undefeated in the regular season, the fact that an undefeated team has actually won the tournament at all is some what surprising, though not unbelievable.
I think we probably should defer to coaches who say this happens because they are the people who have the most insight into the players mindset But then again, it is in the coaches interest for people to believe this even if it is not true, as it makes for a great excuse when they lose to someone they should not.
by Wells on Mar 27, 2008 1:42 PM CDT up reply actions 0 recs
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