67 Yrs Of AP Rankings Final Top 4 Teams Have 47 Titles; 31 Runners-up; 45 F4 Losses

[dlh331]

The AP poll started in 1949. There have been 67 NCAAT since then and 268 Final 4 slots. Except for 2 years in 1974 and 1975 the AP ended their polls prior to the start of the NCAA tournament (IIRC) A breakdown of how each final position did regarding Final 4 visits:

#1 42 times with 21 NCAA Titles, 13 Runners-up, 8 Semi-Final losses
#2 33 times with 14 NCAA Titles, 6 Runners-up, 13 Semi-Final losses
#3 23 times with 8 NCAA Titles, 6 Runners-up, 9 F4 losses
#4 25 times with 4 NCAA Titles, 6 Runners-up, 15 F4 losses

Total for the AP Final Top 4 teams in 67 NCAAT
47 titles
31 Runners-up
45 Semi-Final losses
123 of the 268 Final 4 positions were taken by a Top 4 ranked team

Over those 67 years 4 unranked teams won the title and 5 unranked teams were runners-up.

Rankings matter a Hell of a lot. Not only are teams more in the news, recruiting is helped, the season is more fun and being at the top ALL THE TIME is what makes UK the best program ever. And....while being highly ranked doesn't gaurantee NCAAT success, it sure seems to be hand in hand.

One other thing, of UK's 8 titles here are our final rankings:

1948 No AP but #1 in the Premo-Poretta Power Poll
1949 #1 AP
1951 #1 AP
1958 #9 AP
1978 #1 AP
1996 #2 AP
1998 #5 AP
2012 #1 AP

 

[kybassfan]

That's a good amount of work. As I read your post, I think you are comparing the final four data with the final regular season ranking. Actually, I was surprised at first as to how poor the association was. The final season poll I would have thought to be very strongly linked to final four finishes. However, if we look at it as a predictor of final four finishes and then consider a false positive, the numbers are actually pretty weak, weaker that I would have suspected. Let's put some arithmetic behind this (pardon a bit of hand waving, gotta work with what I have).

So consider we can predict an event with probability p. p = successful outcomes/total outcomes. So then if we presume that one event is a predictor of another, a false positive is when the first event happens but the second doesn't. The computation for that is 1 - p. In our case, let's say we want to see how good a predictor the top spot in the final poll is relative to the actual winner. So we can use this notion to infer false positives from your data. Looking at the top spot in the poll as a predictor of the tourney winner, the false positive rate on that predictor is 1 - 21/67 = .69 or 69% of the time, that predictor is wrong. I'm not really surprised, though, that's a given ranking in a given spot which doesn't leave a lot of wiggle room.

So, now that we have the groundwork, let's crank a few numbers with rounding to the hundredths place.

False positive for top rank leading to tourney winner
1-21/67 = .69 or 69% false positive (as above)

False positive for top rank leading to final four finish
1-42/67 = .37 or 37%. Better, but still, nearly 40% of the time that top spot is an early out. I really didn't expect it to be that high.

So, let's group some stuff.

False positive for the top four rank leading to a tourney winner.
1- 47/67 = .30 or about 30% false positive. AH! A better predictor of a winner is to pick the top spot is to look at the top 4 rankings. Still, we are going to be wrong 30% of the time.

Now, here comes the handwaving. Using our model, we'd expect the the false positive for top four rank leading to a final four appearance would be:
1-123/268 = .54 or 54%. THAT SUCKS! I don't believe it, actually. What's happening here is some of these events aren't mutually exclusive (but they are independent when we get to the semi's because there is still two brackets at that point. So I think the actual false positive is really to consider the finishes as independent events leading to
(1-47/67)(1-31/67)(1-45/134) = .40*.46*.34 = .06 or about 6% false positive. Well, now. That's better and that's mostly correct (there's still an error factor in there but not a large one). Why? The probability of two independent events, a and b both happening is p(a)*p(b). Each round finish is independent the other.

So, here's the conclusions we can draw.

The polls are very poor predictors for any given finish. Shockingly so for an end of season poll. I was surprised how bad for both the specific ranking and the group ranking.

The polls are much better predictors for the group at the top finishing in the group at the top of the tourney.

I was surprised at how poor the polls were at predicting finish, until I thought for a bit . . . We know that top seeds end up on the side of the road early on such as when Duke took it on the chin from a 15 (a really great day)

Given all this, we can say that the polls really are not much more than fan candy. Any benefit folks think they have is perceived and not demonstrable. They don't tell us anything particularly meaningful. While we didn't compute actual correlation factors, we saw that the false positive rates are very high in most cases suggesting that correlation is weak. We also demonstrated that they can be useful at seeding in our last computation as our false positive rates dropped to something that is marginally useful as a predictor.

I'll also mention that I do not gamble because of the above math. There is a classic prob stat problem called the random walk. It is based on the theory above. The answer to the problem is that the guy ALWAYS falls off the cliff. Kenny Rodgers was right, you really have to know when to fold'em.