Calculating implied NCAA 2nd RD MLs?

[djiddish98]

(For the record, I am ignoring all this play-in game = 1st round nonsense that the NCAA has been pushing the past 2 years. The 1st round in this post refers to field of 64, while the 2nd round refers to field of 32).

We've got a lot of useful data points to work with during March Madness. One method I'm trying to determine the value of is related to calculating 2nd round implied MLs, based upon the known 1st RD MLs and the Sweet 16 odds.

Here is how I've setup the calculation (using pinny pricing as of 8:20 AM EST)

1st RD ML
SD St.: +121 (44.14% no vig)
NC State: -134 (55.86%)

Belmont: +153 (38.57%)
Georgetown: -170 (61.43%)

Will make it to the sweet 16?
Georgetown: Yes +144, No -169 (Yes = 39.48% no vig)
SD St.: Yes +600, No -858 (13.76%)
NC State: Yes +269, No -330 (26.10%)
Belmont: Yes +284, No -351 (25.07%)


The calculation of P(Will make sweet 16) should be equal to P(Win game 1) * P(Win game 2), if my basic understanding of probability is correct.

Since we have P(Make sweet 16) & P(Win Game 1), we can solve for P(Win Game 2) by dividing P(Make sweet 16) by P(Win Game 1).

Some interesting results occur, mainly that IF Belmont wins their game against Georgetown, they have an implied 2nd RD ML of 65.01%. That seems pretty high to me: I would expect a spread of around -2 maybe against NC State or SD State, as opposed to what appears to be -4.5 (just guessing). Additionally, if I'm filling out my bracket, and have Belmont beating Georgetown, it seems as if I might as well advance them another round given these odds.

My question is - is this calculation valid? One error I can see if that, when calculating will make Sweet 16 odds, I'm taking the no-vig % of the yes/no odds, as opposed to the no-vig of all the yeses of the group. There's a bit of an over-round by doing this for the group (Sum = 104.41%), but typically, I'll only have odds from 2 or 3 of the teams from the bracket cluster, as opposed to a full set like this one.

Are there any other mistakes? Is this information not really that interesting?

[djiddish98]

As a follow up, I calculated the odds by taking all the Yes values for (Will make sweet 16), for the cluster, and compared it to the results from taking the Yes/No noVig%

Belmonth - 62.29% vs. 65.01%
NC St - 44.75% vs. 46.72%
Georgetown - 61.54% vs. 64.26%
SD St - 29.85% vs 31.17%

The numbers still don't add up to 200%, so there's probably some tweak I need to make.

[cyberbabble]

I'll try it.
You have four teams - A, B, C, D.
1st round - two games - AB and CD
2nd round - one game, but four matchup possibilities - AC, AD, BC, BD
What you want, I think, is the implied odds lines for each of the 4 matchups.
These all need to be worked out separately. Odds for (A in AC game) not = odds for (A in AD game).
Right?

I used the SBR>tools>Odds converter to get no vig probabilities for 1st round games.
SD St +121 ---> 45.25% NC St -134 ---> 57.26% but 45.25 + 57.26 = 102.51, so adjust win %,
SD St --> 45.25/102.51 = .44 = no vig win probability NC St --> 57.26/102.51 = .56 no vig win probability.
Same process for the others.
Bel --> .39 and GT --> .61 no vig probabilities in their game.
SD St .13, NC St .25, Bel .24, GT .38 - no vig probabilities to get to 16-round.

pr(2nd round game is AC) = pr(A wins in round 1) * pr(C wins round 1).
This gets probabilities for which MATCHUP will occur in the 2nd round, not individual team odds.
Four of these gets probability for each of the matchups that can happen in the 2nd round game.

pr(A in Sweet16) = pr(AC matchup)*pr(A wins AC game) + pr(AD matchup)*pr(A wins AD game).
pr(A in Sweet16), pr(AC matchup), pr(AD matchup) are known, want to calculate pr(A wins AC game), etc.
Make 3 more of these equations. Solve them. I think that this would work.

You get a projection for what the teams and odds will be in the 2nd round game when the matchup is determined, but what is the bet you want to make?

[Jayvegas420]

So as long as you're right in the 1st round you would have a certain win with GT meeting NCST, to see who goes to the sweet 16 but, you end up losing 10-15 units by losing the all other games besides NCST?