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Pairwise Rankings


jimdahl

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Michigan has won 8 in a row and 10 of their last 12. After a sweep at the hands of Western Michigan at the end of January (2-3 and 1-5), they reversed the tables in the first round of the CCHA playoffs, beating the Broncos 4-3 on Friday night and then SMOKED the defending CCHA playoff champions 5-1 on Saturday night. The Wolverines have not played Miami since October and will face them Saturday afternoon at Joe Louis Arena in front of a nice partisan maize and blue crowd. I've got Michigan winning Saturday...but closer than the experts think.

Michigan is hot at the right time. They're scary because a team thats playing for their season is extremely tough to beat. Add to that a team that is playing well and you've got your hands full.

I think Michigan beats Miami and nips Notre Dame for the title.

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Methodology

Unlike the regular season forecasts which are based on monte carlo simulations, the above tables were produced by exhaustively searching all remaining possible outcomes, so the table should be complete. The probabilities presented in the forecasts are the share of remaining possible outcomes in which that event occurs. The predictions about the likelihood of a team making the NCAA tournament assume that the PWR rankings will perfectly mimic the NCAA selection process, as they have in the past, and that any ties will be broken by RPI.

Jim, do I understand this correctly?: The probabilities used are the share of the remaining combinations, without any weight given to the likelihood of the outcomes? (i.e. The system considers scenarios equally likely where UND or CC wins the first game.)

If that's the case, I think I should prefer results found with a monte carlo simulation.

(BTW, I really like the way the results are presented in that blog post.)

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They are the sexy pick right now, and I believe they would get Quinnipiac, the locked in number 1 seed, correct?

No, as the host of the Grand Rapids regional, they would be placed there. Quinnipiac should get placed in Providence, the closest regional to their school.

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No, as the host of the Grand Rapids regional, they would be placed there. Quinnipiac should get placed in Providence, the closest regional to their school.

unless Brown were to upset them and win the ECAC then brown would go their as the host school and QU would be sent elsewhere.

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Jim, do I understand this correctly?: The probabilities used are the share of the remaining combinations, without any weight given to the likelihood of the outcomes? (i.e. The system considers scenarios equally likely where UND or CC wins the first game.)

If that's the case, I think I should prefer results found with a monte carlo simulation.

(BTW, I really like the way the results are presented in that blog post.)

That's right, the table is the share of remaining possible outcomes.

The big reason I do it that way is because it's mathematically irrefutable. I can state these shares as fact, and no one can come up with any disagreeing predictions. A weighted prediction would instead require me to use some subjective predictor of game outcomes.

There are a couple reason it's not as bad as you think -- The predictors aren't as strong as during the regular season. Using KRACH, participants in a single conference's tournament tend to have similar strengths, such that 90% of the games don't become more biased than 65-35. Quinnipiac is an obvious exception; but on the flip side, KRACH says Michigan is a 2:3 underdog. So, I'm instead trying to give people the facts and let them ascertain what they think is likely.

And the predictors' deviations from 50-50 are only magnified for very low probability events. Teams that make it through in about 50% of scenarios also make it through in a similar number of weighted scenarios. It's the guys who make it in only 4% of scenarios that might find that the 4% is a pretty unlikely corner, such that it's only 1% weighted.

However, doing a weighted run so people can see and compare should be no problem. I'll try to do it.

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unless Brown were to upset them and win the ECAC then brown would go their as the host school and QU would be sent elsewhere.

Dear jesus no.....please no. That is not good. Then BC would get sent to that regional with Brown, and likely UND as like a #2 seed and possibly a Niagara or a Notre Dame as a three.

No....just no.

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That's right, the system is share of remaining possible outcomes.

The big reason I do it that way is because it's mathematically irrefutable. I can state these shares as fact, and no one can come up with any disagreeing predictions. A weighted prediction would instead require me to use some subjective predictor of game outcomes.

There are a couple reason it's not as bad as you think -- The predictors aren't as strong as during the regular season. Using KRACH, participants in a single conference's tournament tend to have similar strengths, such that 90% of the games don't become more biased than 65-35. Quinnipiac is an obvious exception; but on the flip side, KRACH says Michigan is a 2:3 underdog. So, I'm instead trying to give people the facts and let them ascertain what they think is likely.

And the predictors' deviations from 50-50 are only magnified for very low probability events. Teams that make it through in about 50% of scenarios also make it through in a similar number of weighted scenarios. It's the guys who make it in only 4% of scenarios that might find that the 4% is a pretty unlikely corner, such that it's only 2% weighted.

However, doing a weighted run so people can see and compare should be no problem. I'll try to do it.

Jim

Jim, I respect your intellect a ton, especially when it comes to this stuff. However, when I read information like this, it reminds me of when I was a kid watching the Snoopy Halloween, Thanksgiving, or Christmas specials...you know, the ones where you don't have a clue what the teacher in Charlie Brown's class is saying and can't understand why it's just gibberish?

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Jim, I respect your intellect a ton, especially when it comes to this stuff. However, when I read information like this, it reminds me of when I was a kid watching the Snoopy Halloween, Thanksgiving, or Christmas specials...you know, the ones where you don't have a clue what the teacher in Charlie Brown's class is saying and can't understand why it's just gibberish?

In close to plain English, I'm saying that the tables I published assume that each game has an equal chance of going either way. Kirk is saying he would prefer that the outcomes that depend on Minnesota beating Colorado College be listed as more likely than vice versa. I replied that the problem with that is choosing how much more likely Minnesota is to win... do they stand an 80% chance, a 60% chance?

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Dear jesus no.....please no. That is not good. Then BC would get sent to that regional with Brown, and likely UND as like a #2 seed and possibly a Niagara or a Notre Dame as a three.

No....just no.

I'm not scared of BC this year. they are a good team but not of the caliber of ones we have seen in the last 5-6 years. i'd take being in a regional with them over minnesota any day of the week.

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I guess I'm in the court that says, at this point, when you can define and run all 300-plus-thousand scenarios and then look at the statistical outcomes, why not do it that way.

And right now, things like KRACH may be undervaluing Michigan's current play and overvaluing Quinnipiac's recent play. I was never a fan of the "Last 16 Games" criteria when the Committee used that in selections, but I'd argue it makes some sense in doing analysis like Jim is doing here. As Tommy Lasorda used to say, "You're only as good as your last at bat." Michigan's last at bats are pretty good but KRACH really doesn't show that.

Knowing all the scenarios (inputs) and outcomes (outputs) makes it pretty clear who needs what to happen. I like that when it's a defined possible set.

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