Now that the brackets have all been set for the second round of the CCHA tournament, I started thinking about what Michigan's chances are of advancing to the Joe. Western stole a game off of us, so they aren't to be taken too lightly, but they aren't a good hockey team either.
One of the neat things about the KRACH ratings system (as previously discussed) is that you're supposed to be able to compare teams' KRACHs to give you an expected winning percentage. Using a little (fairly simple) probability theory1, it's then possible to predict the chances each CCHA team has of winning its series and predicting the chances of a sweep or whether Game 3 is on the horizon.
Chart? Chart.
Well then. Notre Dame and Michigan are both-near locks to advance. Miami is fairly solid, though KRACH doesn't take into account how hot Northern has been lately, so that's probably a bit high. Likewise, it's really down on Alaska, and it's kind of unfair, though not without its reasons. Alaska had a brutal and short list of non-conference opponents, losing to anyone with half a pulse. They did get a tie against a very good Northeastern team, but that was a. the season opener and b. in Alaska. Non-conference games are disproportionately valuable in any college hockey ranking system, so Alaska's KRACH got hammered by losing to Maine and getting swept by Anchorage. This is reflected in the fact that OSU is a 2:1 favorite to advance. Realistically, I'd put it at more like a 55% chance that the Buckeyes make it through. The first game in the series is often a very tough one for a team that's just arrived in Alaska. Couple that with a well-rested Chad Johnson in goal and I like the Nanooks' chances in Game 1. If they take that game, suddenly the numbers say they're a 5:3 favorite to advance. Projecting a little further out, the question then turns to what are the chances of each of these teams of hoisting the Mason Cup? Well, we'll assume that each team will have to play the toughest possible schedule (by KRACH) to claim the championship. For example, Michigan has to beat Western, then Miami, then Notre Dame. Northern would have to beat Miami, then Notre Dame, then Michigan on its theoretical path. Let's go to the chart:
Way to go, Captain Obvious. Yeah, I know. It's shocking to learn that Northern, Western, and Nebraska-Omaha are ridiculous longshots to win it all, and that their best shot at the finals is to buy tickets at the group rate. It is interesting, however, to see that Miami's such a longshot, and that we're slightly better than a 50/50 bet to make the finals. We'll see how this all plays out on the ice.
Notre Dame
vs. UNO Michigan
vs. Western Miami vs.
Northern Alaska vs.
Ohio State
Team 1 KRACH
540.3
391.3
238.9
137.0
Team 2 KRACH
115.2
89.9
136.9
216.9
T1 sweep
67.94%
66.13%
40.41%
14.99%
T2 sweep
3.09%
3.49%
13.27%
37.56%
P(Game 3)
28.97%
30.38%
46.32%
47.45%
T1 series win
91.82%
90.83%
69.86%
33.35%
T2 series win
8.18%
9.17%
30.14%
66.65%
Probability of winning...
This
Series Semi-
final Final
Notre Dame
91.82%
65.52%
38.00%
Michigan
90.83%
56.40%
23.69%
Miami
69.86%
36.61%
11.23%
Alaska
33.35%
12.16%
6.41%
Ohio State
66.65%
31.71%
9.08%
Northern
30.14%
6.09%
1.58%
Western
9.17%
1.31%
0.36%
UNO
8.18%
1.86%
0.61%
1 – If you really want the math, leave a comment2.
2 – If you really want the math, you almost certainly know how to do it already. And are a dork.
5 comments:
I have a suggestion for the advancement probabilities. Instead of assuming the hardest possible schedule, you should use all possible schedules with your previous calculations and get the total probability.
For example, Michigan's chances of winning the next round would be .5640*.6986 + (Prob Michigan beats Northern)*.3014
It probably wouldn't change any of the numbers by more than a few percentage points. Although Miami, Alaska and Ohio St would be candidates for change.
I'd try to do something like that, but my limited knowledge of probability makes that unwieldy. To know the true chances, I'd have to figure out the chances of Michigan playing each team in the next round, which means I'd have to figure out the probability of things like "What if Northern and UNO both advance?" If you total up the last column right, there's a 9.5% chance that some other path is needed for any of these teams to win the title. My gut tells me Notre Dame probably benefits the most from a fuller analysis, since they'd get first crack at any weaker seed advancing, with the effects trickling down to Michigan.
There's also the effect that re-seeding has on the field. For example, Michigan can't play Northern in the next round. If Michigan and Notre Dame advance, no lower seed can be left in the field, so they have to play Notre Dame. If Notre Dame fails to advance (I know, good one), then Michigan is the top remaining seed and must play UNO, the lowest remaining seed. Maybe I can find a method to mitigate the pain of figuring out all the possible combinations.
looks like there's a 9% chance no team wins the final......
Right, I totally forgot about the re-seeding. That does make it a lot more complicated and probably would make Notre Dame benefit the most.
It shouldn't require much more probability theory, each matchup is independent so the probability of Northern and UNO advancing is just the product of their individual probabilities of advancing. Each team's chance of winning next round would be the sum of Prob(winning a matchup)*Prob(that matchup occurs) for all possible matchups.
It does however require a decent amount of combinations. There are 16 choices of semifinal teams. After that though, there are only 8 possible finals teams and you already have the probability of each one occuring. Basically, all the hard work is in the semifinal round.
@chriscamzz: Not really. There's a 9% chance that the winner has to take some path we haven't identified here. For example, we're assuming that Notre Dame will have to beat UNO, OSU, and Michigan to win the title, when in reality Notre Dame could end up playing Alaska, OSU, Northern, or Western in the semifinal and Miami, Alaska, OSU, or Northern in the title game. Unlikely paths to the championship are where the extra 9% is.
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