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Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodies
- Thread starter TonyTheTiger20
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TonyTheTiger20
#SOAR
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie
All of our systems are down at work today so actually getting this done at noon was easy
Week VII Posters Poll
Week VII Chart: http://i.imgur.com/E6Zwmdt.jpg
Mercyhurst even more of an outlier this week.
All of our systems are down at work today so actually getting this done at noon was easy
Week VII Posters Poll
Code:
[U][B]Rank Votes Team (1st place votes) [I]Range (Mode)[/I] Last week (change)[/B][/U]
1. 168 Boston College (15) [I]1-2 (1)[/I] 2 (+1)
2. 145 Minnesota (1) [I]1-5 (2)[/I] 1 (-1)
3. 136 Wisconsin (1) [I]1-5 (3)[/I] 3 (0)
4. 119 Quinnipiac [I]3-5 (4)[/I] 5 (+1)
5. 109 Harvard [I]2-8 (5)[/I] 4 (-1)
6. 66 Boston University [I]6-NR (6)[/I] 6 (0)
7. 58 Clarkson [I]5-NR (7)[/I] 9 (+2)
8. 45 Bemidji State [I]6-NR (8)[/I] ARV (+3)
9. 41 Mercyhurst [I]6-NR (6)[/I] 8 (-1)
10. 14 North Dakota [I]6-NR (10)[/I] 10 (0)
[U][B]Also Receiving Votes:[/B][/U]
10 Cornell [I]6-NR (10)[/I] 7 (-4)
9 Minnesota-Duluth [I]7-NR (10)[/I] ARV
8 Vermont [I]9-NR (10)[/I] ARV
7 Ohio State [I]8-NR (7.5)[/I] ARV
[U][B]Dropped Out:[/B][/U]
St. Lawrence
Yale
Northeastern
RITWeek VII Chart: http://i.imgur.com/E6Zwmdt.jpg
Mercyhurst even more of an outlier this week.
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie
This looks way more accurate than the official polls.
This looks way more accurate than the official polls.
TonyTheTiger20
#SOAR
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie
Collectively anyway.
I'm telling you, we're smarter than those people!
Collectively anyway.
Hux
Alfond to Ridder & rinks in between
What did you do, plant a virus or something of the like?.
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie
None of us is as dumb as all of us.
None of us is as dumb as all of us.
Clearly
Timothy A
Let's go RED!
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie
That's a telling stat. I'm not a pairwise expert, but does bc's creme filled pastry opponents record hurt them in the pairwise?
I've been a proponent of Mercyhurst, but this opponent's cumulative record is 9-33-6, not so good. Based on that, sure looks to me like bc is getting a free pass and then some. I for one think I have them (bc) over-ranked. Mercyhurst has OSU next week, that will be a telling game.
The Midwestern Elitist in me looks at these numbers and says hmmm....
Record of opponents:
Minnesota - 33-21-8
WisconSIN - 29-22-7
bc - 8-28-8
More hmmm.... Minnesota has played one opponent with more wins (9) than the combined win total for all of bc's opponents.
Whoopie pies...Cupcakes...whatever the hell you want to call them, bc has devoured them.
That's a telling stat. I'm not a pairwise expert, but does bc's creme filled pastry opponents record hurt them in the pairwise?
I've been a proponent of Mercyhurst, but this opponent's cumulative record is 9-33-6, not so good. Based on that, sure looks to me like bc is getting a free pass and then some. I for one think I have them (bc) over-ranked. Mercyhurst has OSU next week, that will be a telling game.
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie
I am!
I am!
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie
I was one of the ones who put BC not-first, for exactly this reason: we simply can't tell how good they are against tough opposition. I toyed with keeping them at #3 because Wisconsin and Minny have both had much harder schedules to date, but the fourth-line production against Providence persuaded me that BC have depth that will count in the long run. But, yes, right now it's hard to tell whether their results are due to them genuinely being top-rank or due to their cupcakey opponents. They're good, but how good exactly?
I was one of the ones who put BC not-first, for exactly this reason: we simply can't tell how good they are against tough opposition. I toyed with keeping them at #3 because Wisconsin and Minny have both had much harder schedules to date, but the fourth-line production against Providence persuaded me that BC have depth that will count in the long run. But, yes, right now it's hard to tell whether their results are due to them genuinely being top-rank or due to their cupcakey opponents. They're good, but how good exactly?
TonyTheTiger20
#SOAR
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie
Yes. The biggest component is RPI, which is calculated as 30% BC's record, 24% BC's opponent's records, and 46% BC's opponent's opponent's records.
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Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie
The biggest component of a team's RPI is its own record, despite what the coefficients are. That's because the value for the winning percentage in question converges rapidly to .500 with each step. There is far more variance in the winning percentage of individual teams than there is in the aggregate winning percentage of full slates of opponents, and there is a lot more variance in the aggregate winning percentage of a single team's slate of opponents than there is in the aggregate winning percentage of all of the opponents of all of those teams. The coefficients have to keep getting bigger in order for there to be any difference between the values returned to the formula and I'd be curious to know just how much of a difference the 0.46 times opponents' opponents' winning percentage actually makes. My guess is not a lot.
The biggest component of a team's RPI is its own record, despite what the coefficients are. That's because the value for the winning percentage in question converges rapidly to .500 with each step. There is far more variance in the winning percentage of individual teams than there is in the aggregate winning percentage of full slates of opponents, and there is a lot more variance in the aggregate winning percentage of a single team's slate of opponents than there is in the aggregate winning percentage of all of the opponents of all of those teams. The coefficients have to keep getting bigger in order for there to be any difference between the values returned to the formula and I'd be curious to know just how much of a difference the 0.46 times opponents' opponents' winning percentage actually makes. My guess is not a lot.
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie
It's .46 times opponents' win%, .24 time opponents' opponents' wins, just to be accurate.
Rutter has the current table: http://math.bd.psu.edu/faculty/rutter/Current_D1_RPI.html. Currently, WINP goes 1 to 0, OPWP goes 0.85 to 0.21, and OPOPWP goes 0.63 to 0.29. So currently about as much range is provided by OPWP (range is 0.2756) as WINP (range is .3, by definition). You'll expect to see both of these get pulled in as the season goes on. Range provided by OPOPWP is 0.08; as the season goes on you'd expect to see that diminish too. It would be interesting to look at the figures from the end of last season, but I don't know if they're still available.
It's .46 times opponents' win%, .24 time opponents' opponents' wins, just to be accurate.
Rutter has the current table: http://math.bd.psu.edu/faculty/rutter/Current_D1_RPI.html. Currently, WINP goes 1 to 0, OPWP goes 0.85 to 0.21, and OPOPWP goes 0.63 to 0.29. So currently about as much range is provided by OPWP (range is 0.2756) as WINP (range is .3, by definition). You'll expect to see both of these get pulled in as the season goes on. Range provided by OPOPWP is 0.08; as the season goes on you'd expect to see that diminish too. It would be interesting to look at the figures from the end of last season, but I don't know if they're still available.
TonyTheTiger20
#SOAR
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie
So you want the part that matters the least in determining how good someone is -- because everyone's OPOPW% is going to be pretty close anyway -- to make the biggest difference?
So you want the part that matters the least in determining how good someone is -- because everyone's OPOPW% is going to be pretty close anyway -- to make the biggest difference?
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TonyTheTiger20
#SOAR
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie
Nah wwhyte you have it backwards
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie
You're right, I do. That's crazy!
You're right, I do. That's crazy!
TonyTheTiger20
#SOAR
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie
By the way, here are the RPI rankings with different multipliers:
Win%,OppWin%,OppOppWin%
.30/.24/.46 (Actual)
1 Quinnipiac .6802
2 Boston College .6718
3 Minnesota .6669
4 Wisconsin .6564
5 Dartmouth .6379
6 Harvard .6343
7 Boston University .6184
8 Princeton .5939
.33/.33/.33 (Equal)
1 Minnesota .6825
2 Quinnipiac .6760
3 Wisconsin .6712
4 Boston College .6499
5 Boston University .6262
6 Dartmouth .6180
7 Harvard .6155
8 Clarkson .5893
.14/.29/.57 (Progressive)
1 Minnesota .6474
2 Wisconsin .6381
3 Quinnipiac .6330
4 Boston College .6298
5 Boston University .6103
6 Bemidji State .5965
7 Princeton .5810
8 Clarkson .5796
.57/.29/.14 (Regressive)
1 Quinnipiac .7430
2 Minnesota .7308
3 Dartmouth .7292
4 Harvard .7281
5 Wisconsin .7193
6 Boston College .7177
7 Boston University .6719
8 Mercyhurst .6379
By the way, here are the RPI rankings with different multipliers:
Win%,OppWin%,OppOppWin%
.30/.24/.46 (Actual)
1 Quinnipiac .6802
2 Boston College .6718
3 Minnesota .6669
4 Wisconsin .6564
5 Dartmouth .6379
6 Harvard .6343
7 Boston University .6184
8 Princeton .5939
.33/.33/.33 (Equal)
1 Minnesota .6825
2 Quinnipiac .6760
3 Wisconsin .6712
4 Boston College .6499
5 Boston University .6262
6 Dartmouth .6180
7 Harvard .6155
8 Clarkson .5893
.14/.29/.57 (Progressive)
1 Minnesota .6474
2 Wisconsin .6381
3 Quinnipiac .6330
4 Boston College .6298
5 Boston University .6103
6 Bemidji State .5965
7 Princeton .5810
8 Clarkson .5796
.57/.29/.14 (Regressive)
1 Quinnipiac .7430
2 Minnesota .7308
3 Dartmouth .7292
4 Harvard .7281
5 Wisconsin .7193
6 Boston College .7177
7 Boston University .6719
8 Mercyhurst .6379
ARM
Fan of chipmunk-like mascots.
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie
Disclaimer: Now Cornell could very well be much better than it has shown so far, but RPI doesn't know that.
Ideally, I don't want RPI used at all, but I doubt that is an option in my lifetime. The best way to get an at large berth under the current system is schedule the softest group of opponents possible. If you are a team that is in the neighborhood of the top 10 or 12 teams, you will win enough games to get in. If you don't, you aren't good enough to get in with any other scheduling approach anyway. It isn't a coincidence that the RPI, and thus, PWR, rank as No. 1 and No. 2 a pair of teams that haven't played any TUC opponents. Little ventured, but much gained.
Disclaimer: Now Cornell could very well be much better than it has shown so far, but RPI doesn't know that.
TonyTheTiger20
#SOAR
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie
Well let's be fair here -- PWR isn't supposed to be a midseason measuring stick. It's supposed to be used to compare an entire season's body of work. It's not perfect and KRACH is probably better (I have no idea what the formula is) but at the end of the season they aren't really all that far apart.
Granted, that's likely just because by the end of the season many teams have solidified their positions and would be ranked similarly regardless of method... but still.
Well let's be fair here -- PWR isn't supposed to be a midseason measuring stick. It's supposed to be used to compare an entire season's body of work. It's not perfect and KRACH is probably better (I have no idea what the formula is) but at the end of the season they aren't really all that far apart.
Granted, that's likely just because by the end of the season many teams have solidified their positions and would be ranked similarly regardless of method... but still.
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie
I expressed no opinion whatsoever in that post as to what the correct formula to use is; my opinion on that is the same as ARM's, namely something that junks RPI altogether. The flaws of RPI are in its basic concepts rather than its specific implementation. All I was trying to do was to point out that, whether it's good or bad, you can't just look at the values of the coefficients to determine what the biggest part of RPI is. You have to look at the relative differences in the values that the coefficients are multiplied against as well.
I expressed no opinion whatsoever in that post as to what the correct formula to use is; my opinion on that is the same as ARM's, namely something that junks RPI altogether. The flaws of RPI are in its basic concepts rather than its specific implementation. All I was trying to do was to point out that, whether it's good or bad, you can't just look at the values of the coefficients to determine what the biggest part of RPI is. You have to look at the relative differences in the values that the coefficients are multiplied against as well.
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