The 2014 Pairwise, Bracketology and History Thread`

[Numbers]

Re: The 2014 Pairwise, Bracketology and History Thread`

Quick question for JimDahl or anyone who has done the RPI calculations.

Tonythetiger20 on the Women's Board is trying to set up an RPI sim for next year. He is struggling with the RPI calcs. I am assuming that the win%, oppwin% and oppoppwin% are calculated the same way on the women's side, although the women don't have the home/road weighting factor, and the 25-21-54 is replaced by some other ratio, which he has found from the Women's handbook.

Apparently his issue is how to do the oppoppwin%. So, I thought I would ask here. He has been doing.....

1)Take the opponent for each game. Here we will use Game 1 as example. Take that opponent's entire schedule and average the win% of the opponents. Save this number.
2)Add all those up for the entire schedule of the team in question.
3)Divide by number of games, and this is your answer.

I seem to recall something about this not being how it is done, and rather it goes
Average over each different opponent rather than each game....

Anyway, I can't remember for sure.

Any help available?

Thanks.

[Craig P.]

Re: The 2014 Pairwise, Bracketology and History Thread`

Your procedure is the way I remember it being done.

If there are any differences, they would come from removing games against certain teams, but as best I recall, that only happens with owpct, not oowpct.

[UnionHockeyManiac]

Re: The 2014 Pairwise, Bracketology and History Thread`

Priceless for chits and giggles, if Yale swept the ecac's with no losses, would they still be a four?

I was wondering about this too. I've said this before: I like Yale and I like their fans so I hate the fact that I have to root against them just to avoid having Union shipped out west.

[Priceless]

Re: The 2014 Pairwise, Bracketology and History Thread`

Priceless for chits and giggles, if Yale swept the ecac's with no losses, would they still be a four?

No. Before the simulator crapped the bed, they were around 12 with a sweep this weekend. An ECAC title would put them solidly in 3 seed territory, maybe a 2.

[UnionHockeyManiac]

Re: The 2014 Pairwise, Bracketology and History Thread`

No. Before the simulator crapped the bed, they were around 12 with a sweep this weekend. An ECAC title would put them solidly in 3 seed territory, maybe a 2.

So if they lose this weekend, they're out. If they win, they still have a shot at an at-large if they lose in Lake Placid?

[Priceless]

Re: The 2014 Pairwise, Bracketology and History Thread`

So if they lose this weekend, they're out. If they win, they still have a shot at an at-large if they lose in Lake Placid?

In: win ECAC / sweep this weekend win Friday
Out: lose 2 this weekend
Anything in between is up in the air.

[JimDahl]

Re: The 2014 Pairwise, Bracketology and History Thread`

Tonythetiger20 on the Women's Board is trying to set up an RPI sim for next year. He is struggling with the RPI calcs. I am assuming that the win%, oppwin% and oppoppwin% are calculated the same way on the women's side, although the women don't have the home/road weighting factor, and the 25-21-54 is replaced by some other ratio, which he has found from the Women's handbook.

Apparently his issue is how to do the oppoppwin%. So, I thought I would ask here. He has been doing.....

1)Take the opponent for each game. Here we will use Game 1 as example. Take that opponent's entire schedule and average the win% of the opponents. Save this number.
2)Add all those up for the entire schedule of the team in question.
3)Divide by number of games, and this is your answer.

I seem to recall something about this not being how it is done, and rather it goes
Average over each different opponent rather than each game....

I believe that you're missing that in the opponents win% you remove games against yourself. e.g. In calculating oppwin% for Team A, when averaging in Team B's win% you actually use their win% only vs opponents other than Team A.

The opponents' opponents' win% is then the average of the opponents win%'s (across games, not opponents). That's a slightly different number than iterating over the opponents opponents and averaging their win%'s.

[JimDahl]

Re: The 2014 Pairwise, Bracketology and History Thread`

My last regular season forecast

I'm seeing the breakpoints as:
#7 Quinnipiac is the highest ranked team that could drop to the top of the bubble with some bad play and luck
#10 North Dakota is the highest ranked team that that is likely to drop onto the bubble if they don't win this weekend
#13 Cornell is the highest ranked team that is most likely to drop outside contention if they don't win this weekend
#19 Minnesota-Duluth is the highest ranked team that is unlikely to make the bubble even with two wins
#24 Clarkson is the highest ranked team that is very unlikely to break #20 even with two wins

After this weekend we should be able to actually exhaustively calculate all the remaining possibilities and what outcomes lead to each.

[Numbers]

I believe that you're missing that in the opponents win% you remove games against yourself. e.g. In calculating oppwin% for Team A, when averaging in Team B's win% you actually use their win% only vs opponents other than Team A.

The opponents' opponents' win% is then the average of the opponents win%'s (across games, not opponents). That's a slightly different number than iterating over the opponents opponents and averaging their win%'s.

Thanks Jim. I think we are getting somewhere. A little more help, please. In opponents' opponent's, you still leave out games against the team you are evaluating? Meaning, average over all games except the ones against Team A? And, in doing the 2nd level, all games count, right?. So, if I an doing Minnesota, and need UW's win%, I don't count Minnesota games. Then, if I need UW's Opp win %, I count all games when evaluating each of their opponents, but I do not count Minnesota s an opponent?

[JimDahl]

Re: The 2014 Pairwise, Bracketology and History Thread`

In opponents' opponent's, you still leave out games against the team you are evaluating? Meaning, average over all games except the ones against Team A? And, in doing the 2nd level, all games count, right?. So, if I an doing Minnesota, and need UW's win%, I don't count Minnesota games. Then, if I need UW's Opp win %, I count all games when evaluating each of their opponents, but I do not count Minnesota s an opponent?

Not quite.

When I'm doing Minnesota's oppwin% and need UW's win%, I don't count UW-Minnesota games.

When I'm doing Minnesota's oppoppwin% and am going through UW's opponents to get UW's oppwin% so need Ohio State's win%, I don't count Ohio State-UW games.

This has the handy calculation attribute that if you calculate oppwin% excluding self for each team and save the result, Minnesota's oppoppwin% is a trivial average of the saved oppwin%'s of each of Minnesota's opponents.

Man I hope I said that right

[TonyTheTiger20]

Re: The 2014 Pairwise, Bracketology and History Thread`

I've got the calculations correct! Hooray! Well, I do for the teams that don't have a "bad wins" adjustment. Everyone else's is correct.

I'm not sure where I'm going wrong in my bad wins adjustment.

I'll use Minnesota as an example. I'm taking all of Minnesota's games and calculating a "game RPI" by multiplying [1, 0, 0.5] for W/L/T, times OppWP and OppOppWP, adjusted by the weights. Then I'm adding up all the game RPIs and dividing by the number of games Minnesota has played.

This is giving me the correct unadjusted RPI according to USCHO's RPI except for those 8 teams with bad wins.

I'm then comparing the "game RPI" for each win, and if it is lower than the total RPI, removing it from my RPI average.

So for the Minnesota example, if Minnesota's RPI is .650, and they've played 38 games, and a win against Lindenwood has a game RPI of .600, I am doing {[(.650*38)-.600]/37}, which will tell me how much the win hurt the unadjusted RPI. I take all of those amounts that are >0, sum them, and add that back in to the original unadjusted RPI.

Somehow this isn't giving me the correct answer...

Any ideas on what I'm doing wrong?

[Numbers]

Re: The 2014 Pairwise, Bracketology and History Thread`

I've got the calculations correct! Hooray! Well, I do for the teams that don't have a "bad wins" adjustment. Everyone else's is correct.

I'm not sure where I'm going wrong in my bad wins adjustment.

I'll use Minnesota as an example. I'm taking all of Minnesota's games and calculating a "game RPI" by multiplying [1, 0, 0.5] for W/L/T, times OppWP and OppOppWP, adjusted by the weights. Then I'm adding up all the game RPIs and dividing by the number of games Minnesota has played.

This is giving me the correct unadjusted RPI according to USCHO's RPI except for those 8 teams with bad wins.

I'm then comparing the "game RPI" for each win, and if it is lower than the total RPI, removing it from my RPI average.

So for the Minnesota example, if Minnesota's RPI is .650, and they've played 38 games, and a win against Lindenwood has a game RPI of .600, I am doing {[(.650*38)-.600]/37}, which will tell me how much the win hurt the unadjusted RPI. I take all of those amounts that are >0, sum them, and add that back in to the original unadjusted RPI.

Somehow this isn't giving me the correct answer...

Any ideas on what I'm doing wrong?

Since you put it that way, Tony, I can help you.

What you are trying to do is count how much each bad win affected the RPI, and then subtract that. In stead of subtracting off the difference, you should just recalculate the average.

What you have to do is take .650*38 = Total of Game RPIs. (This number you have in your calculation already). Now, instead of trying to say (How much did Lindenwood affect this?), just subtract all the game RPIs that are below that .650, so .650*38 - .600 - .??? etc, until you have subtracted them all off. Let's call that ADJSUMRPI. The final total will be ADJSUMRPI/(#games-#subtractedgames). Your method will be slightly wrong because if there are 2 games, you are going to subtract some number like{(.650*38-.600)/37}-.650 + {(.650*38-.605)/37}-.650 where all the numbers you subtract have 37 for a denominator. But, the right answer has to have 36 in the denominator, because it is literally (RPI with bad games removed) which means, "Calculated without those games."

There is still one possibility of trouble. I am not sure how this would work, but it may be possible that you will miss a subtracted game or two. That is because the real definition of subtracted games is not "When Game RPI is lower than season RPI", but rather "When SUMGAMERPIs/SUMGAMES is less than (SUMGAMERPIS(-gameRPIinquestion))/(#games-1). So, what I mean is that you could have a situation where one game lowers the RPI by a lot, and one by only a little. When you average, using all games, the RPI calculated using all games may fall far enough that the game which would lower RPI by only a little isn't found by only looking at averages. For example, if the calculated RPI is .670, and one game has .570, that .570 will lower the total RPI by about .003. If some game has .671, that game maybe should be included, too. I am not sure. I don't know whether the 'remove games' thing is iterative or not.

Jim?

[TonyTheTiger20]

Re: The 2014 Pairwise, Bracketology and History Thread`

Since you put it that way, Tony, I can help you.

What you are trying to do is count how much each bad win affected the RPI, and then subtract that. In stead of subtracting off the difference, you should just recalculate the average.

What you have to do is take .650*38 = Total of Game RPIs. (This number you have in your calculation already). Now, instead of trying to say (How much did Lindenwood affect this?), just subtract all the game RPIs that are below that .650, so .650*38 - .600 - .??? etc, until you have subtracted them all off. Let's call that ADJSUMRPI. The final total will be ADJSUMRPI/(#games-#subtractedgames). Your method will be slightly wrong because if there are 2 games, you are going to subtract some number like{(.650*38-.600)/37}-.650 + {(.650*38-.605)/37}-.650 where all the numbers you subtract have 37 for a denominator. But, the right answer has to have 36 in the denominator, because it is literally (RPI with bad games removed) which means, "Calculated without those games."

There is still one possibility of trouble. I am not sure how this would work, but it may be possible that you will miss a subtracted game or two. That is because the real definition of subtracted games is not "When Game RPI is lower than season RPI", but rather "When SUMGAMERPIs/SUMGAMES is less than (SUMGAMERPIS(-gameRPIinquestion))/(#games-1). So, what I mean is that you could have a situation where one game lowers the RPI by a lot, and one by only a little. When you average, using all games, the RPI calculated using all games may fall far enough that the game which would lower RPI by only a little isn't found by only looking at averages. For example, if the calculated RPI is .670, and one game has .570, that .570 will lower the total RPI by about .003. If some game has .671, that game maybe should be included, too. I am not sure. I don't know whether the 'remove games' thing is iterative or not.

Jim?

You are absolutely, 100% correct! The first calculation was the way to go, and it is indeed iterative. My spreadsheet is DONEEEEEEEEE!!!! Thank you a TON, I've been working on this for about a week and a half at this point.

If BC is in Philly make sure you hit me up for your first beer.

[Numbers]

Re: The 2014 Pairwise, Bracketology and History Thread`

You are absolutely, 100% correct! The first calculation was the way to go, and it is indeed iterative. My spreadsheet is DONEEEEEEEEE!!!! Thank you a TON, I've been working on this for about a week and a half at this point.

If BC is in Philly make sure you hit me up for your first beer.

No way for me to get to Philly. I am in Guam at present, and will be on Saipan next week. But, congrats.

Now, all you have to do is calculate the full PWR.....

[LTsatch]

Re: The 2014 Pairwise, Bracketology and History Thread`

No way for me to get to Philly. I am in Guam at present, and will be on Saipan next week. But, congrats.

Now, all you have to do is calculate the full PWR.....

Reenacting the liberation of the Pacific in WWII?