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TonyTheTiger20
03-07-2017, 07:42 AM
Hello, hockey party people --

A couple years ago I tried my hand at building a computer ranking system:

http://board.uscho.com/archive/index.php/t-111945.html

It was fun to build, but it was pretty rudimentary and had a lot of flaws (for example, all losses were treated the same by the system regardless of how good the team you beat was.

I started over from scratch and gave it another go, and wanted to share what I have. Enter the brand new GRaNT (Grant's Reasonable and Not Terrible) Computer Rankings!

Think of it as essentially KRACH for margin of victory. But instead of margin of victory, what's used is the percentage of goals each team scores in each game (i.e. if you win 3-1, you scored 75% of the goals in the game). The ratings are set such that if you add up the sum of the actual G%'s for each team, it equals the expected G% against each team. It is calculated the same way KRACH is in that you set each team's rating equal to 100, run through the calculations, get a new rating, and then run that new rating through the calculations, over and over until the ratings for each team don't change after successive runs.

It avoids messy problems with shutouts (i.e. even though a 1-0 win and a 5-0 win both have 100% of goals scored in each game) by dealing with the season as a whole instead of individually. So, for example, if Team A wins its two games 1-0 and 3-1, its combined G% will be 4 out of 5 goals = 80%, and if Team B wins its two games 5-0 and 3-1, its combined G% will be 8 out of 9 goals = 89%.

Some more details and a full ranking of teams for both men's and women's hockey can be found here: http://www.bcinterruption.com/boston-college-hockey/2017/3/7/14839436/2016-2017-ncaa-mens-and-womens-college-hockey-grant-computer-rankings

Here's a screenshot of the men's rankings after this weekend's games below.

All feedback and criticism are welcome!

<a href="http://www.bcinterruption.com/boston-college-hockey/2017/3/7/14839436/2016-2017-ncaa-mens-and-womens-college-hockey-grant-computer-rankings">
<img src="http://i.imgur.com/zoyUQKf.png" alt="Click here to go to the GRaNT Computer Rankings!" height="800">
</a>

Snively65
03-07-2017, 09:42 AM
HEA would have seven teams in the NCAA's!

Numbers
03-07-2017, 10:01 AM
Is this a Krach-style calculation? So that, effectively, you treat each goal as if it were a full game? So, if Minnesota sweeps Penn State in 4 games by a total of 14-3 in goals, then the calculation says, "Minnesota scored 14 times against PSU. PSU scored 3 times." So, the difference in Ranking in those games is 14/17 for Minnesota?

If so, I see a problem extending that to a full season.

TonyTheTiger20
03-07-2017, 10:26 AM
HEA would have seven teams in the NCAA's!

Six -- we refuse to accept responsibility for Notre Dame.

TonyTheTiger20
03-07-2017, 10:40 AM
Is this a Krach-style calculation? So that, effectively, you treat each goal as if it were a full game? So, if Minnesota sweeps Penn State in 4 games by a total of 14-3 in goals, then the calculation says, "Minnesota scored 14 times against PSU. PSU scored 3 times." So, the difference in Ranking in those games is 14/17 for Minnesota?

If so, I see a problem extending that to a full season.
I think this is a similar question to something someone posed on the women's forum, actually.

It's set up the same way KRACH is in that everyone's rating is determined by everyone else's rating, but while you would use KRACH to determine what percentage of games Team A would win against Team B, you would use GRaNT to determine what percentage of goals Team A would score in a game against Team B.

Here's an example I posed in the women's forum, looking at Wisconsin vs. Bemidji women:

KRACH: UW = 1837, BSU = 108.7. So UW would win 1837/(1837+108.7) = 94.4% of games.

GRaNT: UW = 497.82, BSU = 82.25. So UW would score 497.82/(497.82+82.25) = 85.8% of goals in a season against Bemidji.

Looking at real-life results, UW obviously won 100% of games against BSU vs. 94.4% expected by KRACH.

In four games against Bemidji, Wisconsin won by scores of 5-0, 6-0, 6-1, and 4-2. That comes out to 21 out of 24 goals scored, or 87.5% -- which is less than one Bemidji goal away from what GRaNT says to expect.

Minnesota cleaned Penn State's clock in men's this year, so they probably aren't the best example, but GRaNT actually does better than KRACH for them too.

KRACH: UM = 284.1, PSU = 246.0. So UM would win 284.1/(284.1+246.0) = 53.6% of games.

GRaNT: UM = 159.95, PSU = 160.0. So UM would score 159.95/(159.95+160.0) = 49.99% of goals in a season against Penn State.

Minnesota won 100% of games against PSU, vs. 53.6% expected by KRACH.

In four games against PSU, Minnesota won by scores of 5-1, 5-2, 6-3, and 4-3. That comes out to 20 out of 29 goals scored, or 68.97%, vs. the 49.99% expected by GRaNT.

Numbers
03-07-2017, 11:23 AM
It's an interesting idea. However, I think it might end up with results a little skewed in favor of lower scoring teams. Beating someone 2-1 is more important in this calculation than beating them 3-2. Not sure what to do about that, though.

TonyTheTiger20
03-07-2017, 11:46 AM
It's an interesting idea. However, I think it might end up with results a little skewed in favor of lower scoring teams. Beating someone 2-1 is more important in this calculation than beating them 3-2. Not sure what to do about that, though.
That's the other point someone raised! haha

I think it would be accurate to say that a team that wins all its games 2-1 better than a team that wins its games 3-2. If a team routinely scores 2x as many goals as it allows, I would say that's a good argument for them to be better than a team that scores 1.5x as many goals as it allows.

A team that wins its games on average 3-2 is, statistically, more likely to be closer to .500 than a team that wins its games 2-1 on average.

Numbers
03-07-2017, 03:33 PM
That's the other point someone raised! haha

I think it would be accurate to say that a team that wins all its games 2-1 better than a team that wins its games 3-2. If a team routinely scores 2x as many goals as it allows, I would say that's a good argument for them to be better than a team that scores 1.5x as many goals as it allows.

A team that wins its games on average 3-2 is, statistically, more likely to be closer to .500 than a team that wins its games 2-1 on average.

By how much would you count the 2-1 winners to be better?

TonyTheTiger20
03-07-2017, 04:36 PM
By how much would you count the 2-1 winners to be better?
Well, a 2-1 winner scored 67% of the goals in the game.
A 3-2 winner scored 60% of the goals in the game.
A 4-3 winner scored 57% of the goals in the game.
A 5-4 winner scored 56% of the goals in the game.

So it approaches 50%, and the lower the score, the bigger the difference. I.e. there's really not much difference between winning 7-6 vs. 8-7, but there's a big difference between winning 2-1 and 8-7.

TheRevengeance
03-07-2017, 04:40 PM
It's an interesting idea. However, I think it might end up with results a little skewed in favor of lower scoring teams. Beating someone 2-1 is more important in this calculation than beating them 3-2. Not sure what to do about that, though.

While that makes sense in theory, it must not be the case, because Northeastern either wins or loses 5-4 on a daily basis and is somehow 14th here

Numbers
03-07-2017, 04:45 PM
Well, a 2-1 winner scored 67% of the goals in the game.
A 3-2 winner scored 60% of the goals in the game.
A 4-3 winner scored 57% of the goals in the game.
A 5-4 winner scored 56% of the goals in the game.

So it approaches 50%, and the lower the score, the bigger the difference. I.e. there's really not much difference between winning 7-6 vs. 8-7, but there's a big difference between winning 2-1 and 8-7.

Right. Your system says the 3-2 guys are
10% worse than the 2-1 guys. I don't think that works empirically.

I think goal differential is a better marker than goal ratio.

TonyTheTiger20
03-07-2017, 10:16 PM
Right. Your system says the 3-2 guys are
10% worse than the 2-1 guys. I don't think that works empirically.

I think goal differential is a better marker than goal ratio.

Think of it as projected out through the full season --

If your results are projected to be 2-1, then over the course of a season you would be projected to score 200 goals and allow 100 goals (for example).
On the other hand, if your results are projected to be 3-2, then over the course of a season you would be projected to score 200 goals and allow 133 goals.

Surely you'd agree that the first team is more likely to have a better record?

As for goal differential... I can't say that I agree. A 4-1 win is certainly "better" than a, say, 15-12 win. Even aside from just the fact that one team is only only scoring close to half the goals in the game, the same season-extension thing applies as above. If you project those scores out over the course of a full season, the team scoring 4x as many goals as its opponents is going to have a much, much better record than the team scoring only 1.25x more goals. I mean... right?

chickod
03-07-2017, 10:33 PM
A 4-1 win is certainly "better" than a, say, 15-12 win.

It is? Why?

No offense...I just think you're trying too hard. I think in a sport where scoring is relatively low anyway, the sample size is just too small to quantify "superiority" based on only goals scored. I could somewhat see if you did it in football, where the much greater number of points would give you more data with a higher degree of confidence. If a football teams wins every game by 20 points, that is more significant than a hockey team winning by one goal, even if the % of the points scored is less for the football team, because the minuscule sample size for hockey skews the data. Just my opinion... :)

TonyTheTiger20
03-07-2017, 10:43 PM
It is? Why?
Well, for the reason above -- a team scoring 4x as many goals as its opponents (a bunch of 4-1 wins, or 400 goals scored and 100 goals allowed) over the long run is going to have a much, much better record than the team scoring only 1.25x more goals (a bunch of 15-12 wins, or 400 goals scored and 320 goals allowed).


No offense...None taken! All this discussion is exactly what I was looking for.


I just think you're trying too hard. I think in a sport where scoring is relatively low anyway, the sample size is just too small to quantify "superiority" based on only goals scored.
I think that's a fair point, but when you consider that KRACH uses wins and losses -- I mean, hockey is low scoring, yes, but there are more goal scoring datapoints than there are win/loss data points. Know what I mean?

The way I sort of figured this calculation would be is if KRACH uses wins/losses, then GRaNT is a sort of "KRACH prime" in that it goes one layer beneath the wins/losses. I'd say something like "KRACH double prime" would be doing the same thing based off, say, percentage of shots taken in a game (if Corsi is your thing).

Just another methodology to go alongside the others that are out there :cool:

theprofromdover
03-08-2017, 05:31 AM
Bump

Cat lover
03-08-2017, 08:14 AM
Personally I think they over think these rating systems. The NHL and every other pro sport league uses only one way to rank teams WINS PERIOD.

I would make it simple Wins count for 75% and SOS 25% this will make those schools from lower leagues want to schedule teams from top leagues to
boost their SOS while those top teams would want to schedule them to try to hurt their winning %. Too many teams right now in strong league wont
schedule teams that hurt its SOS just look at St CLoud still has a chance to make NCAA's and under .500 only because of its SOS.