Tuesday, October 31, 2006

Power Rankings

Another spreadsheet for your viewing enjoyment.

What I'm essentially trying to come up with is a simple version of the standings that takes into account a team's record (represented by points percentage) and goal differential. The rankings here simply provide an average of team's rankings in the two categories.

The other detail included on the spreadsheet is a look at the record required in the remaining games for a team to claim a playoff spot. It's a work in progress, but as you can see at the moment, the Buffalo Sabres need to go 37-34-0 in order to hit 95 points — which based on last season's standings should be enough to make the playoffs.

I haven't yet worked out the formula to factor in ties — right now they're counted as half wins/losses — but I should have that cleared up in the next few days.

24 Comments:

At 8:10 PM, October 31, 2006, Anonymous Anonymous said...

Any thoughts on factoring in strength of schedule?

 
At 8:14 PM, October 31, 2006, Anonymous David Johnson said...

I have found goal differential to not be the best indicator of how good a team is. It is really no better, and more likely worse, than straight won-loss records. What really needs to be done is to account for differences in schedule difficulty to get more accurate power rankings.

 
At 8:30 PM, October 31, 2006, Anonymous Nicky said...

Isn't this more or less what Sagarin does?

http://www.usatoday.com/sports/sagarin/nhl0607.htm

Not to discourage you, however.

 
At 8:48 PM, October 31, 2006, Anonymous David Johnson said...

Yes, Saragin does include strength of schedule, as do I.

 
At 9:05 PM, October 31, 2006, Blogger James Mirtle said...

I guess simple is the operative word for me. I want a set of standings where all of the numbers are presented, and one can easily see how the ranking is derived.

I'm going to have to look into how big a factor goal differential really is. (Have you written about this David?)

 
At 9:36 PM, October 31, 2006, Anonymous David Johnson said...

I haven't written about it but when I was developing my power ranking system and game prediction system I looked into using goal differential and I didn't find any benefit to using it over won-loss record. I should revisit that and write something up because I think it might be interesting to many people. I think if you did some searching you will find that in baseball teams that win the close games (1-run games) are the better teams. I think the same is true for hockey. The good teams aren't the ones that can score the 6th and 7th goals in a 7-1 rout but the ones that can score the 3rd goal in the 3-2 game. Adding a teams record in 1 goal games to your table is probably fairly useful.

 
At 11:33 PM, October 31, 2006, Blogger PDO said...

David Johnson said...
I have found goal differential to not be the best indicator of how good a team is.


Well that just flies in the face of logic, no offense. Check out some teams records in 1 goal games, and check how that relates to their actual standings:

Hint, it has 0 correlation.

GD is very important, and the best indicator (combined with common sense) of just how good a team is. Obviously Detroit wasn't as good as their GD was last year.. but neither was their record. Apply some common sense (which is figuring out the difficulty of schedule) and you're going to find the best barometer for teams that elminates luck as much as possible.

- PDO

 
At 11:59 PM, October 31, 2006, Anonymous Nicky said...

David - out of curiosity,when you developed your power ranking system, was that before or after the shoot-out rules? After seeing what happened with Dalls (way better in the shoot-out than in regular play), I would think that might be relevant.

 
At 1:11 AM, November 01, 2006, Anonymous David Johnson said...

I don't consider the shootout in my power rankings. Games that go to a shootout I consider as ties. In my power rankings Dallas wouldn't get any benefit for their amazing shootout record.

bk: Do you have the data? I am curious to see it. You may be right and one goal win percentage isn't that good. I don't know. As for goal differential, I am not saying that it is a bad indicator, just that it doesn't really tell you anything more than actual win percentage. In fact, win percentage might be the better predictor of future performance than goal differential.

 
At 11:09 AM, November 01, 2006, Blogger J. Michael Neal said...

I have found goal differential to not be the best indicator of how good a team is. It is really no better, and more likely worse, than straight won-loss records. What really needs to be done is to account for differences in schedule difficulty to get more accurate power rankings.

In part, this is because goal differential is the wrong measure. It will consistently bias in favor of offensive teams. What you want is goal ratio. However, even here, it likely isn't a first order correlation.

In baseball, the most accurate measures are modifications on the Pythagorean ratio. Roughly speaking, the expected ratio of a team's wins to losses is the square of the ratio of runs scored to runs allowed. There are a variety of different modifications of this that people have come up with to improve upon it. Bill James pointed out the pythagorean relationship back in the 1970s.

BK has it not quite right. There is correlation between a team's record in 1-run games (speaking baseball here, still) and its overall record. It would be somewhat hard for there not to be, given the percentage of games that are decided by one run. What is true is that, again roughly speaking, being good in 1-run games is not a repeatable skill. hat that means is that having a good record in 1-run games in the recent past is not a good predictor of record in 1-run games going forward; they remain pretty close to a 50/50 proposition.

(I say roughly speaking, because there is evidence of positive correlation between the quality of a bullpen and the ability to win 1-run games. It's not very strong, though.)

On the other hand, there is a strong correlation between blowout wins and future winning percentage. While it may not matter much that a team is able to score that eighth run, it is very important that they are able to get themselves into a situation where scoring more doesn't matter.

Again, all of the above is for baseball. I would expect similar things to hold for hockey, though the formulas are likely to be different. (In basketball, for instance, the formula would clearly deviate greatly from straight Pythagorean.)

As for James project, he's probably better staying away from strength of schedule. Good measures of strength of schedule are pretty complex. KRACH, used for looking at NCAA hockey, is the best I've found.

http://www.uscho.com/FAQs/?data=krach

 
At 11:28 AM, November 01, 2006, Blogger ninja said...

The good teams aren't the ones that can score the 6th and 7th goals in a 7-1 rout but the ones that can score the 3rd goal in the 3-2 game.

It is funny you mention this, as during the Sens-Habs game this week, the broadcast noted how the Sens are the former, and not so much the latter. So despite scoring the most goals in the league last year, they had a tremendous let down in tight games. And, as you note, winning tight games is the sign of team strength.

Just curious, but if you factor out Ottawa's 05-06 stats in goal differential does it become a more reliable indicator? Because I agree with the old skool idea that GD is vital to team success.

 
At 11:59 AM, November 01, 2006, Anonymous David Johnson said...

Ottawa's record when they scored fewer than 4 goals (i.e. usually close games) last season was dreadful while in games where they scored 4 or more goals they were nearly unbeatable. In other words teams with good defenses and goaltending had success against them. And unfortunately for the Senators teams that do good in the playoffs are usually teams with good defenses and goaltending.

Again, being able to beat up on bad teams doesn't make you a good team. Being able to beat the best teams, likely in close games, does.

 
At 1:14 PM, November 01, 2006, Blogger James Mirtle said...

David, in my goal differential calculations, the winning shootout goal looks like it's counting — that's probably something I should take out, no?

I didn't realize they were counting those in the standings.

 
At 1:27 PM, November 01, 2006, Anonymous David Johnson said...

Yeah, I would suggest taking out that shootout goal. I don't understand why the NHL includes them in the team totals when no player actually gets credited with a goal.

 
At 10:34 PM, November 01, 2006, Anonymous Chris DeGroat said...

I take both strength of schedule and goal differential into account in my rankings....

http://www.degroat.net/power_rankings/

Why?

Goal Differential....

Sure, there are some negatives to using goal differential. But, more often than not if a team has a .600 winning percentage but their goal differential is about even eventually they're going to come back down to earth.

Strenght of Schedule...

The way I calculate in SOS isn't rocket science by any means, but in this day and age with so many divisional games, I think it's important to give the teams with the harder SOS a little extra 'credit'

 
At 10:49 PM, November 01, 2006, Anonymous Anonymous said...

The best team is the one that gets its name engraved on the heavy silver cup. Everything else is B(C)S.

 
At 11:16 PM, November 01, 2006, Blogger J. Michael Neal said...

The best team is the one that gets its name engraved on the heavy silver cup. Everything else is B(C)S.

There is nothing wrong with this definition. However, it is entirely a backwards looking statement. It can tell us a lot about what has happened, but almost nothing about what will happen. If we are interested in making any sort of predictive statement, then we have to look elsewhere.

 
At 11:22 PM, November 01, 2006, Blogger James Mirtle said...

The way I calculate in SOS isn't rocket science by any means, but in this day and age with so many divisional games, I think it's important to give the teams with the harder SOS a little extra 'credit'.

I guess the thing I'm looking to determine with the rankings is how the regular-season standings will ultimately turn out, as opposed to any 'strength' determination. In that sense, the teams with 'easy' divisional schedules are going to have those matchups throughout the year, and presumably, their positioning in the standings will benefit from that.

 
At 11:35 PM, November 01, 2006, Blogger J. Michael Neal said...

Chris DeGroat:

Some comments on your formula.

As stated above, goal differential is the wrong measure; it will inherently lead to teams that are good at scoring goals being more highly rated than teams that are good at preventing goals. Goal ratio is closer to what you want, though one would have to run some regressions to find the proper order.

I'm very dubious about the usefulness of a team's record over the last twelve games. That strikes me as an arbitrary, and much too small, sample size to use. Then again, I'm never very fond of assigning meaning to streaks; the data is more noise than signal. In baseball, it has been shown that hot streaks (either for a hitter or for a mean) have no predictive value whatsoever. My assumption is that hockey is somewhat more susceptible to momentum issues, but I suspect that it isn't very different.

With the unbalanced schedule, a simple SoS measure, such as you have, is going to strongly regress every team's ranking towards the mean. This is especially true if you do not remove the games that the team in question has played against its opponents. A measure of the Blackhawk's SoS, for instance, should have all of the games played against Chicago removed from the calculation of its opponents' winning percentage. This is because, under your formula, every time the Blackhawk's win, they drive down their opponents' winning percentage, forcing them back towards the mean. The same thing is true do to the unbalanced schedule. You will conflate the strength of a division with the strength of a team.

Sorry to get pedantic about the whole thing, but that's what I'm best at.

 
At 8:51 AM, November 02, 2006, Anonymous chris degroat said...

LOL.... I'm sorry, but some of you think way to hard about this. These are POWER RANKINGS for Christ's sake. They aren't intended to predict the Stanley Cup winner. They aren't even intended to predict who will win tonight. Power rankings are nothing more than an alternate representation of who is playing good hockey right now.

As stated above, goal differential is the wrong measure; it will inherently lead to teams that are good at scoring goals being more highly rated than teams that are good at preventing goals. Goal ratio is closer to what you want, though one would have to run some regressions to find the proper order.

I understand that you have a different opinion than me, but don't tell me "what I want". What I want is goal differential. If I wanted to use something else, I would have.

I'm very dubious about the usefulness of a team's record over the last twelve games. That strikes me as an arbitrary, and much too small, sample size to use.

Again, these are POWER RANKINGS, not some sort of prediction analysis. If you don't put some sort of value on how a team has played in recent games you might as well rank the teams by the overall standings.

With the unbalanced schedule, a simple SoS measure, such as you have, is going to strongly regress every team's ranking towards the mean.

I'm aware of the effect that my SOS calculation has on the rankings as I've been using it for last three years. It accomplishes what I want it to accomplish.

 
At 4:41 PM, November 02, 2006, Blogger J. Michael Neal said...

I understand that you have a different opinion than me, but don't tell me "what I want". What I want is goal differential. If I wanted to use something else, I would have.

Fine. However, most of the people who come to look at your power rankings won't realize that you have an inherent preference for offense over defense and weak divisions over strong divisions.

 
At 4:49 PM, November 02, 2006, Blogger James Mirtle said...

The thing I wonder is: Don't teams in weak divisions become 'power' teams?

 
At 6:32 PM, November 02, 2006, Anonymous Chris DeGroat said...

you have an inherent preference for offense over defense

No, I have an inherent preference for teams that score more goals than they give up. In my calculation, a 2-0 victory is the same thing as a 4-2 victory. Each one represents a goal differential of 2 goals per game.

The top two teams in my rankings are the two teams that have gotten at lesat a point in each game. The next two teams are the two teams with the fewest goals against.

Meainwhile, the 2nd and 3rd highest scoring teams are 5th and 19th. And even thought Toronto is the 3rd highest goal scoring team in the league they are getting a deduction in the goal diff portion of the calculation because they have given up 3 more goals than they have scored.

weak divisions over strong divisions

No, teams in strong divisions get kicked up by the SOS portion of the calculation.

 
At 10:57 PM, November 02, 2006, Blogger J. Michael Neal said...

No, I have an inherent preference for teams that score more goals than they give up. In my calculation, a 2-0 victory is the same thing as a 4-2 victory. Each one represents a goal differential of 2 goals per game.

No empirical research that I've ever seen backs you up. A team that consistently beats its opponents 2-1 is just as good as a team that consistently beats them 4-2, and is significantly better than a team that consistently beats them 3-2. Aside from the empirical research, this makes sense at the basic mathematical level; statistical distributions are never based upon absolute differences, but rather relative ones.

Using goal differential produces an inherent bias in favor of teams that produce greater total number of goals in their games.

No, teams in strong divisions get kicked up by the SOS portion of the calculation.

Yes they do, but not by as much as they should. Because of the unbalanced schedule, the aggregate record of each division is pushed towards .500 from where they would be if each team played all 29 other teams an equal number of times. This becomes perfectly obvious at the extreme; if teams only played the teams within their division, and never outside of it, each division would have an aggregate .500 record, regardless of which division, in fact, has the best teams.

By playing a disproportionate number of games against better than average teams, a team in a good division will have a record lower than it would have if it played a balanced schedule. This affects the SoS of every other team in its division, making it appear as if they have played a softer schedule than they really have. The exact opposite happens in a weak division.

Meainwhile, the 2nd and 3rd highest scoring teams are 5th and 19th. And even thought Toronto is the 3rd highest goal scoring team in the league they are getting a deduction in the goal diff portion of the calculation because they have given up 3 more goals than they have scored.

This demonstrates that I made my point quite incorrectly. Let me try again. You are correct; the fact that Toronto is high scoring is currently pushing them down your rankings. I was, unfortunately, thinking only of the good teams. In fact, the bias for high scoring teams is away from even. Since the Leafs have a negative differential (or a ratio less than one, which is the same statement), they are pushed down.

 

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