FOF - Calculating a "power rating"

[QuikSand]

Though this might be a worthwhile discussion, and possibly an exercise that miht bear some fruit.

In my multiplayer leagues, I have had some occasion to look at the league "power ratings" -- and have reached a conclusion similar to most, i.e. they are not very reliable.

So - the task is this: Come up with a formula that would assign a reasonable set of "power ratings" to teams based on the information and stats that are available in the FOF game. Ideally, this would be scaled so that the really good teams get ratings that aproach 100 - more or less like the system works right now, only (presumably) with a keener insight into what's really going on with the teams.


In my opinion, there's an inherent trade-off between simplicity and precision here. You might make a slightly better system by adding in twenty more stats than someone else does... but does that necessarily make it "better?" I think there is a case to be made that a fairly simple system that does a "good" job might be better than a hideously complictaed one that does a "very good" job. Open to debate.

I think for purposes of this discussion, it's probably best to assume that the league being analyzed is a "mature" league with at least 10 games played in the current season. (This exercise gets a lot sticker, IMO, if you're at the start of a season with few and sketchy stats to work with)


Any takers?

[cthomer5000]

I think the rankings in these categories are very important:

Yards Per Pass Attempt
Yards Per Run Attempt
Yards Per Pass Attempt Allowed
Yards Per Run Attempt Allowed

I also think the disparity in yards gained per game vs. yards allowed per game is probably pretty important.

[cthomer5000]

dola. of course that doesn't take into account special teams, which I feel should be included.

Total Yards gained vs. Total yards allowed would be my guess for the #1 most important stat in determining the "POWER" of a team.

[cthomer5000]

double-dola. I imagine Vegas Vic would have some insight here.

[QuikSand]

In the “fairly simple” category, I’ll try this for starters:

Three components, based on:
-winning percentage
-scoring for and against
-yards from scrimmage for and against

Details:

W = 40 * (team winning percentage)

S = 40 * [total points / (total points + points allowed)]

Y = 20 * [(yards per carry + yards per attempt) / (yards per carry allowed + yards per attempt allowed)]

and

Power Rating = W + S + Y


This calculation has no theoretical bounds… since Y could be any value. But realistically, I’m guessing a dominant team on both sides of the ball might be able to generate a score as high as 40 for Y… making the theoretical maximum power rating about 120. Realistically, a really strong team going something like 14-2 would probably end up at about 80-90 or so… which is a little low for my tastes.

[Huckleberry]

What about the preseason power ratings? I'd like to see a formula that can be applied in the preseason as well.

[Passacaglia]

I find it interesting that FOF provides power ratings for leagues that haven't played a game yet. In the HFL, my Patriots have the highest power rating in the league, but I wonder what it's based on.

[Daimyo]

The WSY probably has merit, but I imagine for the S and Y you'd want to use some exponent similar to the pythag formula for baseball. I saw an article once on figuring the precise exponent best for those sorts of things (I think has total "points" go up so does the exponent, but I can't remember), but I don't know how to find it now.

[QuikSand]

A pythagorean approach (or some derivative) might work... but I think there might be a complexity/accuracy trade-off there.

[gstelmack]

I think you also need to weight recent wins/losses higher than early wins/losses. Need to account for teams pulling together or falling apart as the season progresses. I'll have to think about this some.

[QuikSand]

I kind of agree... but am not sure how to do it. It would be easy to include something like wins and scores from the last X games as a separate factor... but that gets pretty arbitrary, in my view. If you look at 5 games, for example - what about 6 games ago?

[CraigSca]

According to the book "The Hidden Game of Football", the statistic that provides the most correlation between wins and losses is (not surprisingly) points for and points against. To make a simple "power rating", the book suugests taking the average margin of victory and adding a constant to this to ensure everyone has a positive power rating. Then, adjust accordingly based on the power ratings of your opponents (i.e. if you opponents avg a positive power rating, add a few points to your power rating, since you faced a tougher schedule). The problem is, adjusting power ratings due to scheduling changes everyone's power rating, causing you to run the whole process over again until you get valid numbers.

Maybe take a team's average margin of victory plus a constant and perform some kind of magical calculation based on their opponents winning percentage?

[gstelmack]

Originally Posted by QuikSand

I kind of agree... but am not sure how to do it. It would be easy to include something like wins and scores from the last X games as a separate factor... but that gets pretty arbitrary, in my view. If you look at 5 games, for example - what about 6 games ago?

Couldn't you just do a sliding scale? I could even see something like "Week 1 games are worth .05, week 2 .1, week 3 .15" or somesuch, and then normalize the win-loss factors by the total game factor. So early games are just always worth not a whole lot.

[Subby]

The thing that bothers me there is that you might as well list teams according to record...

What about the really good team that has gotten a few bad breaks or had one real bad loss? While I certainly don't want to see a 7-3 team rated above a 10-0 team, it seems like there should be more variation.

Maybe take the power ranking each week and as mentioned earlier, multiply that rating by a value representative of that week. Aggregate the total and divide...

[KWhit]

Strength of schedule should be included as well, in my opinion. For a purely theoretical example, lets say Astoria has only played cupcakes. Their power rating should be manipulated to reflect that.

[QuikSand]

Originally Posted by Subby

The thing that bothers me there is that you might as well list teams according to record...

Me, too.

Based on those IHOF results, I'm now thinking that the variability in record is inherently far more than that in either of the other two stats... so even though the weighting seems pretty much equal, it's not so at all.

Maybe a simple tweak of the weightings would make more sense. Something like:

W = 20 * (team winning percentage)

S = 60 * [total points / (total points + points allowed)]

Y = 40 * [(yards per carry + yards per attempt) / (yards per carry allowed + yards per attempt allowed)]

and

Power Rating = W + S + Y

[VPI97]

Originally Posted by QuikSand

Something like:

Edit - Bad data

[cthomer5000]

I think we're at least in the ballpark.

[cthomer5000]

dola. I think it's also important to point out that Astoria should fall in the "cupcake" range if the system works correctly.

[sovereignstar]

These are of the 20/60/40 sort.

[VPI97]

Originally Posted by QuikSand

I think the "points" component is being calculated in reverse, though -- making the last two components basicaly wash out.

Now, I'm thinking that it was better the first time.

Ack...something like that. Here's the original 40/40/20 distribution

city	WL	WinPct	Pts	YPS	Tot
Fairbanks	(10 - 0)	40	27.36	26.72	94.08
Conyers	(8 - 2)	32	24.66	23.63	80.29
Chesapeake	(8 - 2)	32	25.62	22.41	80.03
Columbus	(8 - 2)	32	25.29	22.16	79.45
Ann Arbor	(7 - 3)	28	23.90	24.61	76.50
San Antonio	(7 - 3)	28	22.30	23.03	73.33
Orlando	(7 - 3)	28	23.76	20.57	72.34
Bordeaux	(7 - 3)	28	20.96	22.48	71.44
North Plainfield	(7 - 3)	28	21.53	21.30	70.83
Telluride	(6 - 4)	24	22.13	21.28	67.41
Miami	(6 - 4)	24	21.56	20.01	65.57
Tucker	(6 - 4)	24	20.92	19.42	64.33
Gothenburg	(6 - 4)	24	20.21	20.00	64.21
Rochester	(6 - 4)	24	20.10	17.48	61.58
Syracuse	(5 - 5)	20	19.88	21.13	61.01
Astoria	(5 - 5)	20	20.10	20.84	60.94
Anaheim	(5 - 5)	20	21.19	19.69	60.88
Frederick	(5 - 5)	20	20.46	20.09	60.55
Outer Banks	(5 - 5)	20	17.40	20.52	57.92
RayCo	(5 - 5)	20	18.94	17.31	56.25
Minnesota	(4 - 6)	16	18.68	19.18	53.86
Fort Worth	(4 - 6)	16	18.88	17.52	52.40
Maassluis	(4 - 6)	16	17.71	16.46	50.18
Boston	(3 - 7)	12	18.83	18.90	49.73
San Luis Obispo	(3 - 7)	12	16.64	19.52	48.17
Asheville	(3 - 7)	12	18.61	16.44	47.05
Georgia	(2 - 8)	8	16.16	18.57	42.73
Brooklyn	(3 - 7)	12	13.26	16.85	42.11
Vicksburg	(1 - 9)	4	15.54	21.95	41.49
Springfield	(2 - 8)	8	13.86	18.52	40.38
Paris	(1 - 9)	4	16.81	17.41	38.22
Boulder	(1 - 9)	4	12.32	16.40	32.71

[MIJB#19]

I'd be a really cool system if Maassluis would end up above Astoria.

Minor observation, in FOF the power rankings are also based on roster value, which is something that stats based rankings can't traslate with.

[sovereignstar]

Originally Posted by MIJB#19

Minor observation, in FOF the power rankings are also based on roster value, which is something that stats based rankings can't traslate with.

True, but the whole point behind "ratings" is that they only reflect what you've done on the field and not anything "on paper".

[VPI97]

Now with 20/60/40

city	WL	WinPct	Pts	YPS	Tot
Fairbanks	(10 - 0)	20	41.05	53.43	114.48
Conyers	(8 - 2)	16	36.99	47.26	100.25
Chesapeake	(8 - 2)	16	38.44	44.82	99.26
Ann Arbor	(7 - 3)	14	35.84	49.22	99.06
Columbus	(8 - 2)	16	37.94	44.32	98.26
San Antonio	(7 - 3)	14	33.45	46.06	93.51
Orlando	(7 - 3)	14	35.65	41.15	90.80
Bordeaux	(7 - 3)	14	31.44	44.96	90.39
North Plainfield	(7 - 3)	14	32.29	42.60	88.90
Telluride	(6 - 4)	12	33.20	42.56	87.76
Miami	(6 - 4)	12	32.33	40.02	84.36
Gothenburg	(6 - 4)	12	30.31	39.99	82.31
Tucker	(6 - 4)	12	31.38	38.83	82.21
Syracuse	(5 - 5)	10	29.82	42.25	82.08
Astoria	(5 - 5)	10	30.15	41.67	81.83
Anaheim	(5 - 5)	10	31.79	39.37	81.16
Frederick	(5 - 5)	10	30.69	40.17	80.87
Outer Banks	(5 - 5)	10	26.09	41.04	77.14
Rochester	(6 - 4)	12	30.15	34.97	77.12
Minnesota	(4 - 6)	8	28.01	38.36	74.37
RayCo	(5 - 5)	10	28.41	34.62	73.04
Boston	(3 - 7)	6	28.24	37.81	72.05
Fort Worth	(4 - 6)	8	28.32	35.03	71.35
San Luis Obispo	(3 - 7)	6	24.97	39.05	70.02
Vicksburg	(1 - 9)	2	23.31	43.90	69.22
Maassluis	(4 - 6)	8	26.57	32.93	67.50
Asheville	(3 - 7)	6	27.92	32.87	66.79
Georgia	(2 - 8)	4	24.23	37.14	65.38
Paris	(1 - 9)	2	25.22	34.82	62.04
Springfield	(2 - 8)	4	20.79	37.03	61.83
Brooklyn	(3 - 7)	6	19.89	33.70	59.59
Boulder	(1 - 9)	2	18.47	32.80	53.27

[cthomer5000]

edit: looks like VPI revised it. never mind.

[QuikSand]

I'm thinking that Daimyo is right... we need some sort of "pythagorization" to more closely bunch up the teams that are part of the pack. I don't think there ought to be as big a spread between #15 and #16 as between #1 and #2. Adding an exponent to the fractional calculations might get there a bit better.

But that does make it a good deal more complex and less intuitive, even without adding new stats.

[QuikSand]

That 20/60/40 spread for the IHOF seems pretty good... puts the top team way out front, and has a pretty sizable number of teams out of record order. Also, the spread from top to bottom in each category is roughly the same -- meaning (in very gross terms) that they are being accorded roughly equal value, which gets back to a simplicty argument, and passes a simple "smell test" in my opinion.

[sovereignstar]

Bring it.

[VPI97]

Originally Posted by sovereignstar

Bring it.

Heh...when you think Fairbanks, think of the '99 Rams with a top 5 defense.

[cthomer5000]

Originally Posted by sovereignstar

Bring it.

*prays that Jim will allow the option to import/export teams for exhibition games at some point*

Imagine a tournament of the multiplayer league champs at the end of each season?

[albionmoonlight]

One of the criticisms that the NorthStars will always have to bear is the idea that we were only good early because we lucked out in the "random" dispersal draft. People can believe what they want concerning that issue--I have my own opinions, but I am not really an objective observer.

I hope that by improving upon last years team with this years team that I can demonstrate that the NorthStars' success has had some small thing to do with the GM and is not purely a matter of luck.

[VPI97]

Originally Posted by QuikSand

I'm thinking that Daimyo is right... we need some sort of "pythagorization" to more closely bunch up the teams that are part of the pack.

Well, if you square the components, add, and take the square root of the result, you get:

city	WL	Tot
Fairbanks	(10 - 0)	70.28
Ann Arbor	(7 - 3)	62.47
Conyers	(8 - 2)	62.11
Chesapeake	(8 - 2)	61.17
Columbus	(8 - 2)	60.50
San Antonio	(7 - 3)	58.62
Bordeaux	(7 - 3)	56.62
Orlando	(7 - 3)	56.21
Telluride	(6 - 4)	55.30
North Plainfield	(7 - 3)	55.26
Miami	(6 - 4)	52.83
Syracuse	(5 - 5)	52.68
Astoria	(5 - 5)	52.40
Gothenburg	(6 - 4)	51.60
Anaheim	(5 - 5)	51.58
Frederick	(5 - 5)	51.54
Tucker	(6 - 4)	51.35
Vicksburg	(1 - 9)	49.75
Outer Banks	(5 - 5)	49.65
Minnesota	(4 - 6)	48.17
Rochester	(6 - 4)	47.71
Boston	(3 - 7)	47.57
San Luis Obispo	(3 - 7)	46.73
RayCo	(5 - 5)	45.89
Fort Worth	(4 - 6)	45.75
Georgia	(2 - 8)	44.53
Asheville	(3 - 7)	43.54
Maassluis	(4 - 6)	43.06
Paris	(1 - 9)	43.04
Springfield	(2 - 8)	42.66
Brooklyn	(3 - 7)	39.59
Boulder	(1 - 9)	37.70

(Based on 20/60/40 splits)

[cthomer5000]

I also think the strength of your schedule (your opponents raw power ratings) should be included in some way. Otherwise there is nothing to drag down those who've gone 8-2 with "cupcake" schedules, and nothing to give a bump to teams who've gone 6-4 against a brutal schedule.

edit: so maybe 2/3 your Power ranking, 1/3 your opponents average = Adjusted Power Ranking?

The only problem is it goes from being very easy to calculate to being a real pain in the ass.

[Cringer]

This is a great discussion, I am going to have a guy in my league check this out. He is making up his own Power Rankings every week for us, he might find this useful.......

[Buzzbee]

Originally Posted by VPI97

Well, if you square the components, add, and take the square root of the result, you get:



(Based on 20/60/40 splits)

While it's nice to see Vicksburg so high on the list, I'm not sure a 1-9 team should have a power ranking higher than some of the teams we're ranked above. Yes, my offense moves the ball fairly well, but they don't score points. Turnovers kill me.

I do believe we are better than 1-9, and believe a power ranking should show that. Having us listed above Rochester (6-4) and Outer Banks (5-5) just seems wrong.

[KWhit]

I still think it should include some version of strength of schedule in it. If you play in a really tough division, your team should be rewarded for that.

[cthomer5000]

Originally Posted by KWhit

I still think it should include some version of strength of schedule in it. If you play in a really tough division, your team should be rewarded for that.

Absolutely. Trust me when I say my 7-3 from this year is much stronger than my 7-3 from last year. As Vegas Vic said, last year we had K-State's schedule makers.

[Dutch]

Turnover margin plays such a huge roll in the outcome of games. I think teams that are consistantly able to win the turnover battle should get some credit in a power rating scheme.

The turnover margin, over the course of a season says a lot about which teams are winning football games, and which ones are losing. More so than passing yards, maybe.

[MIJB#19]

Originally Posted by Dutch

Turnover margin plays such a huge roll in the outcome of games. I think teams that are consistantly able to win the turnover battle should get some credit in a power rating scheme.

The turnover margin, over the course of a season says a lot about which teams are winning football games, and which ones are losing. More so than passing yards, maybe.

Oh yeah.
Last season, my team was #2 in most turnovers (25 int's, 15 fumbles), we ended up as the worst of the bunch (despite a dozen of close games.)
This season, we're #2 in the league in recovering opponent fumbles (for a total of -2) and all of a sudden we're only a missed 21-yd FG away from .500 land.

[QuikSand]

Originally Posted by Dutch

Turnover margin plays such a huge roll in the outcome of games. I think teams that are consistantly able to win the turnover battle should get some credit in a power rating scheme.

The turnover margin, over the course of a season says a lot about which teams are winning football games, and which ones are losing. More so than passing yards, maybe.

My feeling is that stuff liek turnovers shows up indirectly in the team scoring... and also in winning percentage. Therefore, I'm fairly comfortable that its value as a predictor of future outcomes is sufficiently covered there (through indirect means). Just an opinion, though -- I don't disagree that it's important, particularly in explaining how past games were won, but I wonder how good a predictive tool turnovers are.

[PSUColonel]

When determining a point spread I have usuallly gone on points alone(for better or worse)

Example: For each of the two teams in a given game:Take the average points scored per game minus the average points given up per game. That will leave you with two numbers. The higher value is the favorite, while the lesser the dog. The difference is the point spread. This does not take into account injuries, homefield advantage, or strenght of schedule.

What is does do, is give you a geneal idea on whether the odds makers may be overpumping a game, or just what kind of margin of error there might be by any given sportsbook.

[PSUColonel]

One note about Strenght of Schedule- In the NFL I fell it is less important than it once was. The level of competition is much closer to the center for all 32 teams than it ever used to be. I don't think it carries much weight as a factor. Teams are much streakier now than they ever seemed to be in the past.

[wade moore]

CFL Distribution looks good except that my team (Tampa Bay Torpedoes) seems either very out of place or they have some sheer luck getting them to the record they are at... I'm not even trying to be selfish here... it just seems weird that we are 10-3 and there are 3 8-5 and 2 9-4 teams ahead of us in any kind of power ranking. But beyond that, it looks relatively logical to me.

[cthomer5000]

Originally Posted by QuikSand

My feeling is that stuff liek turnovers shows up indirectly in the team scoring... and also in winning percentage. Therefore, I'm fairly comfortable that its value as a predictor of future outcomes is sufficiently covered there (through indirect means). Just an opinion, though -- I don't disagree that it's important, particularly in explaining how past games were won, but I wonder how good a predictive tool turnovers are.

My team has been shitty or average in the turnover department, and we're second only to Fairbanks in wins in IHOF over these two seasons. I now it's like we're playing with fire, but i think it's at least some anecdotal evidence that turnover margin doesn't have to be a strong predictor of success or failure.

[Buzzbee]

I tend to agree with Quik that the TO margin is somewhat built into the W-L and scoring measures. Sure, you're going to have interceptions returned for TD's (too many in FOF2k4 in my opinion) but you are also going to have interceptions followed by three and outs.

I guess my theory is that a powerful team would be able to translate turnovers by the opposing team in to points/wins whereas a weaker team either couldn't convert, or couldn't cause the turnovers in the first place. This would show in the final score and the W-L column.

[Dutch]

I tend to agree with Quik that the TO margin is somewhat built into the W-L and scoring measures.

My natural response would be, "Then, isn't passing yardage and rushing yardage somewhat built into W-L and scoring?"

Maybe I don't understand the rules of the think fest.

Sure, you're going to have interceptions returned for TD's (too many in FOF2k4 in my opinion) but you are also going to have interceptions followed by three and outs.

You are also going to have 80 yard drives that end in a fumble or missed FG. That's the basic philosophy of the "Bend but don't break" defense. Let them keep going for first downs, cover the deep routes and wait for the offense to screw up (i.e. turnovers)

Anyway, just something for you all to chew on and spit out if you like.

[QuikSand]

Originally Posted by Dutch

My natural response would be, "Then, isn't passing yardage and rushing yardage somewhat built into W-L and scoring?"

I don't think anyone would argue that winning, scoring, and gaining yards are independent of one another. The point of using all three of them is just to try to be a little more accurate than you could be with any one of them.

The question is basically whether there is something else in a set of game stats that is so separate from those things that it requires its own additional inclusion. You're making the case (as I see it) that turnovers are important enough to merit that kind of attention. I basically disagree.

Not a big deal, and it's not a matter of "rules." Just different perspectives, that's all.

[QuikSand]

Originally Posted by VPI97

Well, if you square the components, add, and take the square root of the result, you get

I think this might be a different kind of "pythagorization" than I had imagined.

Instead, I was thinking that you would use some exponent to the components of the formula itself. Something like this, using a simple square as the exponent:

S = 60 * [total points^2 / (total points^2 + points allowed^2)]

I think that would have the effect of compressing the spread of results a bit more. I'm not sure that it would necessarily be more accurate, but there is some evidence that using exponents in this fashion makes this kind of narrow-to-broad statistical correlations stronger.

[Samdari]

Originally Posted by albionmoonlight

I hope that by improving upon last years team with this years team that I can demonstrate that the NorthStars' success has had some small thing to do with the GM and is not purely a matter of luck.

I, for one, do not think it was purely luck. I do think that many of us were inexperienced with setting of sliders for the preference draft, and what that would mean to the computer. I interpreted the sliders far differently than I the algorithm ended up, and therefore drafted a lousy roster. You simply guessed better than the rest of us at what the sliders would bring you in terms of player's abilities.

Luck did have something to do with the initial talent distribution. There were several cases where even while correctly executing my desires, the drafting scout took players which were far less talented than those still on the board meeting the same criterion.

[cthomer5000]

Originally Posted by Samdari

I, for one, do not think it was purely luck. I do think that many of us were inexperienced with setting of sliders for the preference draft, and what that would mean to the computer. I interpreted the sliders far differently than I the algorithm ended up, and therefore drafted a lousy roster. You simply guessed better than the rest of us at what the sliders would bring you in terms of player's abilities.

Luck did have something to do with the initial talent distribution. There were several cases where even while correctly executing my desires, the drafting scout took players which were far less talented than those still on the board meeting the same criterion.

Agreed on both counts. I think some of us just had better ideas on how to make the sliders give us a result as close to possible as a hand-picked roster would have been. My roster was pretty much what I expected (with pleasent surprises at LB). My secondary was so insanely deep that I got a lot in return when trading off 3 players over the course of 2 years. Albion just got both the skills he needed and a great mix of ready to play but not ready to retire (Stillwater/Telluride).I don't think it is luck by any means, as we've seen a number of teams clearly under-perform their level of talent (*cough* 2005 Syracuse *cough*). Winning when you have the talent is usually a direct reflection of the GM'ing, and I think albion has done an outstanding job there. Amazingly he seems to have made the team even better in it's second go-round.

And on a micro-level the AI definitely made some odd selections for everyone in the initial draft. A number of guys who were drafted in rounds 10-20 (of 53) are sitting in the FA pool right now.