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ziller
Joined: 30 Jun 2005
Posts: 126
Location: Sac Metro
PostPosted: Tue Aug 23, 2005 5:59 pm Post subject: Marginal Point Differential Reply with quote
God I sound pretentious with topic subjects like "Marginal Point Differential" and "Smart Ratings."
Anyways, I've been looking at point differentials, or scoring margins, for last season's Western Conference teams.
I looked at scoring margin overall, and was thinking what the best way to interpret it was. Is raw scoring margin the best measure? Or is it better to rate teams based on how many more (or less) points they scored than their opponents relative to how many points their opponents actually scored?
I thought about it on a game-to-game basis. If San Antonio beats Seattle 80-70, its raw scoring margin is +10, and its proportional scoring margin is 14.2% (the Spurs scored 14.2% more points than the Sonics).
If Phoenix beats Houston 113-100, its raw scoring margin is +13 - much better than San Antonio's. But its proportional scoring margin is 13%.
San Antonio, scoring 14.2% more points than Seattle (or forcing Seattle to score 14.2% less points than it scored) performed better than Phoenix, then, given that both played at home (or on the road) and Houston and Seattle are of equal difficulty.
Looking back at the full season (which accounts for those home/road splits and schedule strength within each conference), here's the proportional scoring margin for the teams of the west.
Code:
Team Scoring Margin
SAS 8.83
PHX 6.89
DAL 5.94
HOU 4.43
MEM 2.52
SEA 2.37
SAC 2.13
DEN 2.08
MIN 1.52
LAC -0.80
GSW -2.14
LAL -2.91
POR -4.13
UTA -4.39
NOH -7.41
I'll note that there is only one difference between this list and the list that ranks teams based on raw points differential: Memphis and Seattle both had identical raw differentials of +188. But the Grizzlies gave up about 450 less points overall.
I think this type of ranking adds depth to team comparisons. To wit, San Antonio's raw differential was <60 points better than Phoenix's - which doesn't seem like much. But SA's 2% advantage over Phoenix in proportional scoring margin seems more telling.
Most of my time in this area, though, has been spent charting scoring margins over the season for all the Western Conference teams. Essentially, I raided B-R for game results, separated the points for and against to get the individual game differentials, then made it cumulative.
For an example, here's Denver's running scoring margin. Each figure represents the team's cumulative scoring margin at the end of that game (regular season only):
Code:
DEN
-11
-9
-33
-44
-64
-56
-68
-62
-44
-16
-14
-28
-22
-13
-32
-23
-10
-4
10
-1
-9
-8
-15
-37
-39
-54
-68
-71
-66
-74
-78
-87
-105
-114
-102
-112
-122
-116
-106
-108
-112
-129
-123
-116
-96
-99
-83
-73
-79
-74
-89
-85
-91
-70
-67
-66
-43
-34
-18
-5
-2
-7
12
31
42
71
92
106
97
108
126
132
135
146
149
165
181
195
204
176
162
166
The Nuggets have one of the more funs lines in the graph. Obviously, by looking at their record, you could tell when they sucked, when they started getting better and when they became a good team. But looking at the points differentials, you can tell a little earlier and a little more accurately.
I can't exactly lay it all out in a forum post, but the Excel file (graph included! - I'm not worthy, Kupfer) is hosted here: http://www.geocities.com/thallnorcal/04 ... argins.xls
Oh, and longest. post. ever. Sorry.
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MDC
Joined: 11 Jun 2005
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PostPosted: Tue Aug 23, 2005 8:06 pm Post subject: Re: Marginal Point Differential Reply with quote
ziller wrote:
I looked at scoring margin overall, and was thinking what the best way to interpret it was. Is raw scoring margin the best measure? Or is it better to rate teams based on how many more (or less) points they scored than their opponents relative to how many points their opponents actually scored?
I thought about it on a game-to-game basis. If San Antonio beats Seattle 80-70, its raw scoring margin is +10, and its proportional scoring margin is 14.2% (the Spurs scored 14.2% more points than the Sonics).
If Phoenix beats Houston 113-100, its raw scoring margin is +13 - much better than San Antonio's. But its proportional scoring margin is 13%.
San Antonio, scoring 14.2% more points than Seattle (or forcing Seattle to score 14.2% less points than it scored) performed better than Phoenix, then, given that both played at home (or on the road) and Houston and Seattle are of equal difficulty.
I think what you want to do here is use points per 100 possessions to eliminate the pace factor. Using the difference of points per 100 possessions, Seattle, Sac and Denver rise above Memphis which more accurately reflects their win records from last season than the scoring margin.
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Ed Küpfer
Joined: 30 Dec 2004
Posts: 785
Location: Toronto
PostPosted: Tue Aug 23, 2005 8:31 pm Post subject: Re: Marginal Point Differential Reply with quote
ziller wrote:
God I sound pretentious with topic subjects like "Marginal Point Differential" and "Smart Ratings."
You think that's pretentious? Once, I interupted a study on pace adjustments with a digression on the early haiku work of World B Free.
Your move, Mr. Bond.
ziller wrote:
Anyways, I've been looking at point differentials, or scoring margins, for last season's Western Conference teams.
I looked at scoring margin overall, and was thinking what the best way to interpret it was. Is raw scoring margin the best measure? Or is it better to rate teams based on how many more (or less) points they scored than their opponents relative to how many points their opponents actually scored?
Something to keep in mind is that point differentials (PDs) essentially tell you the same thing as Pythagorean win estimates. A single per game PD is worth about 2.5 extra wins. Also, if you're looking at game level PD you don't even have to worry too much about pace. And even over the course of the season, pace adjusted PDs don't really tell us more than raw PDs.
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MDC
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PostPosted: Tue Aug 23, 2005 9:16 pm Post subject: Re: Marginal Point Differential Reply with quote
Ed Küpfer wrote:
And even over the course of the season, pace adjusted PDs don't really tell us more than raw PDs.
Really? Looking at the rankings in the west last season, Memphis comes out tied with Seattle for 5th in raw PD, and 8th in pace adjusted PD. Since the 8th place is closer to the actual standings, it seems like pace adjusted PD is the better predictor. Although they only differ by half a point in pace adjusted PD.
This is just one example though. I guess I'm curious why it's not a significant difference (I'm new to the stats game).
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Ed Küpfer
Joined: 30 Dec 2004
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Location: Toronto
PostPosted: Tue Aug 23, 2005 9:32 pm Post subject: Re: Marginal Point Differential Reply with quote
MDC wrote:
Ed Küpfer wrote:
And even over the course of the season, pace adjusted PDs don't really tell us more than raw PDs.
Really? Looking at the rankings in the west last season, Memphis comes out tied with Seattle for 5th in raw PD, and 8th in pace adjusted PD. Since the 8th place is closer to the actual standings, it seems like pace adjusted PD is the better predictor. Although they only differ by half a point in pace adjusted PD.
This is just one example though. I guess I'm curious why it's not a significant difference (I'm new to the stats game).
That is because every team and their opponents have the same number of possessions over the course of a season, by definition. It's when you isolate offense and defense that you need to adjust for pace. I'm guessing that any differences in between a team's Pts Pyth and their RTG pyth [*] is due to differences in the Pythagorean exponent, along with random variation.
[* RTG = pts/possession.]
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MDC
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PostPosted: Tue Aug 23, 2005 9:54 pm Post subject: Re: Marginal Point Differential Reply with quote
Ed Küpfer wrote:
That is because every team and their opponents have the same number of possessions over the course of a season, by definition. It's when you isolate offense and defense that you need to adjust for pace. I'm guessing that any differences in between a team's Pts Pyth and their RTG pyth [*] is due to differences in the Pythagorean exponent, along with random variation.
[* RTG = pts/possession.]
I apologize, but I still don't get it. Am I mistaken in believing that a victory with a margin of 20 points in a game with a 100 possessions is less meaningful than a victory by 20 points in a game with 80 possessions?
Suppose there are two hypothetical basketball games. In the first the victor scores 120 points and the loser scores 100. Each team has 110 possessions. The difference in their points per possesion would be .18, or 18 points over a 100 possessions. In the second game, the victor scores 80 points and the loser scores 60, and each team has 70 possessions. There is a difference of .28 points per possession, or 28 points over a 100 possessions. So it would seem logical to assume that the victor in the second game thrashed their opponent more thoroughly than the victor in the first hyptohetical game. Adjusting to possessions would capture this, raw differential clearly doesn't.
Are you saying that not enough scenarios like this occur for it to be considered significant? That could be, but it seems like modeling with pace is a more true representation of what is happening and it's not a difficult calculation. I would think the inproved accuracy is what we are striving for.
Or is it statistically not significant (or something else that's over my head?)? Unfortunately my statistics courses won't be for another quarter.
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MDC
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PostPosted: Tue Aug 23, 2005 10:44 pm Post subject: Reply with quote
BTW, I apologize to Ziller for taking this slightly off-topic!
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ziller
Joined: 30 Jun 2005
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Location: Sac Metro
PostPosted: Tue Aug 23, 2005 10:58 pm Post subject: Reply with quote
Apology accepted! I was actually tackling this more just to get my own feet wet testing theories and calculating stuff, like most of my previous forays into statgeekism. (I mean that in a good way!)
When I mentioned I was adjusting for pace, I only meant it in the aspect that the % figures better representative the importance of margin than raw margins do. For example, the 10 points being more important in a low-scoring game than in a high-scoring game. Pace was the wrong word to use, because I did no pace adjustment. Just based the margins on points allowed, which factors in the pace by association.
This stuff is really sludge for those of you who actually are deep into hoops statgeekism - you guys could do this and explain it clearly in your sleep. Me, not so much. Soon, though. Smile
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Ed Küpfer
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PostPosted: Tue Aug 23, 2005 11:44 pm Post subject: Reply with quote
It appears I may have skipped a few steps. I'll go over it again, from the beginning. Forgive me if you already know some of this stuff.
Maybe the most important thing Bill James ever came up with was a runs-to-wins converter, which he called the Pythagorean Method. It is easily transferred to other sports. Here is the hoops version:
WIN% = PTS_scored^x / (PTS_scored^x + PTS_allowed^x)
where x is some exponent -- 14 works fine. Take the 05 Wiz, who scored 8241 points and allowed 8268 points, or 100.5 and 100.8 per game. The Wiz's Pythagorean Win% (hereafter PYTH) is:
PYTH = 100.5^14 / (100.5^14 + 100.8^14) = 0.49
or about 40 wins. They actually won 45, so the Pyth was off by 5 wins. Generally, it's much more accurate: 2/3 of all teams' actual win% fall within 3 wins of their PYTH predicted win%.
(The exponent that minimizes errors varies from year to year. The errors do not get minimized all that much, however, and you're probably just better off sticking with 14.)
Anyway, if you look at the PYTH equation, you can see that essentially it is measuring the difference between a team's points scored and points allowed -- the team's points differential. The bigger the difference between points scored and allowed, the greater the number of predicted wins.
Now, around here we usually adjust for pace. We do this by expressing stats as "per possession" -- or, more commonly, "per 100 possessions." The latter we usually denote as ORTG or DRTG for offensive and defensive ratings. The are points scored and points allowed per 100 possessions.
(Possessions, 'round here, are defined as the alternating periods of time during which only one team controls the ball. That means an offensive rebound off a missed shot does not start a new possession.)
The 05 Wiz had an ORTG of 104.0 and a DRTG of 104.2. Sticking those numbers into the PYTH equation,
PYTH = 104.0^14 / (104.0^14 + 104.2^14) = 0.49
The pace-adjusted numbers deliver the same predicted win% as the non-pace-adjusted numbers. That is because under our definition of possession, teams alternate possessions, guaranteeing that a team's offense will end up using as many possessions in a season as the team allowed their opponents. That is why pace-adjustments don't do anything here.
Your adjustment for margins may tell us something, but I'm skeptical. I haven't looked at this, but I can't imagine why low offense games' margins tell us any more than high offense games'. I'll see if I can pour over the data tomorrow.
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MDC
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PostPosted: Wed Aug 24, 2005 12:30 am Post subject: Reply with quote
Ed Küpfer wrote:
The pace-adjusted numbers deliver the same predicted win% as the non-pace-adjusted numbers. That is because under our definition of possession, teams alternate possessions, guaranteeing that a team's offense will end up using as many possessions in a season as the team allowed their opponents. That is why pace-adjustments don't do anything here.
Thanks for the explanation. I'm afraid that I still don't get it though, lol. It still seems like pace adjusted differentials come up with different results than non-pace adjusted differentials.
Using RTG Points Differential, Miami is ahead of Phoenix (8.4 compared to 8.2), whereas with Raw Points Differential, Phoenix is ahead of Miami (7.12 compared to 6.52).
Using the Pythagorean Method with raw points and an exponent value of 14, we get 101.54^14/(101.54^14+95.02^14) = 71.7%, or 58.8 games.
Using the Pythagorean Method with offensive and defensive ratings taken from B-R.com, we get 108.2^14/(108.2^14+99.8^14) = 75.6%, or 62 games.
Doing the same calculations with Phoenix, I end up with 71.8% (58.9 games) using raw points and 74.4% (61 games) using RTG.
I end up with Phoenix rating higher in both raw points differential and raw Pythagorean Method Win%, and Miami rating higher in both RTG differential and RTG pythagorean Method. The values of the RTG PYTH differ by a couple wins from the raw PYTH, and nearly 4% in the case of Miami.
So to get back to your post, it seems in this example that the pace does do something. Is it doing it better than the raw values, or is it just errors in the coefficient and perhaps the record of possessions that is making these values differ? Because if there were differences between the two I can't help but feel that the pace adjusted model would be the one to go with simply because possessions more accurately describe basketball than per Game values nearly everywhere else in basketball stats.
And I apologize if I'm being obtuse, overly-persistent, or just don't have enough statistical knowledge to understand this. I'm just trying to wrap my head around this.
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Kevin Pelton
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PostPosted: Wed Aug 24, 2005 1:07 am Post subject: Reply with quote
MDC wrote:
Using RTG Points Differential, Miami is ahead of Phoenix (8.4 compared to 8.2), whereas with Raw Points Differential, Phoenix is ahead of Miami (7.12 compared to 6.52).
Using the Pythagorean Method with raw points and an exponent value of 14, we get 101.54^14/(101.54^14+95.02^14) = 71.7%, or 58.8 games.
This is presumably a fluke owing to the way we estimate possessions.
If you divide the points per game by the per-100 possession ratings, you'll find that we're estimating the Heat has 93.8 possessions per game, their opponents 95.2.
Presuming the Heat doesn't actually do some thing systemtically to cause them to not get the last shot of quarters - and I'm going to go ahead and do this - this difference doesn't reflect reality. It might have something to do with Shaquille O'Neal and Dwyane Wade getting as many three-point plays as they do or something (step in here any time now, Crazy From The Heat).
If you make the possessions equivalent, you get essentially the same Pythagorean winning percentage as with points per game.
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MDC
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PostPosted: Wed Aug 24, 2005 3:14 am Post subject: Reply with quote
Thanks for your patience guys. I'm now at ease with not pace-adjusting differentials in the PYTH function. I suppose if I had stopped and done some algebra I would have seen values in the numerator and denominator that would have canceled out if the possessions were accurate (and I would have saved you all some trouble!).
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