Power Ranking

[mystic]

4 games last night, the prediction based on my Power Ranking was:
Heat +10.1
Spurs +5.8
Kings +5.4
Blazers +12.1

RMSE for the last 22 games:

with HCA: 11.27
without HCA: 12.57
only HCA: 14.58

[J.E.]

Here's a small demonstration how RAPM derived power ratings work, using Chicago as an example

First, find Chicago's games in the bbv dataset, listing the newest one first

CHI {0: '20120104CHIDET', 1: '20120103ATLCHI', 2: '20120101MEMCHI', 3: '20111230CHILAC', 4: '20111229CHISAC', 5: '20111226CHIGSW', 6: '20111225CHILAL'}

Game 6 is too old, so we first look at game 5: 20111226CHIGSW
For every Chicago player that played in that game get a) the number of possessions he was involved in b) his current total RAPM rating taken from http://stats-for-the-nba.appspot.com/ranking_rec

726 Watson, C.J. -0.001753 79.0
-0.0692435 79.0 -0.78885

The first number is the player's bbv playerID. Watson played 79 possessions and he has a rating of -0.0017 (per 200possessions), We scale that player's rating to 100 possessions and multiply his rating with the # of possessions, leading us to the "-0.0692435", which is the current team strength. Obviously we're not done yet

880 Asik, Omer 0.005247 39.0
0.033073 118.0 0.252251694915

Asik has a rating of 0.005. It gets scaled to 100, then multiplied with his possessions, then added to current team strength, which is now 0.03. The '118' tracks the total amount of possessions so far in this game.

755 Rose, Derrick 0.028747 155.0
2.2609655 273.0 7.45373241758

Lots of possessions from a good player does good things to your team rating, which is now at 2.2. We're still not done yet

54 Korver, Kyle 0.016247 67.0
2.80524 340.0 7.42563529412
617 Brewer, Ronnie 0.005747 58.0
2.971903 398.0 6.72038366834
270 Hamilton, Richard -0.014253 94.0
2.302012 492.0 4.21099756098
518 Boozer, Carlos 0.006247 100.0
2.614362 592.0 3.97453682432
122 Deng, Luol 0.044747 164.0
6.283616 756.0 7.4804952381
811 Gibson, Taj 0.007747 89.0
6.6283575 845.0 7.05978905325
686 Noah, Joakim 0.013747 100.0
7.3157075 945.0 6.96734047619

So we end up with a team rating of 7.3, but it was a fast game with 945 possessions. Scaling the team rating to standard pace (*900/945) gives us the final rating of 6.9 for that game

Here's Memphis at Chicago

880 Asik, Omer 0.005247 33.0
0.0865755 33.0 2.36115
755 Rose, Derrick 0.028747 59.0
0.934612 92.0 9.14294347826
54 Korver, Kyle 0.016247 32.0
1.194564 124.0 8.67022258065
617 Brewer, Ronnie 0.005747 59.0
1.3641005 183.0 6.70869098361
726 Watson, C.J. -0.001753 19.0
1.347447 202.0 6.00347673267
518 Boozer, Carlos 0.006247 50.0
1.503622 252.0 5.37007857143
122 Deng, Luol 0.044747 65.0
2.9578995 317.0 8.39782192429
811 Gibson, Taj 0.007747 35.0
3.093472 352.0 7.90944545455
686 Noah, Joakim 0.013747 38.0
3.354665 390.0 7.74153461538

Player possessions are not counted when there's a >20 point difference at the start of the possession. Notice how there are only 390 total possessions because the game had lots of garbage time. After scaling the current team rating (3.3) to 900 possessions we get the final team rating for that game, 7.7.

The final ratings for the last 6 games are, with possessions in brackets, newest game at the bottom:
6.96 (945.0)
5.93 (975.0)
6.93 (885.0)
7.74 (390.0)
8.44 (910.0)
6.23 (915.0)

I use an arbitrary weighing scheme, which is 6/5/4/3/2/1. We want to give newer games more weight, with the newest game getting the largest weight. Games are also weighed by possessions to avoid weird effects in games that had lots of garbage time.

The final rating then is (6.23*915*6+8.44*910*5+.....)/(915*6+910*5+..) = 7.1

[mystic]

Thanks for sharing. It would be interesting to see whether such system is better at predicting than a system based on all games equally included. Well, the latter is what I'm doing, because I think that with such a low sample like only 5 games a fluke game has a too big of an impact.

Anyway, last night had two games screwing up a lot. The Nets winning at Raptors by 12, but I expected -18.3 for them. Also, the Suns winning by 25, while I expected them to have -20.4.

RMSE for the last 34 games:

with HCA: 13.79
without HCA: 14.70
only HCA: 14.31

I also tested a pace adjusted, because the rating points are adjusted to 100 possessions.

Pace adjusted: 13.69

[J.E.]

Mystic, I'm not sure what we are supposed to gain from you constantly posting RMSE when you have never explained how you ratings work. I also don't see an explanation on your site.
Because you compare your RMSE only to HCA (we can't compare it with mine because it's a different sample) we can't tell whether it's good or bad, either

[mystic]

Mystic, I'm not sure what we are supposed to gain from you constantly posting RMSE when you have never explained how you ratings work. I also don't see an explanation on your site.

Explanation in short: Team performance level per 100 possessions against an average team, if such an average team scores 1 point per possessions. Portland had 116 before last night, means: Portland is expected to win by 16 against an average team, if the pace is 100 of that game.
Phoenix had 92.6 -> 92.6 - 116 = -23.4 -HCA-> -20.4

I now compare those -20.4 with the +25. That's what the RMSE is about.

Because you compare your RMSE only to HCA (we can't compare it with mine because it's a different sample) we can't tell whether it's good or bad, either

As I pointed out I started on Tue, Jan 3, 2012. The predictions are based on all games played prior to this date. All the 34 games played are included. Each day I calculate the Power Ranking and use the most recent Ranking to make the prediction for the respective games. That means for last nights games I used the Power Ranking based on all games played before last night.
Unfortunately I don't have any prior data to include those games before the Tue, Jan 3, 2012. If you can calculate the RMSE starting from Tue, Jan 3, 2012, it becomes comparable.

Btw, I have no idea how good that is anyway, it might be in fact pretty bad.

[J.E.]

That tells us nothing about how you get those ratings

[DSMok1]

How do you arrive at the rankings, Mystic? Is it a basic least-squares model, similar to SRS but with efficiency instead of points?

[mystic]

That tells us nothing about how you get those ratings

Indeed, it doesn't. I misunderstood your question and thought you want to know how I get the RMSE.

Anyway, short explanation for the rating:

1. Calculate average player rating (PRA not SPM) for the team.
2. Calculate expected scoring margin based on player rating.
3. Calculate expected scoring margin from real win% while adjusting for strength of schedule.
4. Combine both and make an adjustment for league average.
5. Adjust to 1 point per possession as league average.

The coefficient for the combination was found by trying to find the best predictor for playoff results. Granted, I used only 5 seasons from 2003 to 2007.
The last step is done for an easier comparison between different years and it seems easier to understand that the average is 100 instead of 104 or whatever.


DSMok1, not quite, but I have to admit that the results are looking quite similar in the end. It could mean that a more simple way to calculate the rating could give the same predictive power (if there is any ).

[Jeff Fogle]

Sorry, been out of pocket for a few days. Visiting the belly of the beast (lol) on a family trip. Amazing how much night-time horse racing there is across the land. NBA has to share screentime with horse racing and college hoops on all the big screens in the sportsbooks. Looks to be minor interest unfortunately. So, "Vegas lines" really are just oddsmakers + sharps at this point. Lakers games are shown more prominently. Still a Lakers town. Noticed that the LA airport (on layover) wasn't selling any Clippers gear yet...still all Lakers.

Will try to get caught up on market ratings by midweek. Watching sports in the Pacific time zone is so weird when you're used to starting times from Central or East...

[EvanZ]

Jerry, is your RMSE calculated based on your ratings before each game or is it a retrodictive error? The reason I'm asking is because my model is giving 12.2 RMSE, but that's using the ratings retrodictively. If your error is being calculated using the pre-game ratings, could you also publish what the retrodictive RMSE would be?

[J.E.]

It's taking the ratings before each game. Don't have the time to look up the retrodiction error, but I'm definitely up for it after the season

[EvanZ]

Ok, that's what I figured. I knew I didn't have you beat that easily.

If I take your current ratings, I can figure it out with my spreadsheet.

EDIT: Ok, done. FWIW, when I use your column (3) and my HCA ratings, you get 11.98 RMSE, so still better than my ratings.

[mystic]

Has someone a link for a good website where I can find the Vegas lines also for past games?

[J.E.]

I've had a discussion with EvanZ on the use of team specific home court advantage (HCA) in forecasting point differential of single games.
Probably due to my bad explanation of my thought process, the topic is still not clear to me.

The basis for the argument are the ridge regressed power ratings with homecourt advantage, posted here
http://thecity2.com/2011/12/30/ridge-re ... advantage/
where DSmok posted team specific HCAs (every team has their own HCA instead of the same HCA for all teams).
Of interest is the 2nd green table, with Denver at the top. It lists estimated HCA for each team

Code: Select all

1 	DEN 	6.49
2 	GSW 	6.07
3 	UTA 	5.67
4 	IND 	5.26
5 	CHA 	4.60
6 	ORL 	4.47
7 	CLE 	4.33
8 	POR 	4.02
9 	PHX 	3.97
10 	CHI 	3.46
11 	TOR 	3.35
12 	HOU 	3.05
13 	WAS 	3.03
14 	LAL 	2.95
15 	SAS 	2.86
16 	NOH 	2.81
17 	MEM 	2.52
18 	MIL 	2.46
19 	ATL 	2.34
20 	LAC 	2.32
21 	MIA 	1.87
22 	OKC 	1.63
23 	SAC 	1.63
24 	PHI 	1.49
25 	DAL 	1.12
26 	BOS 	0.95
27 	NJN 	0.92
28 	NYK 	0.81
29 	DET 	0.65
30 	MIN 	0.59

My basic question is not directly related to the model, but just forecasting point differential with the help of team specific HCAs:
When we forecast point differential between team1 and team2 with the game being played at team1, do we only take the HCA of team1 into account? Or do we take HCA of both team1 and team2 into account?

Here's what I've written so far:
A team specific HCA of 6.5(Denver) means the team plays 3.25 worse away, compared to neutral, and it plays 3.25 better at home, compared to a neutral court, does it?
Say MIN(0.6) plays at DEN(6.5). Does that mean, for forecasting, that the expected HCA *for that game* is (0.6+6.5)/2 = 3.05?
Expected HCA is not just DEN’s HCA, or is it?

If you compute team ratings (say with SRS), then their rating is the average of their home strength and their away strength (if the team had an equal amount of home and away games). Now, having a high team specific HCA in what DSmok1 posted means there is a large difference between their home strength and their away strength.
Say you’re GSW, you have a home game and you can choose between playing Denver or Minnesota. In this example, let both teams have a strength of 0. Given their team specific HCAs, would you rather play Denver or Minnesota?
I think it’s clear you would want to play Denver.

[mystic]

Well, I interpret HCA as difference to the expected result, if the game would be on a neutral place. Meaning: Denver plays 6.5 points better at home than expected. An average team plays 2.83 better. The HCA for the prediction would be just the listed HCA, not the average of both teams.

Taking your example of Min@Den; right now I have Den with +5 and Min with -5.4. On a neutral court I would expect Den wins by +10.4. Taking the average HCA (+2.8) into account it would be +13.2, taking the specific HCA for Den (+6.5) it would be +16.9. Would they play in Min, it would be +7.6 for Denver with average HCA and +9.8 with the specific.

That would be my quick interpretation, BUT your idea makes sense here. I don't know the model specifics, but in the end those HCA numbers can indeed reflect just the difference between home and away. A good home team can also just be a bad road team. It doesn't even need to be symmetric, it can also be 2/3 being good at home and 1/3 being bad on the road.

Well, that doesn't answer your question at all, but at least I agree that this is not clear.