DC4646
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PostPosted: Thu Dec 02, 2010 12:30 pm Post subject: How Does Offensive Efficiency Change Throughout the Season? Reply with quote
Hi all,
Well, the title of the post is pretty self explanatory. I just ran a simple linear regression with week-number (25 weeks in a season) along the x-axis and offensive efficiency along the y-axis. Here is an image of the resulting graph: http://4.bp.blogspot.com/_ldfrs9-ffs0/T ... graph2.png.
As you can see, league-wide offensive efficiency goes up as the season goes on. On average, there is a jump of about .16 pts/100possessions each week. r^2=.76.
Here are few important notes:
a). All the data I used came from basketball-reference. I used 10 years of data (it's conceivable that if you go back farther you get a significantly different results, though I personally don't think you would). The averages on the y-axis were computed as follows. Just for the sake of being concrete, I'll look at the first point on the graph. For this point, I computed how many possessions took place, in each game, for the 1st week of the season (10/28-11/5). Using the score of each game and the number of possessions, I computed the offensive efficiency of every team, in each game that took place in the first week. I then averaged the offensive efficiencies. This process was repeated for all 25 weeks of the season.
b). These offensive efficiency numbers represent global averages. For example, the first data point in the graph represents the average offensive efficiency of the entire NBA for the first week of the season. Because these are global averages, defensive efficiency is exactly the same as offensive efficiency (just like how at the end of the season, league-wide offensive efficiency is exactly the same as league-wide defensive efficiency).
c). Because these are global averages and because they were taken over 10-years, this graph doesn't really describe an individual team's offensive efficiency over the course of one season. For one, rarely is a team's offensive efficiency exactly equal to its defensive efficiency. Secondly, league-wide avg offensive efficiency changes from year to year. For example, last year the league-wide avg offensive efficiency was 107.3 pts/100possessions, which is extremely high in the context of the above graph.
Interpretations of the Data:
a). This graph seems to suggest that as the season goes on offense generally improves, while defense gets worse. One possible explanation is that it takes time for offenses to get into the swing of the things (i.e. new players have to be incorporated, coaches have to institute new offenses, rotations aren't set yet, players are still rusty from the off-season...).
b). The data also suggests that offensive efficiency, taken over the course of a season, generally underestimates how good a team's offense is at the end of the season. This is because when you average over the course of the season, among other things, you do penalize a team for slow starts. This bias may or may not be big enough to have a serious effect on inferences one would like to make using season-long average offensive efficiency. Or, the real issue is whether season-long average offensive efficiency underestimates some teams' end-of-season offenses more than it does others. That's the question I am currently investigating.
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DSMok1
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PostPosted: Thu Dec 02, 2010 12:45 pm Post subject: Reply with quote
I just posted this graph in another thread last week:
My numbers agree with yours. My data is for the last 3 seasons.
After adjusting for team strengths and rest days, I found that average efficiency increased at 0.026 Points/100Poss/Day. (That multiplies out to 0.18/week, very close to your numbers).
The very low number for the first week of the season could be tied to the number of days off; a similar drop in efficiency was observed in my data for the first game for each team after the all-star break.
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Mike G
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PostPosted: Thu Dec 02, 2010 12:46 pm Post subject: Reply with quote
What if you separate the playoff-bound teams from those who have dropped out of the running? It may be that players for lottery teams will slack on defense, while still gunning for impressive offensive stats. This effect would only increase as the year goes on.
And perhaps the opposite effect: greater defensive intensity late in the year among teams vying for playoff seeding.
And then, in playoffs, how have teams fared relative to their competition? There aren't many meaningless games in playoffs.
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DSMok1
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PostPosted: Thu Dec 02, 2010 12:49 pm Post subject: Reply with quote
Mike G wrote:
What if you separate the playoff-bound teams from those who have dropped out of the running? It may be that players for lottery teams will slack on defense, while still gunning for impressive offensive stats. This effect would only increase as the year goes on.
And perhaps the opposite effect: greater defensive intensity late in the year among teams vying for playoff seeding.
And then, in playoffs, how have teams fared relative to their competition? There aren't many meaningless games in playoffs.
In the playoffs, there is a significant drop both in pace and rating.
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Mike G
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PostPosted: Thu Dec 02, 2010 12:53 pm Post subject: Reply with quote
If ORtg drops in playoffs, even relative to better DRtg opponents, then doesn't that suggest the observed season-long increase in league ORtg may be inflated by some experimental lineups, tanking, sloughing on D, etc?
Even playoff teams may rest their stars in late games, allowing lesser players to run amok on offense. It seems that playoffs are closer to the true gauge of where a team's offense and defense really are, at season's end.
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DSMok1
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PostPosted: Thu Dec 02, 2010 2:16 pm Post subject: Reply with quote
Mike G wrote:
If ORtg drops in playoffs, even relative to better DRtg opponents, then doesn't that suggest the observed season-long increase in league ORtg may be inflated by some experimental lineups, tanking, sloughing on D, etc?
Even playoff teams may rest their stars in late games, allowing lesser players to run amok on offense. It seems that playoffs are closer to the true gauge of where a team's offense and defense really are, at season's end.
You know, I was wrong what I said about rating. It is pace that drops. I just plotted out the results of my regression factoring out team ratings and effect of rest days, and here is the resulting chart:
The amazing thing is that the end of the regular season and the beginning of the playoffs just about line up, even though I used a separate modifier for the playoffs. So it doesn't look like there is an issue at all: offenses just get better through the season and then decrease slightly in the playoffs.
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EvanZ
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PostPosted: Thu Dec 02, 2010 3:21 pm Post subject: Reply with quote
DSMok1 wrote:
offenses just get better through the season and then decrease slightly in the playoffs.
Run into tougher defense, right?
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Serhat Ugur (hoopseng)
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PostPosted: Thu Dec 02, 2010 3:26 pm Post subject: Reply with quote
A bit off the topic, I had looked at underdog winning percentages at the end of last year's regular season. I don't know what's your take but I could not detect any trend except for a few weeks.
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DSMok1
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PostPosted: Thu Dec 02, 2010 3:26 pm Post subject: Reply with quote
EvanZ wrote:
DSMok1 wrote:
offenses just get better through the season and then decrease slightly in the playoffs.
Run into tougher defense, right?
That's accounting for opposing defenses already....
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DC4646
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PostPosted: Thu Dec 02, 2010 4:28 pm Post subject: Reply with quote
Serhat Ugur (hoopseng) wrote:
A bit off the topic, I had looked at underdog winning percentages at the end of last year's regular season. I don't know what's your take but I could not detect any trend.
How exactly are you defining "underdog"?
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Serhat Ugur (hoopseng)
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PostPosted: Thu Dec 02, 2010 5:28 pm Post subject: Reply with quote
DC4646 wrote:
Serhat Ugur (hoopseng) wrote:
A bit off the topic, I had looked at underdog winning percentages at the end of last year's regular season. I don't know what's your take but I could not detect any trend.
How exactly are you defining "underdog"?
I'm using point spreads released by sportsbooks for each game.
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DC4646
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PostPosted: Fri Dec 03, 2010 12:22 pm Post subject: Reply with quote
@Serhat
I don't know a whole lot about sports betting. Do you think your findings are saying something about Vegas' point spreads or basketball or both?
If you define "underdog" differently, say by using the difference between pt. differential, you might see trends. In fact, you'd almost certainly see a ton of "upsets" early in the season simply because of the high variability of any of the stats one might think of using to define underdog. That would actually be a major problem.
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DC4646
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PostPosted: Fri Dec 03, 2010 12:42 pm Post subject: Reply with quote
@DSMok1:
I'm glad our numbers are close. To be honest, I'm just sort of getting used to R. At the back of my head, I felt like there was a small chance that I might have plugged in a few numbers wrong. And, my findings would be totally off. And, the study of basketball statistics would be set back 20 years.
p.s.
What software do most people use for basketball statistics? I'm using R mostly because I'm planning on going into biostatistics and I know that I'll probably eventually need to learn R.
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DC4646
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PostPosted: Fri Dec 03, 2010 1:02 pm Post subject: Reply with quote
Going back to this sentence in my original post: "I used 10 years of data (it's conceivable that if you go back farther you get a significantly different results, though I personally don't think you would)." More precisely, I used data from the last 10 seasons.
I just ran the same study for data from 1990-1999, I actually did get (kind of) significantly different results. The graph is here: http://3.bp.blogspot.com/_ldfrs9-ffs0/T ... ph1999.png.
For the sake of comparison, the graph for data from 1999-2010 is here:http://4.bp.blogspot.com/_ldfrs9-ffs0/T ... graph2.png
In the graph using data from 1999-2010, each week there was a jump of .16 pts/100posession. In the graph from 1990-1999, each week there was a jump of only .08 pts/100possessions. r^2 in old graph was .76. r^2 in the new graph is only .4.
I want to say hand-checking rules have something to do with the difference, but that's not really based on anything. Or, maybe it has something to do with parity issues before the 1999 CBA.
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DSMok1
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PostPosted: Fri Dec 03, 2010 1:09 pm Post subject: Reply with quote
DC4646 wrote:
@DSMok1:
I'm glad our numbers are close. To be honest, I'm just sort of getting used to R. At the back of my head, I felt like there was a small chance that I might have plugged in a few numbers wrong. And, my findings would be totally off. And, the study of basketball statistics would be set back 20 years.
p.s.
What software do most people use for basketball statistics? I'm using R mostly because I'm planning on going into biostatistics and I know that I'll probably eventually need to learn R.
I primarily just use Excel. You can do just about anything with it.
I've dabbled in R, and when I get more into Adjusted Plus/Minus calculations, I'll have to. I think R is probably the way to go.
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EvanZ
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PostPosted: Fri Dec 03, 2010 3:26 pm Post subject: Reply with quote
I use Matlab, but I get it for free. I use Apple's Numbers spreadsheet to make prettier plots. I'm also starting to get into R (and learning Bayesian stats).
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DC4646
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PostPosted: Fri Dec 03, 2010 4:26 pm Post subject: Reply with quote
Ah, yeah, that's other big reason I've been using R: it's free.
I've also been getting into Bayesian statistics. It seems like Baysesian statistics could be put to good use at the beginning of the season. Presumably, you could use last seasons' data to come up with prior distributions for parameters...and then go through the whole Bayesian stats routine. It seems like this would be better than just using the current seasons' stats. This is already being done by somebody, right?
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DSMok1
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PostPosted: Fri Dec 03, 2010 4:34 pm Post subject: Reply with quote
DC4646 wrote:
Ah, yeah, that's other big reason I've been using R: it's free.
I've also been getting into Bayesian statistics. It seems like Baysesian statistics could be put to good use at the beginning of the season. Presumably, you could use last seasons' data to come up with prior distributions for parameters...and then go through the whole Bayesian stats routine. It seems like this would be better than just using the current seasons' stats. This is already being done by somebody, right?
That's what I'm doing for Advanced SPM, in a simplified form.
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DC4646
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PostPosted: Fri Dec 03, 2010 9:47 pm Post subject: Reply with quote
Sorry, I'm new to the forum. Does Advanced SPM, stand for Advanced Statistical Plus Minus?
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gabefarkas
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PostPosted: Fri Dec 03, 2010 10:25 pm Post subject: Re: How Does Offensive Efficiency Change Throughout the Seas Reply with quote
DC4646 wrote:
Here are few important notes:
a). All the data I used came from basketball-reference. I used 10 years of data (it's conceivable that if you go back farther you get a significantly different results, though I personally don't think you would). The averages on the y-axis were computed as follows. Just for the sake of being concrete, I'll look at the first point on the graph. For this point, I computed how many possessions took place, in each game, for the 1st week of the season (10/28-11/5). Using the score of each game and the number of possessions, I computed the offensive efficiency of every team, in each game that took place in the first week. I then averaged the offensive efficiencies. This process was repeated for all 25 weeks of the season.
Seems like this doesn't weight all possessions equally. For instance, let's say there are 10 games in a given week. Each game counts towards 1/10th of the average you calculated. However, Game 1 might have had 90 possessions, while Game 2 might have had 120. That means each possession in Game 1 contributed 1/900th of the average, while each possession in Game 2 only contributed 1/1200th of the average.
Instead, why not tally up the total number of possessions among all games in a given week, then tally up the total number of points in that week, and then calculate the efficiency based on those total numbers?
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gabefarkas
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PostPosted: Fri Dec 03, 2010 10:34 pm Post subject: Reply with quote
DC4646 wrote:
Ah, yeah, that's other big reason I've been using R: it's free.
I've also been getting into Bayesian statistics. It seems like Baysesian statistics could be put to good use at the beginning of the season. Presumably, you could use last seasons' data to come up with prior distributions for parameters...and then go through the whole Bayesian stats routine. It seems like this would be better than just using the current seasons' stats. This is already being done by somebody, right?
Do you know about Andrew Gelman's blog (he's a professor at Columbia)? He is big into both R and Bayesian stuff. I'd recommend it to you.
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EvanZ
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PostPosted: Fri Dec 03, 2010 11:20 pm Post subject: Reply with quote
gabefarkas wrote:
DC4646 wrote:
Ah, yeah, that's other big reason I've been using R: it's free.
I've also been getting into Bayesian statistics. It seems like Baysesian statistics could be put to good use at the beginning of the season. Presumably, you could use last seasons' data to come up with prior distributions for parameters...and then go through the whole Bayesian stats routine. It seems like this would be better than just using the current seasons' stats. This is already being done by somebody, right?
Do you know about Andrew Gelman's blog (he's a professor at Columbia)? He is big into both R and Bayesian stuff. I'd recommend it to you.
I'm going through his book right now. Smile
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DC4646
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PostPosted: Sat Dec 04, 2010 12:18 am Post subject: Reply with quote
[Seems like this doesn't weight all possessions equally. For instance, let's say there are 10 games in a given week. Each game counts towards 1/10th of the average you calculated. However, Game 1 might have had 90 possessions, while Game 2 might have had 120. That means each possession in Game 1 contributed 1/900th of the average, while each possession in Game 2 only contributed 1/1200th of the average.
Instead, why not tally up the total number of possessions among all games in a given week, then tally up the total number of points in that week, and then calculate the efficiency based on those total numbers?]
That's a wonderful point! I didn't even consider the problem. Your approach definitely yields a more pure measure of global offensive efficiency. What's even nicer is that I think I can redo the graph pretty easily. I might have a new graph up by the end of the night.
Really, true "global offensive efficiency" (what your proposing) is just different than "average league-wide offensive efficiency". I guess for very large sample sizes, average league-wide offensive efficiency is confusing because it doesn't have much predictive value for an individual teams' performance (as I stressed in my post).
I'm ultimately interested in looking to see whether season-long offensive efficiency uniformly underestimates teams going into the playoffs. So, for the purposes of my research I'm going to be more interested in average league-wide offensive efficiency. Still your post has raised a number of good questions. For example, what would a discrepancy between true global offensive efficiency and average league-wide offensive efficiency mean? Would it just mean that teams with low pace are, as a group, significantly better/worse on offense then teams with high pace?
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DSMok1
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PostPosted: Sat Dec 04, 2010 9:20 am Post subject: Reply with quote
I prefer to look at each game and then average them. If we're averaging pace, we shouldn't weight the average BY the pace, should we? That's double-counting.
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DC4646
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PostPosted: Sat Dec 04, 2010 9:05 pm Post subject: Reply with quote
hm, I'm not sure I follow your point about double counting. Could you expand on your reasoning?
I personally can't think of anything wrong with either statistic. They just measure two different things. One measures the behavior of a typical teams' offensive efficiency over time. The other, in the most literal sense, measures league-wide offensive efficiency.
I do think you can make an argument that the former statistic is, in most contexts, more "interesting". We usually think of the NBA as a collection of distinct teams. Interesting statistics usually reflect this.
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gabefarkas
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PostPosted: Mon Dec 06, 2010 9:16 am Post subject: Reply with quote
DC4646 wrote:
That's a wonderful point! I didn't even consider the problem. Your approach definitely yields a more pure measure of global offensive efficiency. What's even nicer is that I think I can redo the graph pretty easily. I might have a new graph up by the end of the night.
Really, true "global offensive efficiency" (what your proposing) is just different than "average league-wide offensive efficiency". I guess for very large sample sizes, average league-wide offensive efficiency is confusing because it doesn't have much predictive value for an individual teams' performance (as I stressed in my post).
I'm ultimately interested in looking to see whether season-long offensive efficiency uniformly underestimates teams going into the playoffs. So, for the purposes of my research I'm going to be more interested in average league-wide offensive efficiency. Still your post has raised a number of good questions. For example, what would a discrepancy between true global offensive efficiency and average league-wide offensive efficiency mean? Would it just mean that teams with low pace are, as a group, significantly better/worse on offense then teams with high pace?
I'm not sure I understand the distinction you're trying to draw. In your original post, you wrote that "...league-wide offensive efficiency goes up as the season goes on." You also wrote: "b). These offensive efficiency numbers represent global averages. For example, the first data point in the graph represents the average offensive efficiency of the entire NBA for the first week of the season. "
It seems to me that "league-wide offensive efficiency" would be the average efficiency of a possession among the entire league. If that's what you want, wouldn't you want to weight all possessions equally?
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DSMok1
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PostPosted: Mon Dec 06, 2010 10:15 am Post subject: Reply with quote
gabefarkas wrote:
I'm not sure I understand the distinction you're trying to draw. In your original post, you wrote that "...league-wide offensive efficiency goes up as the season goes on." You also wrote: "b). These offensive efficiency numbers represent global averages. For example, the first data point in the graph represents the average offensive efficiency of the entire NBA for the first week of the season. "
It seems to me that "league-wide offensive efficiency" would be the average efficiency of a possession among the entire league. If that's what you want, wouldn't you want to weight all possessions equally?
I would not. If we have, say 3 games: 1 has 70 possessions with an efficiency of 70, 1 has 90 possessions with an efficiency of 90, and 1 has 110 possessions with an efficiency of 110, what would you say the average efficiency is? I would adjust for pace (which is a basic maxim of advanced basketball stats). I would take game 1, game 2, and game 3, and simply average the efficiency and get 90 as the efficiency. However, weighting all possessions equally, you would end up with an average efficiency of (70x70 + 90x90 + 110 x 110)/(70+90+110) = 93.
I believe correcting for pace first is the proper way of calculating an average efficiency.
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DC4646
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PostPosted: Mon Dec 06, 2010 11:24 am Post subject: Reply with quote
@gabefarkas
When I made the original post I wasn't even thinking about the possibility of weighing each possession equally. This is really a language problem. I'll explain more precisely what I originally meant.
"b). These offensive efficiency numbers represent global averages. For example, the first data point in the graph represents the average offensive efficiency of the entire NBA for the first week of the season. " First off, the averages are "global" in the sense that every team is included in each average. When I said the first data point is "the average offensive efficiency of the entire NBA for the first week of the season," again I meant that the average was taken over all all teams in the NBA.
"It seems to me that "league-wide offensive efficiency" would be the average efficiency of a possession among the entire league."
League-wide offensive efficiency to me is the average efficiency of a possession to an individual team. The big distinction is in italics.
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gabefarkas
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PostPosted: Mon Dec 06, 2010 1:23 pm Post subject: Reply with quote
DSMok1 wrote:
gabefarkas wrote:
I'm not sure I understand the distinction you're trying to draw. In your original post, you wrote that "...league-wide offensive efficiency goes up as the season goes on." You also wrote: "b). These offensive efficiency numbers represent global averages. For example, the first data point in the graph represents the average offensive efficiency of the entire NBA for the first week of the season. "
It seems to me that "league-wide offensive efficiency" would be the average efficiency of a possession among the entire league. If that's what you want, wouldn't you want to weight all possessions equally?
I would not. If we have, say 3 games: 1 has 70 possessions with an efficiency of 70, 1 has 90 possessions with an efficiency of 90, and 1 has 110 possessions with an efficiency of 110, what would you say the average efficiency is? I would adjust for pace (which is a basic maxim of advanced basketball stats). I would take game 1, game 2, and game 3, and simply average the efficiency and get 90 as the efficiency. However, weighting all possessions equally, you would end up with an average efficiency of (70x70 + 90x90 + 110 x 110)/(70+90+110) = 93.
I believe correcting for pace first is the proper way of calculating an average efficiency.
In the 70-by-70 game, an efficiency of 70 points per 100 possessions means that each team scored (on average) 49 points, for a total of 98 points. In the 90-by-90 game, an efficiency of 90 points per 100 possessions means that each scored (on average) 81 points, for a total of 162 points. In the 110-by-110 game, an efficiency of 110 points per 100 possessions means that each scored (on average) 121 points, for a total of 242 points.
So, we have a total of 98 + 162 + 242 = 502 points scored.
Also, we have a total of 70 + 70 + 90 + 90 + 110 + 110 = 540 possessions. That's assuming each team had the same number of possessions in their game...a trivial, but basic, assumption given your example.
By my calculation, that means the average efficiency, expressed in points per 100 possessions, would be: 502 / 540 * 100 = 92.96.
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PostPosted: Mon Dec 06, 2010 1:32 pm Post subject: Reply with quote
Yes, that's what I calculated, if you weight each game by the number of possessions in it.
That's probably not the best way to calculate an average efficiency, though. That means you would weight Golden State's game efficiencies more than Portland's. Honestly, though, it probably won't be that huge an effect unless there is a correlation between average efficiency and pace. The correlation was only 0.23 last year...
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