Matthew Yglesias – of the Atlantic – has asked for a specific study of the NBA. In The Statistical Analysis We Need, Yglesias stated the following:

*I was looking at this latest iteration of efforts to use adjusted +/- statistics to evaluate NBA players, and it served as a reminder of how frustrating I find it that such a large proportion of efforts to apply quantitative tools to the analysis of basketball are dedicated to these searches for magic formulae to assess player quality. There are other, more interesting and probably more fruitful, lines of inquiry where quantitative skills could shed some light.*

*For example, there’s a popular conception of a link between pace and defensive orientation — specifically the idea that teams that choose to play at a fast pace are sacrificing something in the defense department. On the most naive level, that’s simply because a high pace leads to more points being given up. But I think it’s generally assumed that it holds up in efficiency terms as well. The 2006-2007 Phoenix Suns, for example, were first in offensive efficiency, third in pace, and fourteenth in defense. But is this really true? If you look at the data season-by-season is there a correlation between pace and defense? When pace changes leaguewide, does scoring efficiency also change? Then there are lots of interesting team level issues to ask. Intuitively, some teams’ offenses are optimized for the fast-paced style and will function less efficiently during games that wind up being played at a slow pace. And vice versa also probably holds. But are there some teams who are making a mistake? Squads who score more efficiently when they play slower, but usually try to play fast?*

*I’m too lazy to actually conduct research into those questions, and I’m not even sure I know how to calculate a coefficient of correlation correctly these days, but I’d read someone who wanted to do it. *

After I read this I decided to stop my work on my “magic formula” and decided to address the question posed by Yglesias.

**The Link Between Pace and Efficiency**

I have data on possessions, offensive efficiency [points scored divided by possessions], and defensive efficiency [points allowed divided by possessions] from 1973-74 to 2006-07. Now possessions have generally decreased across time. So I calculated for each team their relative possessions, where relative possessions are a team’s possessions per game divided by the league average possessions per game in that particular season.

Given this data, is there a link between offensive efficiency and pace? In other words, if a team plays at a faster pace, does the team become more or less efficient?

The answer is no and no. Specifically, the correlation coefficient between relative possessions and offensive efficiency tells us there is no relationship. The correlation coefficient is only 0.03. And when you regress offensive efficiency on possessions you fail to find a statistically significant relationship.

Turning to defense, we find a little more, although not much more. The correlation coefficient between relative possessions and defensive efficiency is 0.17. Regressing defensive efficiency on relative possession reveals that there is a statistically significant relationship. The more possessions a team has per game – again, relative to the league average – the more points the team’s opponents will score per possession. But relative possessions only explains 2.8% of defensive efficiency. In sum, pace doesn’t tell us much about defensive efficiency.

And I suspect that a well-defined defensive efficiency model would tell us, as we found with respect to offensive efficiency, that pace doesn’t matter on the defensive side of the ball either. In other words, the simple univariate model (or a model with only one independent variable) is mis-specified. If I took the time to properly specify the model, by including all the independent variables that impact defensive efficiency, it may very well be the case that the statistical significance of pace will vanish.

Then again, it might not. Anyway, it doesn’t appear that pace has much impact on defensive efficiency.

Hopefully that answers the question. Now I need to get back to working on my “magical formula.”

**On “Magical” Formulas**

Okay, I’m just kidding. I’m not working on any “magical formula.” I am pretty happy with Wins Produced, Wins Score, and PAWSmin. Other than working on how I explain these models, I am not really working on these metrics.

I would note that there is nothing “magical” about the Wages of Wins models, or even adjusted plus-minus (or the models of Dean Oliver). Each of these models are just ways of looking at performance in basketball. And each has their pluses and minuses (pardon the pun).

I sense, though, that people become frustrated with these metrics because they expect “magic.” In other words, people want a number that answers all questions and reduce the cost of thinking to zero. Models, though, help us explain the world we observe. Models are not “magical”, nor do they remove the need to keep thinking. And that is something to think about when you look at basketball measures, or any other models researchers offer to improve our understanding of our world.

– DJ

*Basketball Stories*

Ben Guest

December 3, 2007

Great post, as always.

Jon

December 3, 2007

Dberri I have a question. In the past you have come off as thinking WoW and your metrics are flawless. Now, it seems (or at least this is my interpretation) that while you still obviously love your system more than other peoples (as obviously anyone would who came up with a pretty sound system using economics), you admit it is not perfect. That there may be some flaws. Am I interpreting this correctly?

Patrick

December 3, 2007

It’s actually surprising to me that there is so little correlation between pace and offensive efficiency, even though I would suspect that any correlation would be incidental, not causal. This is simply because teams that are more efficient offensively should push the pace.

Let’s see if I can elaborate:

Assume the Suns have the most efficient offense in basketball. Therefore, vs. any given opponent with an equal defensive efficiency, they should expect to garner more points per possession than their opponent does (and thus win the game).

However, variance is a butt-kicker. It stinks to lose a game you should usually win, just because the opponent made a few 3-pointers more than usual. How to combat this? By playing a game with as many possessions as possible!

Just as you would expect the better team to win more often in a 7-game series than in a 5 (or 3) game series, you would expect the better offensive team (again, assuming equal defensive efficiency) to score more points more often (more “reliably”) if each team gets 100 possessions than if each team gets 80 possessions.

In other words, assuming that increasing the pace has no detrimental effects on your efficiency, the more efficient you are (relative to the opponent) the more you should push the pace.

By contrast, teams with great defensive efficiency and average offensive efficiency would want to SLOW the pace, except vs. very poor offensive teams. This is because you don’t score points by playing defense well, you prevent them. That is, no matter how good your defense is, giving the opposing teams more possessions always means they will score more points. If you are only an average offensive team (meaning you don’t necessarily benefit more than your opponent does from the extra offensive possessions through your offensive efficiency; which again might not be true if you were playing vs. the worst offensive team in the league), you’re taking an unnecessary risk by pushing the pace. This is especially true if your opponent is very good offensively.

Therefore, one would think, that even though playing faster does not make you play better, there would still be some small correlation between pace and offensive efficiency (because coaches with good offenses should tell their players to push the pace).

Make sense or am I employing some logical fallacy?

dberri

December 3, 2007

Jon,

I have never said any work of mine was “flawless.” What you have read is a strawman argument put up by people who did not like the Wages of Wins. The argument is as follows.

1. Berri thinks his model is flawless.

2. No model is perfect.

3. Therefore Berri is wrong.

There is no such thing as a statistical model that is “flawless.” All statistical models have error terms (or residuals).

All that being said, I do think Wins Produced and such are pretty good models for understanding productivity in the NBA.

Pat

December 3, 2007

Essentially this is the difference between the Bulls and the Suns. Bulls= great on defense, Suns= great on offense.

although for God’s sake can the bulls start scoring at some point???

Kent

December 3, 2007

Jon Posner,

Dberri never said his model was perfect. You really need to read this– https://dberri.wordpress.com/2007/11/18/a-guide-to-evaluating-models/

TK

December 3, 2007

Patrick: I’m not clear on why the better defensive team would want to slow the pace. After all, if they enjoy a substantial differential between their excellent defense and an opponent’s average offense, they would want to press that advantage by having as many interactions as possible. If they only get 40 chances to prove that advantage, that’s worse (and introduces more variance) than if they had 60 chances to prove that advantage, no?

Your 7-game-series example suggests the same thing. Any team having any efficiency advantage — whether derived from offense or defense — would expect to demonstrate that advantage more frequently the larger the sample set.

The pre-shot-clock era is the reverse example. College teams that are huge underdogs — whether or not their deficiencies were offensive or defensive — often ran versions of a stall offense. This cut down the sample size. And with fewer possessions per game, they made their bet on variance.

TK

December 3, 2007

Patrick — by the way, I completely agree with the first half of your post.

Jon

December 3, 2007

No I never meant to say you said your work was flawless. I mean that is how some people thought you came off. I don’t think I made myself clear. I am not trying to offend you. I think what I meant was a lot of the “fighting” that went on in these comments is gone. In the past, there seemed to be much more hate between you and your critics, but I have noticed recently that things seem to be more friendly. Like when somebody questions your methods or implys you are wrong or something like that, in the past I think you weren’t as nice in your responses compared to now. I think this is a good thing. I was more just saying I think things are getting friendlier now.

Kent

December 3, 2007

Jon,

Sorry, I misinterpreted what you wrote initially.

dberri

December 3, 2007

Jon,

I think you are just seeing that the critics have mostly gone away.

And I would add, the hostility was not generally coming from our direction.

Ben Guest

December 4, 2007

I think a lot of the critics went away when, last season, the Nuggets traded for AI and several stats gurus predicted they would be an instant championship contender while DB accurately predicted the Nuggets (and the 76ers) final record.

Patrick

December 4, 2007

TK:

This depends on whether or not the team does, in fact, have an advantage from extra possessions. The problem is that defensive and offensive efficiency do not cancel each other out.

Take, for example, the contrived scenario of a team who has the best defense in the league and the worst offense in the league, and they play vs. a team who is average in both.

In this case, extra possessions for both teams won’t help much, because the worst offense in the league vs. an average defense in the league isn’t likely to score more points than an average offense vs. the best defense in the league.

It’s also possible that the differentials aren’t equivalent — i.e. the standard deviation of defensive efficiencies may be greater (or smaller) than that of offensive efficiencies.

Then, or course, there are intangibles. If the reason you are so efficient at offense is because you are pounding it into Shaquille O’Neal in the paint (in his prime), you probably don’t want to push the pace, because that takes Shaq out of the game. If you’re the Pheonix Suns, you do, because Amare is soooo much more efficient running the floor than posting up in the half-court offense.

TK

December 4, 2007

Thanks for clarifying, Patrick .

I thought you were saying that if the efficiency advantage was gained primarily through defensive prowess, somehow a team would want fewer possessions. (At first blush that might seem true, but for the aforementioned reasons, I think it’s actually false.)

Totally agreed that if there’s no efficiency advantage, then there’s no obvious pace decision to make. (Plus the extra intangibles you mentioned.)