Steals, Scoring and Scoring Impact: Marcus Smart and Russ Smith

[hwangjini_1]

What he is saying is that, proportionately, getting 1 steal has the same impact on the final box score as getting 9.1 points. It is a subtle difference, but an important one.

That's not really what he's saying. He's actually saying that a steal has the same PREDICTIVE power as 9.1 points:

"As measured by his difference in SRS (simple rating system, or average margin of victory/defeat adjusted for strength of schedule) with or without him. By comparing the regression coefficients for each variable, we can see the relative predictive value of each (all else being equal). Because we?re particularly interested in how each stat compares with points scored, I?ve set the predictive value of a single marginal point as our unit of measure (that is, the predictive value of one point equals one, and something five times more predictive than a point is five, etc.)."
Source: http://fivethirtyeight.com/features/the-hidden-value-of-the-nba-steal/#fn-5

Again, the obvious explanation for the figure of 9.1 instead of some average point swing (based on sampling) is that a steal is often an indicator of favorable defensive matchup that exists in other possessions as well.

It's important to remember that these stats are drawn retroactively to explain wins and losses. Point differentials and scoring expectations are well understood in terms of correlation to win/loss records. It therefore makes sense to use points as a sort of currency to assess the predictive value of other key stats, but the analysis has to be limited to just that. In this sense, the goal of the researcher/statistician has to hypothesize as to WHY a stat's predictive value (in terms of points or any other metric/currency) is what it is. Saying that a steal has the same predictive power as 9.1 points is not the same thing as saying that a steal itself has the same proportional impact as 9.1 points because a steal is correlated with and/or represents a favorable defensive matchup that limits points scored in other defensive possessions.

Thank you. It is clearer to me now. Tp for the explanation.

[RyNye]

Isn't that implying that all the major counting stats have identical impacts on the box score?  In a literal sense I guess that's technically correct, but in terms of actually affecting the game it seems extremely dubious.

Yes, this is one of my major reservations with the analysis, which I did not mention explicitly in my last post. It treats every counting stat as an independent observation. They DO weight them with respect to contribution to win shares, but it isn't clear how rigorous of a definition that really is. Further, it is a bit of a sticky grey area in statistics (one that is sometimes unavoidable), whereby you are essentially using the measured performance of a system as your parameters for examining the performance of that system. That is, you are assuming that a team scoring 100 points a game is a reliable model for the contribution of points to winning. But, when you look at teams in the league and rank them by scoring (or by steals) you don't tend to see a reliable correlation with their win records.

All basketball statistics are inherently dependent on one another, but our standard statistical techniques assume independence. It is very difficult to analyze dependent observations without detailed information about the nature of the dependency, which at the moment we don't really have (or, rather, we have the information, but have not yet found the right model within which to integrate that information sensibly).

[RyNye]

That's not really what he's saying. He's actually saying that a steal has the same PREDICTIVE power as 9.1 points:

Well, yes and no. To be honest, he seems a bit confused about the underlying math. My last post was referring to the way they generate that 9.1 figure, which is a descriptive (not predictive) model. What the author is trying to do is use the observed parametric relationships of steals and points (and rebounding, etc.) in order to generate a predictive model. It is ... well, it isn't particularly good statistical practice, to be honest. It wouldn't be accepted in many of the well respected statistical journals, for example.

To be clear, the 9.1 figure in and of itself is not predictive, it is simply comparative. However, after making some assumptions about the nature of the data, one can use that comparative figure to make predictions. Again, I am splitting hairs here, and to a casual observer it may not be clear that there is a real distinction to be made here but it is actually a massively significant one.

Here's a non-basketball example. If you measure the heights and weights of 5,000 people you may find that there is some linear relationship between height and weight. Say that for some unit increase in height, you observe a 0.5 unit increase in weight. So the relationship between height and weight is 0.5 in your observed data set. This is a descriptive statistic, and a comparative one. It isn't inherently predictive. However, one can still make predictions based on it ... you may guess that if you sample another 5,000 people you will find something reasonable close to 0.5. You are basically making the assumption that your measure is unbiased, and thus given an infinitely large sample is indistinguishable from whatever the "true" (and unmeasured) relationship between height and weight is.

It's important to remember that these stats are drawn retroactively to explain wins and losses. Point differentials and scoring expectations are well understood in terms of correlation to win/loss records. It therefore makes sense to use points as a sort of currency to assess the predictive value of other key stats, but the analysis has to be limited to just that.

I'm not sure what you mean when you say the analysis has to be limited to just "that"?

In this sense, the goal of the researcher/statistician has to hypothesize as to WHY a stat's predictive value (in terms of points or any other metric/currency) is what it is.

To be fair to the statisticians, they only have to establish that the stat DOES have predictive value, not WHY it does. Essentially, the way all statistical tests are set-up is the opposite of how most people think of a problem. All statistical analysis works under the hypothesis that the measured stat has NO predictive value whatsoever. None. Statistical tests are executed under this assumption. For another non-mathematical example, it's like you start up an car's engine and measure the heat being generated by the engine, and try to prove the engine isn't running. Since you measure some positive amount of heat being generated, you then reject your assumption that the engine isn't running. It's sort of weird, but it is a mathematical imperative for reasons that I won't get into.

Saying that a steal has the same predictive power as 9.1 points is not the same thing as saying that a steal itself has the same proportional impact as 9.1 points because a steal is correlated with and/or represents a favorable defensive matchup that limits points scored in other defensive possessions.

Yes. I agree. But, to be fair, the same thing can be said for points. That is, it represents a favorable offensive matchup. The reason the researcher is focusing on steals is because the observed variability in steals production is low relative to the variability in points production. I am not saying I agree with him completely, but there is a certain amount of sense in trying to measure performance with a relatively consistent measurement.

[loco_91]

If you look at the study, it says that when analyzing a player's impact, "a marginal steal is weighted nine times more heavily when predicting a player?s impact than a marginal point." This is not the same as saying that a steal is worth 9 points. It means that for the purpose of predicting a player's value to a team, a steal is worth that much, because it is strongly predictive of a player's goodness in other ways.

Thus, why I really really really like Marcus Smart, the top ball-hawk and overall the best perimeter defender in the NCAA.

[BballTim]

How does a steal equate to 9 points??

I don't really understand this

Bad Regression analysis.

Part bad regression analysis/interpretation and part bad communication.  The author is likely correct in equating a steal with 9.1 points in terms of predictive ability but he misses the obvious answer as to why the figure is so much higher than the turnover point swing: steals in a game are strong indicators of winning defensive matchups that limit scoring in other possessions as well. Put simply: guys/teams get more steals when they are playing great defense and/or winning individual matchups.

  I don't think this is at all true. There's no real relationship between steals and how well a team defends or how successful the teams are.

[BballTim]

The analysis does not say that a steal is worth 9.1 points. Although I have some problems with the methodology employed, saying that it equates a steal to 9.1 points is fallacious.

What he is saying is that, proportionately, getting 1 steal has the same impact on the final box score as getting 9.1 points. It is a subtle difference, but an important one.

Look, an NBA team averages somewhere between 5 and 9 steals per game. Let's just take the middle ground and say 7. So if a player on that team averages 1 steal per game, on average they are responsible for just over 14% of the team's output in steals.

Similarly, an NBA team averages between 93 and 108 points per game. Again, let's use the middle ground and say 100. A player would have to average 14 points per game to be responsible for 14% of the team's output in steals.

Now, this isn't EXACTLY how they got the 9.1 percent number. The math they used was more sophisticated and weighted to take into account a variety of factors (including team averages in team transition offense/defense and other important considerations). But the logic is essentially the same. It is just a parametric description of the relative impact of a statistic with respect to overall team performance. It doesn't say that 1 steal will produce 9.1 points.

Now, you can debate whether you agree with this number. Certainly it is a very brute-force approach to modeling relative statistical impact; in my mind, a more rigorous approach would be a Bayesian method using distributions of prior probabilities (e.g. Lance Stephenson driving into the paint is more likely to result in a turnover that counts as a steal for the opposing team than Chris Paul; etc.), but this isn't a trivial calculation, and requires knowledge that isn't accessible without access to the Sports VU camera data. However, that does not mean that the 1 steal/9.1 points comparison is inherently meaningless, either. It is actually a very important statistic to understand, it just requires proper contextualization.

This statistic does not tell you that a steal is more important to winning a basketball game than points. It merely tells us that, taken into account the total production an NBA team tends to produce regardless of whether the game is a win or a loss, you have to score 9.1 points to share the same proportional impact as getting 1 steal. That is all. This should be intuitive: when you look at the box score, any team is going to have at minimum 70 points (usually closer to 100), but will tend to only have about 1/10th as many steals. Another way to think about it is that there is greater variability in points than there are as steals (which, again, should be pretty intuitive if you've ever watched basketball). The ability to produce steals is more consistent than the ability to produce points.

  This seems basically like what I was getting out of the article. Something along the lines of "getting a steal has a much bigger impact on you team's steals total than getting a basket has on you team's point total". From there, though, they seem to be saying that, since you're impacting the box score more with a steal, you're impacting the game more with a steal. I don't think he ever really explains that correlation.