# Offense To Defense: An Investigative Report On How Each Side Of The Ball Relates To Success In The NBA

An oft-repeated adage in the NBA states: “Offense wins eyes, but defense wins games”. While this type of platitude has become a commonly perpetuated cliché throughout NBA circles, its statistical applicability is rarely, if ever, challenged. In order to investigate whether there is some kind of significant difference in how offense, as opposed to defense, relates to wins altogether, I decided to investigate, with the 2014-15 NBA season serving as my personal guinea pig. Using team wins as my response variable, I plotted each team’s offensive and defensive rating, as explanatory variables, against the other, in order to differentiate between the predictive power of each as it pertains to regular-season wins in the NBA. All of my corresponding data for this investigation is displayed in the following table, and teams are sorted alphabetically, with “ORtg” denoting each team’s offensive rating (points scored per one-hundred possessions and “DRtg” denoting each team’s defensive rating (points allowed per one-hundred possessions—so, less is more):

Furthermore, the following medley of scatterplots, equations, and explanations in context serves to parse the data I have collected. First, for the initial explanatory variable:

The above scatterplot shows the relationship between team offensive rating, my first explanatory variable, and total teams wins, my response variable. Here, there is a moderately strong, positive, linear relationship between the strength of a team’s offensive rating and the number of games it won. The correlation for these variables is r=0.819. Evidently, teams that score a high number of points per 100 possessions tend to also win a good amount of games.

In order to model the relationship between offensive rating and wins, via the scatterplot, I used the least-squares regression line. The equation of the least-squares regression line is shown along with the scatterplot: wins = 2.92ORtg – 269.5.

In this equation, the slope of the line is the coefficient of the x variable (in this case, ORtg). The interpretation of the slope is the predicted change in the y variable when the value of the x variable is increased by 1. Accordingly, for the least-squares regression line using offensive rating to predict wins, the slope of 2.92 indicates that for every additional point per 100 possessions a team scores, the predicted number of wins will increase by about 2.92.

The y-intercept of the least-squares regression line is a = -269.5, which is where the least-squares regression line crosses the y-axis. In this case, though, the y-axis is not visible on the scatterplot because the horizontal scale starts at a value significantly greater than 0.

Lastly, the standard deviation of the residuals, which estimates the typical distance between a team’s actual number of points scored per 100 possessions and their predicted number of games won, is about 7.85. In other words, this estimates about how far away one should expect the points on the scatterplot to be from the graph of the least-squares regression line. As such, when using offensive rating to predict wins, predicted values will typically be about 7.85 wins from the actual values.

Next, I parsed some of the information I calculated regarding the relationship between the second explanatory variable, DRtg, and the response variable, wins:

The scatterplot above shows the relationship between my second explanatory variable, defensive rating, and my response variable, total team wins. There is a fairly strong, negative, about-linear relationship between the strength of a team’s defensive rating and the number of games it won. The correlation for these variables, accordingly, is r=0.707. Altogether, this makes sense, given the fact that, generally, the less points a team allows per 100 possessions, the more successful it can expect to be.

So as to model the relationship between defensive rating and wins, via the scatterplot, I used the least-squares regression line. The equation of the least-squares regression line is shown along with the scatterplot: wins = -3.45DRtg + 408.5.

Given this equation, the slope of the line is the coefficient of the x variable (in this case, ORtg). The interpretation of the slope is the predicted change in the y variable when the value of the x variable is increased by 1. Accordingly, for the least-squares regression line using defensive rating to predict wins, the slope of -3.45 indicates that for every additional point per 100 possessions a team allows, its predicted number of wins will decrease by 3.45. This, obviously, is because defensive rating and team wins have a negative relationship, as opposed to the positive relationship that exists between offensive rating and wins.

The y-intercept of the least-squares regression line is a = 408.5, which is where the least-squares regression line crosses the y-axis. Again, though, in such a case, the y-axis is not visible on the scatterplot because the horizontal scale starts at a value significantly greater than 0.

The standard deviation of the residuals, which estimates the typical distance between a team’s actual number of points allowed per 100 possessions and their predicted number of games won, is about 9.68. In other words, this estimates about how far away one should expect the points on the scatterplot to be from the graph of the least-squares regression line. As such, when using defensive rating to predict wins, my predicted values will typically be about 9.68 wins from the actual values.

To decide which variable (offensive or defensive rating) is a better predictor of games won, however, I compared the standard deviation of the residuals for each relationship. Because I want my predictions to be as close as possible to the actual values, the explanatory variable that provides the smaller standard deviation of the residuals—offensive rating—proves to be superior predictor.

While this gives me enough reason to believe that offensive rating is actually a better predictor of regular season wins, I used the relationship with this smaller standard deviation of the residuals and crafted a set of hypotheses to test and use to determine whether there is a statistically significant association between offensive rating and wins. As such, using the observed slope from prior (2.92) as my test statistic and wins=2.92ORtg -269.5 as the equation of the least-squares regression line, I deemed the following my null hypothesis: The true slope of the least-squares regression line using x = offensive rating and y = wins is 0. On the other hand, this was my alternate hypothesis: The true slope of the least-squares regression line using x = offensive rating and y = wins is positive.

To investigate this, I, assuming that the true slope is 0, used an online applet to simulate the distribution of the test statistic. However, it is also possible to run such a simulation manually. This could be done by writing the win values on note cards, shuffling the cards, randomly pairing a win value with each value of team offensive rating, and calculating the simulated slope. This process would be repeated many times, and its results would thenceforth be recorded on a doplot. The following visual displays such results of mine, only via an online statistical applet:

The above dotplot displays the results of 100 trials of this simulation. Each dot represents the slope of the least-squares line for predicting wins from points scored per 100 possessions (offensive rating) in one simulated season. Because there were 0 simulated slopes even close to being greater than or equal to the observed slope of b=2.92, my p-value is 0%. If the true slope of the least-squares regression line using x = offensive rating and y = wins is 0, there is just about no chance of getting a slope as great or greater than 2.92 by random chance. Because this p-value is so nonexistent, I reject the null hypothesis. I have convincing evidence that there is a positive association between offensive rating and wins in the NBA during the 2014-15 regular season. It is not really plausible that the observed association was due to random chance. Rather, there is strong evidence in favor of my alternate hypothesis.

Ultimately, not only does this investigation suggest that offensive rating seems to relate more closely to regular season wins than does defensive rating, but there is a strong enough association between offensive rating and wins to indicate that the amount of points a team can score over the course of one-hundred possessions is a major predictor of success in the NBA. Evidently, offense does win games after all. Keep shooting that shot, folks.

# 1 Comment

1. Nice post. I learn something more challenging on different blogs everyday. It will always be stimulating to read content from other writers and practice a little something from their store. I’d prefer to use some with the content on my blog whether you don’t mind. Natually I’ll give you a link on your web blog. Thanks for sharing.