This is a first in what I intend to be an occasional series of posts that explores aspects of Spurs' performance in a semi-rigorous way (as rigorous as data would allow).
Pop described Spurs' performance in recent games since Tony Parker's injury as "playing in the mud". Certainly, we all feel some sympathy with this description. So I went exploring the data to see where our problems lay primarily and whether our gut feelings bear out in the data.
Identifying Our Problem Areas
Cursory look at the data suggests that on average the last six games since the injury, our offensive numbers are about the level we were at for the season pre-injury. Our FG% before the injury was 48.7%. Post-injury it is 48.1%. The 3FG% pre-injury is 38.0% and post-injury is 38.8%. Our FT% is also comparable, along with per game rebound averages, assist and TO averages. Our pace is down a bit and thus, understandably, so is our point output.
When we examine the defensive numbers, particularly opponent statistics, is where we find significant difference. The number that immediate jumps out at you are the opponent 3FG%. Pre-injury, we kept the opponent at 32.5%. Post-injury, this number is a whopping 46.6%. That's almost a 15% jump! You may be thinking, well there were two games that could reasonably be argued as outliers where our opponent shot 60% or better from beyond the arc. But, even removing these two games, the post-injury opponent's 3FG% is at 38.7%. Well enough above the pre-injury season average to suspect our perimeter defense has been a major problem lately.
Part of this can be explained away by Tony's absence. He is one of our better perimeter defenders. However, if you look at the opponent 3FG% when Tony is off the court, it is at 33.6% (pre-injury). If you're wondering, when he's on the court the percentage goes down to 31.6%. So it appears, from simple averages, that our perimeter defense has been sub-par beyond what could be accounted for by the absence of Tony Parker. But...
Is our Perimeter Defense Actually Worse?
In other words, is this difference actually statistically significant? Since, there are variation throughout the season, these recent cases could very well be normal fluctuations in the data. Well, I did some analysis of the raw data (culled from game logs) to see if, indeed, this difference is significant. For those interested parties, I have included a description of my methodology at the end.
First thing I did was to look at the last 6 games vs. 60 games prior to injury. It was no surprise to find that between these two sets of data, the difference in opponent 3FG% was indeed very statistically significant. Next, I decided to exclude the two plausible outlier cases (games against Portland and Minnesota). The difference, in this case, was also found to be convincingly statistically significant.[*] So the analysis confirms our suspicion that our perimeter defense is indeed much worse than usual (and not a statistical fluke). In fact, in only the game against Pistons did we hold our opponent to below season average (31.6%) and only one other game (against OKC) where we held them below 40% (at 35.3%).
But, is this the case if we only compare games in which Tony Parker has not played? Here, we find a small ray of hope. There have been 4 games this season prior to injury when Tony sat out. The average opponent 3FG% in these games is 33.5% with standard deviation of 12.2%. When we compare this number to the 6 games since the injury, the difference is statistically significant, but less confidently so. However, when removing the 2 possible outliers we find that the difference is well below statistical significance. So, there is some cause to believe that our degradation in perimeter defense can be explained away by absence of Tony Parker.
Brief Description of Methodology
First thing I did was to gather the opponent 3FGA and 3FGM data from the game logs for all 66 games thus far and split these into the 60 games prior to injury and 6 games post-injury. I also marked the 60 games prior to injury with a flag to indicate whether Parker played in the game or not. I used, Welch's Student t-test (so my assumption was the two data sets had different true variances) to test for statistical significance in performance differences in all comparison cases with standard p-value of 0.05 (i.e. 5%). Since t-test assumes normal distribution in the data sets, and the data are proportional data, i.e. percentages, which are obviously not normally distributed, I first performed an arcsin transformation on the data to make it resemble a normal distribution.
Couple of caveats, since the data set post-injury consists of only 6 data points, the analysis should be taken with some grain of salt. Also, I did not run any normality test on the (transformed) data to verify the assumption of normal distribution since it would be fairly useless on a 6 point data set.
[*] If you're a stats nerd, both cases would have had null-hypothesis rejected at a p-value of 0.01.
Updated to fix awkward sentence formation and headshake-inducing grammatical errors.