Westbrook’s Brave New World

Here, we will be attempting to perform a quite rudimentary analysis of Russell Westbrook’s statistical probability at averaging a triple double over a full, healthy (I have a caveat for that as well) NBA season. I don’t use the term rudimentary self-deprecatingly: there are many difficult to quantify factors in play here, many of which I will touch upon and many more that will undoubtedly slip by me. As such, any pessimists may see this as a slightly dressed up basic analysis.

Now, in the aims of shortening this already ponderous piece and appealing to some common sense, we are not going to perform any calculations for what Westbrook’s probability of satisfying the double digit points requirements for a triple double is — we’ll just ungenerously give it a 100% chance. If that perplexes you, I would highly recommend not reading the rest of this piece…or anything else I ever write.

Russell Westbrook, by statistical measures, the eye test, and opinions of learned basketball minds, has improved his own skills and taken on different schematic roles in the Thunder offense over the years. Because of this, it’s very tough to really peg where his true rebounds and assist averages or means are. However, one things is clear: Westbrook shares a much larger statistical slice of the pie when he’s not playing with Durant. Over the last two seasons, Westbrook played 46 full games (there are a couple games I excluded here where Westbrook played extremely abbreviated minutes because of injury-related concerns since the small sample size means these numbers could be heavily weighted by instances like his 8:49 minute game on 10/30/2014) without Durant. These games should at least give a fairer representation of similar usage trans seasons, so looking at a collection of both surface and more advanced stats should give an idea of whether Westbrook is actually either a better player this year or plays in a manner that contributes to more rebounds and assists or both. Here is a quick screenshot of how Westbrook ranks in each respective years in points, rebounds, and assists per game, as well as touches, passes made, potential assists, assist to pass percentage adjusted, contested rebound percentage, and rebounds chances per game. If you’re unfamiliar with any of the more esoteric aforementioned stats, consult the definitions at the bottom of this article. The selection of these stats was curated through a combination of my own intuition, accessibility, and the mesmerizing beautiful light blue background of the nba.com stats table.

As is easy to pick up from a glance, while many of Westbrook’s usage indicative stats like touches and passes made are constant over the years, there are clear shifts in the stats more indicative of growth in playmaking and rebounding abilities. Furthermore, the previous two season stats for contested rebounds % and rebound chances were taken from the whole season as opposed to only those few games that Durant missed as I made the executive decision to not bother filtering for only those games.

Ok, so looking at this collection of stats, it does appear Westbrook’s play this year is significantly different this year. Of course, a definitive way to prove this would be a through a quick hypothesis test to determine if the p value would be under a statistically significant alpha level, but 1) I don’t have access to game logs of many of these numbers and 2) I deem that the difference is vast enough that it’s easy to deduce that it’s significant. Point one bears repeating as well when it comes to the prediction nature of this article as, if I did use said game logs I could attempt some sort of multi-linear regression (or any more advanced machine learning techniques, like support vector machines or random forests if you’ll let me name drop in the name of credibility) to determine more accurately what said true means are going forward.

Again, it’s impossible to determine to what extent the split between his numbers this year and past seasons exist. Is Westbrook’s true talent level compromised only of his 2016–2017 numbers? Is it a 50/50 split between this year and the past two seasons? 67/23? 75/25?

If you don’t feel confident in choosing any one of these prognoses over the other, or if you wanted to see calculations dependent on all four ratios, you’ve come to the right (and most likely only) place. Here is a quick breakdown of how Westbrook’s statistical “true” means would be with all four aforementioned (don’t try to read this sentence out loud) splits.

So, means is one thing, but we need to get an idea of variability as well. In this case, it would be sensible to be as inclusive as possible, and sticking with the same sample size of a much larger population, I calculated the sample standard deviation of the 68 games (22 this season, 46 from 2014–2015 and 2015–2016) of rebounds and assists, thanks to the easy spreadsheet format of basketball-reference’s game logs. These numbers came out to, respectively, 3.89 and 3.57. Fairly high, but that’s what happens when you have a point guard who occasionally threatens a 20-rebounds game. Jesus Christ, Westbeast is an animal.

Again, this is a sample standard deviation, so for anyone who is a little familiar with probability tests, keep in mind we are using the “n-1” correction, as we are not looking at whole population of Westbrook games.

Anyways, now we have our means and our sample standard deviations, and we can compute some probability estimates using a normal distribution curve. There are assumptions to make here, when using the normal distribution, chief amongst them being a large enough sample size to necessitate the application of the central limit theorem (which 68 games is).

Below are a few plain-looking snapshots of numbers: first, the respective assist and rebounds numbers Westbrook needs to average from here on out for the rest of the season to maintain the bare minimum 10.0 figures for assists and rebounds that would qualify a triple double season (remember his current averages are firmly above it). Here again, is a gray area of guesswork, as we don’t know exactly how many games Westbrook will play for the rest of the season. Obviously, the fewer games he plays the better his odds are, as they need to be dragged down, not up. I have another set of possible parameters here, with possible values of (a full season in) 60, 55, 50, and an injury plagued keep your fingers crossed this won’t happen no matter how much you want the historical relevance of Westbrook averaging the triple double 30 games. Certainly not all-encompassing, but enough to paint you a picture.

The way these numbers were calculated was pretty straightforward: I subtracted from a sum of (games played + projected games left) * 10 the values of (games played * current averages) and then divided the sum by the number of projected games left.

For example, the first assist figure was calculated through the algebraic completion of 82*10 = 11.3*22 + 60*x.

Now, here comes another large assumption, which I am making based both on the need for definite results and some tailored logic: assists and rebounds are independent random variables. This assumption allows us to multiply the respective probabilities together to acquire the probability of both happening at once, by the law of total expectation.

Of course, this isn’t completely true, as allowing Westbrook to grab a rebounds probably increases his odds of an assist — the Thunder rank only behind the Warriors in fastbreak points per game (per teamrankings.com) and love pushing the ball when Westbrook corrals a defensive board, one of the primary reasons he does have so many uncontested rebounds ceded to him by the Stache Bros and other OKC bigs. However, the Bayesian probability is probably close enough to the probability of statistically independent R.V.’s that we can go ahead and use the probability of the product, and frankly, I don’t have the stats at hand to obtain said Bayesian probability. So fuck you if you have a qualm with it.

The expectation of the product of random variables laid out a little bit.

So, after all those healthy helpings of Caesar dressing, here are the arrays of probabilities we are looking at. These were calculated by getting normalized standard unit scores for the respective minimum numbers required to keep the double digit average as compared to the designated true means, and subtracting from 1 the cumulative distribution function of said standard unit…and then again multiplying these probabilities together to get a holistic probability, for all the ‘games played’ and ‘true talent averages’ ranges. The color ranges correspond to the designated true talent levels noted earlier in this article: yellow for a 100% basis on this year, blue for 50/50, green for 67/23, and red for 75/25 in this year’s favor.

A quick example of the calculation for the first probability (43%). The standard unit of -0.50 was obtained through (9.52–11.3)/3.57 with these numbers being, respectively, the minimum number of assists needed to keep up a 10.0 average, the true mean at 100% 2016–2017 number levels and the sample SD for assists. Then 1 — CDF(-0.5) turned out to be .69 or 69% of the area under the curve lies above this point. In turn, this is multiplied with the rebounds own independent probability value of .62 to give us 43%.

So there you have it! Even at my most negative projection, Westbrook’s odds crest above a quarter, or the odds of flipping tail twice in a row. And if you’re a believer, he’s (roughly) only a single coin flip away from joining the Big O in the triple double season average pantheon.

All stats are updated through Tuesday, December 6, 2016.

Per nba.com, Potential Assists are passes to a teammate which would count as assists if the attempted shot was successful; assist to pass percentage adjusted is the percentage of passes that are assists, free throw assists, or secondary assists; and rebounds chances are the number of occurrences when a player was within 3.5ft of a rebound.