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The Sixers’ Past, Present, and Future

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Using DARKO, a continuously updating machine learning talent projection model, to study how the Sixers’ starting five has changed over the course of their careers

If you follow me on Twitter, you might have seen me talking about something called DARKO (Daily Adjusted and Regressed Kalman Optimized projections), created by Kostya Medvedovsky. DARKO is a (very complex) model projecting, based on past performance, what a player is likely to do moving forwards. DARKO learns from a very wide range of parameters across every game a player has played and is updated daily.

What DARKO allows us to do is, at every game of a player’s career, look at their projections at that exact moment, with a focus on box score number rather than all-in-one numbers. We can see the literal shape of their talent over time while accounting for lag time, variance, aging curve, quality of opposition, back-to-backs, travel, speed, interactions with all their other skills, etc., on a game-by-game basis. Kostya states that, “DARKO constantly updates in response to new information, weighting more recent performance more heavily”. For those that are inclined, DARKO beat two paid-DFS sites’ projections in every stat over three years of data.

Therefore, because it’s a projection tool based on the amalgamation of a player’s entire body of work and environment, the output is considered to be a “true talent”. Again, it is not a “what have you done so far” model, but a projection of your abilities, or true talent, going forward.

Math Warning: Here’s a tweet thread from Kostya explaining the model’s debut.

Math Warning: Another blurb of text on DARKO with more detail that is a living document and a work in progress.

Essentially every box score component (and more) is projected in DARKO, but we’re going to focus on three of them. I’m going to talk about Joel Embiid, Ben Simmons, Al Horford, Josh Richardson, Tobias Harris, and then another player per section that I find interesting.

In a surprise to no one, charts will help explain this.

To learn more about DARKO and make your own graphics, check out the web app.

Free Throw Percentage

Career Numbers via Basketball Reference

Embiid: 1198/1515 (79.1%)

Harris: 1433/1747 (82.0%)

Horford:1395/1853 (75.3%)

Simmons: 489/842 (58.1%)

Richardson: 461/563 (81.9%)

Brandon Ingram: 608/890 (68.3%)

The above numbers are the career totals for each of the players, and are often the initial point of departure for talking about a player’s abilities, but we can do so much better now. However, let’s look at the DARKO talent projections for FT% across their careers.

https://apanalytics.shinyapps.io/DARKO/

Couple things of interest here. First, Horford has played over 4x as many games as Embiid. Secondly, all three players at this moment project as 80-85% from the line. Additionally, you can see that Horford had a precipitous drop in his true FT% talent in the middle of his career that he then rebounded from.

https://apanalytics.shinyapps.io/DARKO/

This is the really interesting one though. Richardson has had a nice solid upward trend his entire career and has settled around 85% true talent for almost a full season of games. Ingram and Simmons were both low (and very low) talent FT shooters after approximately 75 games or so. However, since that time, Ingram has increased his true talent, and in the last 30-50 games has truly taken off. You’ll note that Ben has not. Much of this comes from the interaction between FT% and the host of other shooting-related stats. It’s unlikely that Ben will magically improve to a 75% true talent free throw shooter without improving additional shooting talent as well. However, large scale improvements in FT% talent are possible.

Three Point Percentage

Career Numbers via Basketball Reference

Embiid: 202/643 (31.5%)

Harris: 716/1983 (36.1%)

Horford: 396/1072 (36.9%)

Simmons: 1/20 (5.0%)

Richardson: 451/1221 (36.9%)

Brook Lopez: 465/1359 (34.2%)

https://apanalytics.shinyapps.io/DARKO/
https://apanalytics.shinyapps.io/DARKO/

Looking at these together shows how both Horford and Lopez had massive talent spikes in the middle of their careers as they both began to shoot threes, and shoot them effectively. For both of them, the degree and rate to which DARKO “believed” their talent increase was in part due to their other offensive abilities. A player who has solid 2PT% and FT% who suddenly starts taking and making threes will have a more rapid true talent increase than a player who is a low 2PT% shooter and low FT%.

Harris and Richardson have nice upward trajectories (this is a theme with both of them). You’ll note that Embiid’s true talent 3P% is right around 33%, which is where most fans would love him to settle for the long haul given the rest of his high-quality-shooting skill set.

Now, Simmons. True talent here is most illustrative because his sample size of 20 shots is a half of action for James Harden. As mentioned for Horford and Lopez, Simmons needs improvements across the board in shooting stats to have an actual increase in his talent levels. This is why having him chuck threes at 15-20% alone is not going to magically turn him into Klay Thompson. There is a synergy required amongst all his skill sets.

Daily Box Only Plus/Minus (DPM)

Box only DPM is a variant of BPM (Box Plus/Minus) that is calculated slightly differently than what is linked there from Basketball-Reference. Don’t worry too much about the specifics, but it is a single value metric that is based off of box scores. Higher is better, lower is worse.

DARKO calculates this DPM based off of the box score components it predicts; therefore, its output is a true talent metric, just like FT% or FG%, etc. It’s DARKO’s current best guess at how much talent a player has at that time. If at a given point in time a player’s DPM is +2.14, that means DARKO believes they will play like a +2.14 player going forward, not that they have played at that level so far. Think less about the actual magnitude of the DPM and more about the shape of the curves. FYI, anything over +4.0 is pretty much All-Star levels.

https://apanalytics.shinyapps.io/DARKO/

Embiid’s rapid ascension to awesome is particularly noteworthy if you look at the slope of his talent curve in the first 50 games. He rapidly shoots up, but has in many ways remained stagnant-ish with regards to true talent. Keep in mind, his odd pattern of injuries is fairly atypical for high-end players and DPM underrates excellent defensive players. Harris and Horford appear to be on pretty similarly shaped career paths. Steady initial improvement, with Horford reaching a steady state about 150-200 games ago. It is likely that as Tobias ages into his 30s, he will also hit his steady state.

https://apanalytics.shinyapps.io/DARKO/

Just as Embiid’s true talent DPM does not fully take into account his defense, Simmons is likely dinged similarly. However, what can certainly be said is that he has not substantively improved over approximately the last season of games — this is the primary worry of Sixers fans. There is a possibility that his current true talent is essentially maxed out without improved ability to score, either with improved rim finishing or some semblance of range.

Richardson’s trajectory is interesting as he had a major role change (and change again and change again) over the last season of games where he was asked to do too much for the Heat before being traded over the summer. Once he finally gets healthy and his role stabilizes, I’d imagine his true talent DPM would respond positively. Lastly, if you’ve been following NBA Twitter and/or the Minnesota Timberwolves this year, you’ll note that Andrew Wiggins has had a rather noteworthy season thus far. And more or less, DARKO “believes” in his improvement, with a stark increase in true talent DPM since the start of this year (small orange dots). His rate of talent improvement has outstripped the smoothing line (thick orange line), which will kick upwards noticeably if his current trend continues.

So What?

Presented with this deeply impressive model, I think it’s instructive for Sixers fans to understand how their current talent is expected to improve, stay the same, or decline. For a good while, the “young stars” of the Sixers were about potential, and now we can look at and see a) what level of potential there actual was/is, and b) what type of improvements are possible. Also I built the app and it’s a fun excuse to use it.

Note: I wrote this before Simmons went off against the Cavs which was a nice display of that well rounded offensive talent improvements. Now just do that for 100 more games.


DARKO: Kostya Medvedovsky

DARKO Application: Andrew Patton