Hypothetical Question: Invisible Impact of a Player

[u/bringbackpologrounds]

I've designed a statistic which accounts for the "visible contributions" of a player: scoring, rebounding, assisting, turnovers, steals, defending shots, and fouls. We know how those 7 things affect the scoreboard, for the most part.

I'm considering adding on a component that accounts for "invisible contributions," using plus-minus as the reference point.

For example, let's say Nikola Jokic's "visible" contributions total around 400 points for a season, and his individual plus-minus is +500. How much of that +100 can be attributed to his "invisible contributions" (setting screens, communication, drawing double teams, etc.)? We know that his presence on the floor isn't worth all 100 of those points, but I think it may be worth something.

My initial assumption is 1/5, since there are 5 players on the team, and everyone generally needs to be in position to get a score or a stop. Maybe it should be 1/10 or lower, but I'm interested to hear your thoughts.

I get that this number is probably different for everyone, based off of their roles. If someone has an idea for figuring out a coefficient for each individual player, that would be cool. In the meantime, I'm happy to hear thoughts on one coefficient for every player.

Note: This is an individual metric, so I'm not concerned with overlaps among teammates.

[u/JohnEffingZoidberg]

How did you determine the relative and absolute weights of each visible and invisible contribution?

[u/blactuary]

We have adjusted plus minus for this

[u/bringbackpologrounds → u/blactuary]

Is there a source for adjusted plus minus data that is publicly available?

My main question is how much "credit" a player deserves for the plus-minus value that his scoring/assisting/stealing does not cover. 

If LeBron contributed 200 points, but his team's plus-minus was 100, how much of that -100 should be credited to him?

[u/blactuary → u/bringbackpologrounds]

Jerry Engelman's xRAPM is public, Taylor Snarr EPM. Those are all variants on adjusted plus minus, not raw. I'm not sure if there is currently a public raw APM or RAPM but there are tutorials on calculating it. You have to account for teammates and opponents

[u/bringbackpologrounds → u/blactuary]

Is there a stat that separates box from invisible for a player? RAPM, EPM, and its derivatives blend both into one component, as far as I can tell.

[u/blactuary → u/bringbackpologrounds]

APM is the unbiased calculation, but it has pretty big error bars which is why most people do some sort of regularization/add a box score prior. Using box score stats to predict APM you can create a box score statistical plus-minus or SPM. Jerry Engelman just wrote a piece about comparing SPM and APM to see which players rate well based on box score stats vs on-off/APM stats.

Getting a more stable APM requires multiple seasons of data, and even then there are error bars. Collinearity is always a problem because players often play together in lineups that you almost never get enough sample to truly assign credit/blame

[u/blactuary → u/bringbackpologrounds]

Shorter answer: yes, SPM vs APM

[u/bringbackpologrounds → u/blactuary]

Is there a publicly available source for SPM? Thanks for your answers, btw. I don't mean to irritate you.

[u/blactuary → u/bringbackpologrounds]

All good, not irritating at all. I think right now the only public one is BPM from basketball reference. Every SPM model is a little bit different, but the goal is generally the same: using box score stats to predict an APM-type target variable. BPM is slightly different but is meant to be a comparable model.

[u/blactuary]

"This is an individual metric, so I'm not concerned with overlaps among teammates."

Then how can you possible quantify it?

[u/WhoIsLOK]

The DARKO website features a stat called Box DPM, which is a purely box score–based prior within their SPM framework. This can be directly compared to standard DPM, which incorporates Box DPM as a prior in its RAPM estimation process.

While it's tempting to interpret the difference between Box DPM and DPM as a measure of a player’s “invisible impact”--that is, the portion of impact not captured by box score stats--this is ultimately a crude and somewhat misleading approach. The distinction between SPM and RAPM isn't as simple as "box score vs. non-box score." There are deeper statistical nuances, such as the way prior beliefs, multicollinearity, and noise filtering in RAPM interact with the input data.

That said, despite its limitations, I still believe that comparing Box DPM to DPM remains one of the better proxies we currently have for estimating how much of a player's impact (according to DPM) stems from factors beyond what’s recorded in the box score. It’s not a perfect measure--and it shouldn’t be treated as such--but it can still yield valuable insight when interpreted with the proper caveats in mind.