APBRmetrics

Krishna Narsu and Tim (Cranjis McBasketball) have released a new metric that uses a box-score prior for a form of RAPM. They have dubbed the metric LEBRON (Luck-adjusted player Estimate using a Box prior Regularized ON-off).

The full writeup is at https://www.bball-index.com/lebron-introduction/

What thoughts does everyone have? The concepts look solid to me at first glance.

Sounds good at first read. Boxscore informed RAPM plus more.

Will RPM share more detail? A number of people are tuning them out for lack of promised greater explanation.

The article mention of 538's RAPTOR metric by its full name threw me for a bit.

CraftedNBA.com should add LEBRON to its blend.


Ideally would want to see all the latest metrics in a table for all players and in a team rollup table.

I've seen others discuss making adjustments for "luck" several times here, but I think luck adjustments for the NBA seem more problematic than helpful to me. It makes perfect sense for something like the NFL where turnovers can have a huge effect on the outcome of games and which only occur a few dozen times per season. However, with the NBA, it doesn't make sense at all to me to try to adjust for "luck". Certainly not with respect to any shots that were defended. The sample sizes of shots taken and defended in the NBA are huge over the course of a season. Luck has very little effect on the actual long-term outcomes and coefficients for players. Attempting to "correct" for it is almost certainly going to result in misattributing a well-defended shot to "bad luck" more often than it is to actually correct for it. Remember, in the limit, luck doesn't exist. And in the NBA, over the course of a season, the number of shots taken and defended should be far more than sufficient for luck to not really be much of a factor at all. When players who play thousands of minutes outperform their career shooting percentages behind the 3 point line, it's much more likely to be the result of them having been working on their shot than it is them just having gotten lucky. Same thing with respect to significant decreases in FG%. Those are much more likely to be due to something like recovering from an injury or aging than they are "bad luck". And on the defensive end, when opponents "underperform (bad luck)" it is much more likely to be because the shots were well contested than it was due to being "unlucky". I feel pretty strongly about this one. Sorry if I'm coming across as berating this approach, but this just seems like a really bad idea to me, and I'm someone who DOES adjust for luck in other sports (NFL, MLB, & NHL).

I am ok with luck adjust for opponent FT%. 3 pt... I have mixed feelings. Maybe adjust halfway. Maybe less as season proceeds.

Lot of other things could be affected by randomness.

RAPM should dampen randomness. Doing in boxscore and using RAPM is a lot. Too much? Maybe.

What is luck? I don't understand this concept


...but in all seriousness. Define what you mean by luck.
is it low probability events? A positve outcome against expectation? What is it ? Can it be quantified?

vzografos wrote: ↑Tue Dec 29, 2020 11:47 am What is luck? I don't understand this concept


...but in all seriousness. Define what you mean by luck.
is it low probability events? A positve outcome against expectation? What is it ? Can it be quantified?

I believe in this case, it is where your opponent shoots better or worse than normal, particularly on things like free throws that have basically no player control.

One way to look at it--If a player normally shoots 35% from 3 and shoots 3-3 from 3 in a game--if the same shots were re-shot, what was the most likely EV of those 3 shots? Something higher than 35%, but something lower than 100%. There are ways to assess how much to regress that tiny sample towards the player's normal mean. Nathan Walker and Krishna Narsu have done a lot of work in this area.

DSMok1 wrote: ↑Tue Dec 29, 2020 12:44 pm
I believe in this case, it is where your opponent shoots better or worse than normal, particularly on things like free throws that have basically no player control.

One way to look at it--If a player normally shoots 35% from 3 and shoots 3-3 from 3 in a game--if the same shots were re-shot, what was the most likely EV of those 3 shots? Something higher than 35%, but something lower than 100%. There are ways to assess how much to regress that tiny sample towards the player's normal mean. Nathan Walker and Krishna Narsu have done a lot of work in this area.

I think one has to be careful when using expressions "better/worse than normal" or "most likely EV" because they might mean something in everyday language but something completely different in probability theory.

When we look at a random process (i.e. a player in a game) that generates data (like your example freethrow stats or 3pt stats) we have to look at the whole distribution of that data. So take the simplest of case where we have a Normal (Gaussian) model that describes the 3pt statistic. You look at the mean (average) but you should also look at the variance (or std if you prefer). Those two parameters completely define the Normal model and assuming that your model fits your data well (doubt it) then it fully describes your random process that generates that 3pt statistic.

So the way I interpret the above discussion, from a probability theory perspective, ist that you are just talking about the variance of that distribution (of the 3pt statistic) and, for a lack of a better word, confuse it with luck. The larger the variance the more "random" a process might appear (again dont confuse random in everyday talk with random in prob. theory). The tigher the distribution (lower variance) the more "predictable" the 3pt statistic might appear because the player will appear "consistent" i.e. shooting around his averages. Again I keep using quotations because to me predictable and consistent have nothing to do with how big the variance is.

The theoretical (i.e. asymptotic) EV (which is your mean) does not change if you take 3 shots or 103 shots. Obviously we are talking about sample mean which will of course change and should coverge to the theoretical mean the more shots you take. There are various ways to estimate from small samples and noisy generating processes but I am not going to go into that. I don't think that it is interesting.

I find the whole discussion about "luck" when it comes to statistics to be misplaced. There is one thing to say "luck" and there is another to say uncertainty. The latter can be quantified.

DSMok1 wrote: ↑Tue Dec 29, 2020 12:44 pm what was the most likely EV of those 3 shots? Something higher than 35%, but something lower than 100%. There are ways to assess how much to regress that tiny sample towards the player's normal mean

Not to forget. This is a very common problem that can be easily address with Bayesian theory for starters.

vzografos wrote: ↑Tue Dec 29, 2020 1:26 pm

DSMok1 wrote: ↑Tue Dec 29, 2020 12:44 pm what was the most likely EV of those 3 shots? Something higher than 35%, but something lower than 100%. There are ways to assess how much to regress that tiny sample towards the player's normal mean

Not to forget. This is a very common problem that can be easily address with Bayesian theory for starters.

Right, I believe Bayesian theory is the way it is being addressed. Certainly the way I would look at it.

The distribution of 3 pointers should be wider than binomial, because there are varying shooting conditions driving the results to some extent. FT% should be very close to binomial, for a given player. Underlying skills do change, but not very quickly unless something like an injury causes a shift.

DSMok1 wrote: ↑Tue Dec 29, 2020 4:09 pm Underlying skills do change, but not very quickly unless something like an injury causes a shift.

Yeah actually I wanted to say something about this but I dont want to start some probability theory thread because that is not so interesting for most people.

But the gist is the following. Whenever you hear "regression to the mean", be wary of the following: for regression to the mean to make sense in any statistical way, and assuming you are not looking at the moving average over some time window, the underlying distribution that generated the data should be stationary. This means that the mean (avg) and the standard deviation are fixed. The data might vary but their average is fixed. If the mean and std (or more correctly the moments in the general case) are not stationary then regression to the mean doesnt make much sense.

Now that we have that out of the way, ask yourself. Are the data distributions (of any player stat) really stationary?
I don't think so. Let's look at performance over the years. You dont need data analysis to tell you that performance changes (degrades) and the player gets older. So, say, the 3pt average stat will be different for a 20 year old than the same guy at 40.

Ok let's look at stationarity WITHIN a season. Maybe it is maybe it isnt. You can do stationarity hypothesis tests if you like to make sure (beyond a level of uncertainty). But consider factors that can shift the mean. You already correctly mentioned injury. Also fatigue and ilness. How about psychology when the player knows the team has no change in going to the playoffs.

Anyway, my point is that these methods that rely too much on the "regression to the mean" approach make the (in my opinion) strong assumption of data distribution stationarity. I think this leads them to incorrect conclusions.

I like all the stuff in there, but like some other posters I have some hesitancy about the luck adjustment. Especially considering that towards the end they say, "The LEBRON values only tell you what they tell you, which is what has happened." If your interest is really in telling you what happened then there's no reason to adjust for how many free throws or 3-pointers someone should have made.

If you do insist on adjusting shot making to some baseline, then I think it will be much better with the tracking data that they don't have (but say they will use in their next metric).

vzografos wrote: ↑Tue Dec 29, 2020 4:33 pm

DSMok1 wrote: ↑Tue Dec 29, 2020 4:09 pm Underlying skills do change, but not very quickly unless something like an injury causes a shift.

But the gist is the following. Whenever you hear "regression to the mean", be wary of the following: for regression to the mean to make sense in any statistical way, and assuming you are not looking at the moving average over some time window, the underlying distribution that generated the data should be stationary. This means that the mean (avg) and the standard deviation are fixed. The data might vary but their average is fixed. If the mean and std (or more correctly the moments in the general case) are not stationary then regression to the mean doesnt make much sense.

Now that we have that out of the way, ask yourself. Are the data distributions (of any player stat) really stationary?
I don't think so. Let's look at performance over the years. You dont need data analysis to tell you that performance changes (degrades) and the player gets older. So, say, the 3pt average stat will be different for a 20 year old than the same guy at 40.

Anyway, my point is that these methods that rely too much on the "regression to the mean" approach make the (in my opinion) strong assumption of data distribution stationarity. I think this leads them to incorrect conclusions.

Exactly! Couldn't agree more. I think it's a fool's errand to try to account for most of what people are referring to as "luck" for precisely these reasons. As sample sizes increase, the sample mean approaches the population mean. Players who play sufficient minutes shouldn't have large errors due to "luck". The ones who would actually be subject to good or bad luck would have very low minutes to begin with, and would thus have their RAPM values heavily regressed toward 0 anyhow.

Most of the adjustments being made for "luck" are actually misattributions of skill. I'd wager good money on it.

Here's a prime example of what I'm talking about. Here's a link to a recent article from 538 that highlights my exact concern about adjusting for "luck".

https://fivethirtyeight.com/features/wh ... ba-season/

The relevant paragraph from this article is quoted below. I've added bold font for emphasis.

For those interested only in the predictions, skip a few paragraphs ahead. But if you’re still with me here, let’s talk about what’s changed since our projections were, um, not so great in last year’s playoffs. In Year 1 of RAPTOR, we were actually using an alternative version of the stat called “PREDATOR”1 that was intended to down-weight “lucky” events, such as opponent 3-point shooting, in order to be more predictive. With the benefit of an offseason to test, though, we found that standard RAPTOR outperforms PREDATOR in essentially every way, so we will only be using RAPTOR for both our player evaluations and our team forecasts going forward.