APBRmetrics

Many threads have discussed replacement level on this board... here's a Google search:

https://www.google.com/search?q=replace ... s-wiz-serp

As I have dug into one-number metrics over the years, I'm realizing why there was so much debate in the early years.

To summarize--teams can be as bad as -12 or even -15 as a whole. If replacement level is -2....do we really believe the team as a whole is below replacement level?

But conversely--when looking at ASPM and BPM 1.0 and RAPM, the average rating of minimum salary or 10-day contract players was in the vicinity of -2.0.

I argued then that worse players than replacement level were being played, in general, for development purposes and/or small sample size and luck made them appear worse than they actually were.

I've been working with better prior-informed RAPM data, and I think what was actually happening was this:
1. RAPM shrinks all players toward 0 (particularly low minutes players)
2. Metrics like BPM are built on this "shrunk" basis and also by nature of regression don't capture the full space (box score can't capture full impact).
3. We look at low minutes players and see -2.0.

Well, with some better prior-informed RAPM data, I think I'm ready to change my tune. I have tuned the prior so the model residuals are centered nicely around 0 for low minutes players--there is no minutes-based bias throughout the minutes spectrum.

With that in place, low minutes players average more like -3.5!

Now, again some of that may be from "development players", but certainly not enough to still argue for -2.0.

The new version of BPM/VORP will likely feature a lower replacement level.... Possibly around -3.0. Research continues.

Yes.

That estimate does seem to make more sense. Median EPM is ~-1.5 and median DPM is ~-1, so replacement level being about 2 points below that seems about right.

A prior with a mean around -4 is what I have found in hyperparameter tuning to be best for predictive purposes in my own work (which combines an extended box score and on/off type data), so that jibes with this also, presuming you assume the prior for an entirely unknown player would be representative of a replacement level player.

v-zero wrote: ↑Fri Feb 02, 2024 11:53 am A prior with a mean around -4 is what I have found in hyperparameter tuning to be best for predictive purposes in my own work (which combines an extended box score and on/off type data), so that jives with this also, presuming you assume the prior for an entirely unknown player would be representative of a replacement level player.

Yes, this is in the range of what I have found as the best fit for a 0 MPG player.

That said, I do think there are players available that are better than -4. Again, development players tend to be worse than what a true replacement player could be.

If I'm just looking at low MPG players, that do have enough minutes to be a little more confident that I'm not just looking at the prior, they fall a bit higher on that MPG versus production curve more like -3.5.

Is there a difference between a Replacement player and an Available player?
I had concluded a Replacement was whoever a team had on roster (or could find) who would literally replace a rotation player who gets injured. Sometimes a 6th man, sometimes 12th, etc.

Of 420 players who have 100+ minutes this season, exactly 1/3 are below -2.0 BPM; leaving 9.33 players per team who have some VORP going on. Of course not all 280 are actually available now, due to some injuries etc.

I routinely add 5.25 to players' BPM to make their BPM-wins sum to and align with their Win Shares or eWins.
It's perplexing to suppose that replacements will win any games.

Klay Thompson played for a replacement's salary in 2015, his best year by every measure. I don't think he was available to other teams, but if you average in his future salaries, it might make more sense.

"Of 420 players who have 100+ minutes this season, exactly 1/3 are below 2.0 BPM"


Did you mean -2?

Here is a visualization of a couple of RAPM datasets, BPM, and a proposed prior for a new RAPM dataset.

This will allow you to evaluate replacement levels with several adjustable parameters.

Note--this probably won't work on phone screens:
https://public.tableau.com/views/RAPMa ... share_link

I can see on my phone.