Hi,
One topic I've been thinking about is mapping a player's projected plus/minus to effect on wins to salary to get a sense of underpaid and overpaid players. The simplest way I can think of doing this is taking a method like RAPTOR, scale to minutes/game / 48, map to pythagorean and then use the salary/salary cap as a percentage. What is the state-of-the-art way to do this? Are there better all-in-one metrics than RAPTOR or more accurate plus/minus to wins mapping than pythagorean? Is the accuracy bump to a more complicated method worth the complexity?
Thanks!
Mapping projected plus/minus to wins to salary
Re: Mapping projected plus/minus to wins to salary
Generally, the key to mapping a stat to salary is to determine the "replacement level" (i.e. minimum salary) level for that statistic. Then sum up all value in the league for that stat (remember to include playing time) and divide the total available salary (subtracting out minimum salary for every slot) by that league total value for that statistic. Then multiply the player's stat value by that factor, add minimum salary to each player, and you have a value.
@kmedved (Kostya Medvedovsky) recently put up salary estimates based on DPM, which I would consider superior to LEBRON.
https://twitter.com/kmedved/status/1633 ... 79136?s=20
@kmedved (Kostya Medvedovsky) recently put up salary estimates based on DPM, which I would consider superior to LEBRON.
https://twitter.com/kmedved/status/1633 ... 79136?s=20
Re: Mapping projected plus/minus to wins to salary
Thanks for the reply!
To follow up, I had (edit:)four questions:
a) For replacement level, do you then set all below replacement players to be 0 and add the absolute value to all other players? E.g. if replacement level for your APM metric is -2, then for all values do val = max(0, val + 2) ?
b) Done this way, does this imply a linear relationship between the APM metric and salary? Is that a reasonable assumption?
c) How is the "replacement level" usually determined?
Edit: d) When comparing pure player trades can we use this method and simply compare salary scaled by projected minutes? Is this almost as good as we can do before considering more heuristics (or build a model) for fit?
Thanks!
To follow up, I had (edit:)four questions:
a) For replacement level, do you then set all below replacement players to be 0 and add the absolute value to all other players? E.g. if replacement level for your APM metric is -2, then for all values do val = max(0, val + 2) ?
b) Done this way, does this imply a linear relationship between the APM metric and salary? Is that a reasonable assumption?
c) How is the "replacement level" usually determined?
Edit: d) When comparing pure player trades can we use this method and simply compare salary scaled by projected minutes? Is this almost as good as we can do before considering more heuristics (or build a model) for fit?
Thanks!
Re: Mapping projected plus/minus to wins to salary
For what it is worth I think the linear application of value is wrong. Fundamentally if your aim is to win championships, then you are going to have to have a guy who is +4.5 or more on an impact metric at a bare minimum, and ideally more like one +5 guy and one +3 guy etc. In my opinion those players cannot be replaced in the aggregate, it will work fine in the regular season but they will be found out in the playoffs. That being the case I think the calculus becomes a lot more complicated than Value = VORP*K + L where K is some constant salary factor and L is the league minimum.
Bit of an aside, but for instance looking at the DARKO estimates: it has Curry overpaid, Giannis overpaid... The smell test in these cases is, I think, pretty useful.
Anything below around +3 it is probably fine to apply the linear value theorem, but beyond that I would say you need to throw it out of the window.
Bit of an aside, but for instance looking at the DARKO estimates: it has Curry overpaid, Giannis overpaid... The smell test in these cases is, I think, pretty useful.
Anything below around +3 it is probably fine to apply the linear value theorem, but beyond that I would say you need to throw it out of the window.
Last edited by v-zero on Fri May 12, 2023 4:08 pm, edited 1 time in total.
Re: Mapping projected plus/minus to wins to salary
A counter-argument.
The league is largely "going small", with emphasis on quickness and athleticism. Dunks as a % of FG are going up each season. The only way to stop some of these explosive moves is to stand in the way. More players are getting injured and taking days off to avoid/recover from injury.
Therefore it seems advantageous to have an army of pretty-good players, rather than over-rely on one or two superstars. This can be just as true in playoffs. Every round has its matchups, energy is at a premium, fatigue happens.
A superstar who isn't playing is overpaid. A role player who is filling a niche may be underpaid and/or can always be packaged into a trade.
The league is largely "going small", with emphasis on quickness and athleticism. Dunks as a % of FG are going up each season. The only way to stop some of these explosive moves is to stand in the way. More players are getting injured and taking days off to avoid/recover from injury.
Therefore it seems advantageous to have an army of pretty-good players, rather than over-rely on one or two superstars. This can be just as true in playoffs. Every round has its matchups, energy is at a premium, fatigue happens.
A superstar who isn't playing is overpaid. A role player who is filling a niche may be underpaid and/or can always be packaged into a trade.
Re: Mapping projected plus/minus to wins to salary
I wouldn't really say the league is going small. We had a brief blip when everybody wanted to find a new Steph Curry, but we are now in a situation where the best players in the league are three big men, and outside of that is predominantly a cohort of oversized guards playing as wing players. Each team lacking quality length is being found out. The league is no longer very interested in big men who can't play two ways and who are too lumbering to switch defensively, but otherwise we are again trending tall.
Outside of that, it is of course valuable to have plenty of pieces, but none of that replaces the need to be able to put on the floor truly dominant players. Look at how teams who lack truly top-tier pieces (Knicks, Cavs, Hawks, TWolves, Kings) have fared in these playoffs. Look back at previous years and you will see the same pattern emerge.
Outside of that, it is of course valuable to have plenty of pieces, but none of that replaces the need to be able to put on the floor truly dominant players. Look at how teams who lack truly top-tier pieces (Knicks, Cavs, Hawks, TWolves, Kings) have fared in these playoffs. Look back at previous years and you will see the same pattern emerge.
Re: Mapping projected plus/minus to wins to salary
The point that salary should not be linear with production is something that has been debated for a long time. I am inclined to agree that it should not be linear.
In fact, it's fairly well known that for a player to have positive impacts on winning a championship in the playoffs, the player needs to perform at around League average or better. In other words, replacement level in the playoffs is approximately league average.
But it's also clear that players between the regular season replacement level and replacement level in the playoffs do deserve a scale of salary increase.
In fact, I believe a player's value is not necessarilythe same for all teams. Different teams have different goals for a season. If your goal is to develop players for the future that will look different than if you are a veteran team in championship or bust mode.
Another good way to look at things is to plot actual salary versus vorp or any other production metric that includes replacement level and playing time. Typically those charts do look pretty linear with the highest paid players truncated due to the maximum salary limitations.
In fact, it's fairly well known that for a player to have positive impacts on winning a championship in the playoffs, the player needs to perform at around League average or better. In other words, replacement level in the playoffs is approximately league average.
But it's also clear that players between the regular season replacement level and replacement level in the playoffs do deserve a scale of salary increase.
In fact, I believe a player's value is not necessarilythe same for all teams. Different teams have different goals for a season. If your goal is to develop players for the future that will look different than if you are a veteran team in championship or bust mode.
Another good way to look at things is to plot actual salary versus vorp or any other production metric that includes replacement level and playing time. Typically those charts do look pretty linear with the highest paid players truncated due to the maximum salary limitations.