True Value of Players: Quantitative Metric

[mtron929]

To meaningfully compare values between different players, it is best to use some quantitative metric such that the numbers itself makes sense. And many of the arbitrary numbers just does not have much meaning to them. So a good one, is one where the values become additive. As such, if we assign Lebron = 100, Kevin Love = 50, and Kyrie Irving = 50, then we are saying that the value of Lebron is equal to the value of having both Love and Irving. So let's extend this idea to a sample team: the Cavs. For normalization purposes, I would put Lebron = 100.

Lebron = 100
Kevin Love = 35
Kyrie Irving = 40
Tristan Thompson = 20
Mo Williams = 15
J.R. Smith = 15
Imam Shumpert = 15
Delly = 10

This implies that I would rather have Lebron over both Kevin Love and Kyrie Irving on the current Cavs team as that team would give me the better chance of winning a title. But once I add Tristan Thompson to the mix, then the value becomes close Lebron (100) vs Love (35) + Irving (40) + Thompson (20). Moreover, the value of Love is roughly equivalent to Thompson + J.R. Smith. So if we assign numbers such that any combination of comparisons between the players make sense, then we have a meaningful system. Now, we can attach salary on top of this to see the true value.

Lebron: 100/$23 million = 4.35/ million
Love: 35/$19.5 million = 1.79 / million
Irving: 40/$14.7 million = 2.72 / million
Thompson: 20/$14.2 million = 1.41 / million
Wiliams: 15/$2.1 million = 7.1 / million

So you see that if we look at the value/cost, then we have something deceiving, which states that Williams (7.1) is more valuable than Lebron (4.35) because he is so much cheaper. This intuitively does not make sense but this happens a lot when you just look at the rate. An easy solution to this problem is to multiply the rate by the value. So again,

Lebron: 4.35 * 100 = 435
Love: 1.79 * 35 = 63
Irving: 2.72 * 40 = 109
Thompson: 1.41 * 20 = 28
Williams: 7.1 * 15= 106

So here it is reasonable, and what I would call the true value index. We have Lebron having much more value than everyone else. But it is possible that a "steal" like Williams can have more value compared to Love given his very very low salary. And someone like Thompson can have very low value due to him being overpaid. I suspect that we can do this for different teams as well to see the values of each of these players in a more meaningful way.

[-Sammy-]

As a math junkie, I can appreciate this concept. I'm not sure how much value it has in evaluating players, though, because you're still starting with arbitrary initial variables, unless you have a calculus in place for determining the 0-100 value you're giving each guy to start with.

[dorkestra]

That's a cool way to look at it. One thing to consider would be your initial judgment: talking about would you rather have LeBron or Love and Irving. Because by having Love and Irving, considering you can only have five players on the court and all teams have the same roster size, would mean that you should really be comparing Love + Irving to LeBron and a league average player. So in essence you'd want to be judging the value premium that the player provides, which is what WARP tries to do, but with wins added instead of a more abstract, but holistic sense of value that you imply.

[mtron929]

As a math junkie, I can appreciate this concept. I'm not sure how much value it has in evaluating players, though, because you're still starting with arbitrary initial variables, unless you have a calculus in place for determining the 0-100 value you're giving each guy to start with.

I think the initial arbitrariness is ok since we do not care about absolute numbers but how the numbers compare to one another. Accordingly, even if I scored Lebron another number instead of 100, the conclusions would have been the same.

[mtron929]

That's a cool way to look at it. One thing to consider would be your initial judgment: talking about would you rather have LeBron or Love and Irving. Because by having Love and Irving, considering you can only have five players on the court and all teams have the same roster size, would mean that you should really be comparing Love + Irving to LeBron and a league average player. So in essence you'd want to be judging the value premium that the player provides, which is what WARP tries to do, but with wins added instead of a more abstract, but holistic sense of value that you imply.

Yes, that is a good point. But I think once you start with the assumption that you can replace the said players, then I think you come to a pretty weird conclusion that Lebron is worth more than all the other Cavs combined. Why? Because I would rather have Lebron and 11 average players compared to the Cavs squad minus Lebron and an average player to replace Lebron.

[mtron929]

So I guess to get rid of the idea that one can replace players, this would just be a 1 year value. Accordingly, it becomes difficult to replace players unless you call someone from the D-league. And then, you are not getting an average player, but a very bad one.

[yoyoboy]

Mo Williams is more like a -15. Definitely a lot lower than Delly.

[Bolivar]

I got 87 value for Delly with that, beats Love too

I think the OP makes sense, but I'd prefer to have more formulae behind the whole thing.

[Ricard]

Steph is the GOAT.

[zimpy27]

It seems like your initial assessment is a self-fulfilling prophecy of the result.It's arbitrary in assignment.

Only thing you accounted for was the value/cost ratio but it doesn't take into account the salary cap. You can't say Mo is more valuable than Kyrie in the context of price when you need to spend a minimum of 60m regardless.

Also, I know it's just an example but surely Mo would be rated below Shump and JR.

[mtron929]

It seems like your initial assessment is a self-fulfilling prophecy of the result.It's arbitrary in assignment.

Only thing you accounted for was the value/cost ratio but it doesn't take into account the salary cap. You can't say Mo is more valuable than Kyrie in the context of price when you need to spend a minimum of 60m regardless.

Also, I know it's just an example but surely Mo would be rated below Shump and JR.

It is not arbitrary as the initial numbers should be additive. As an example, in my first post, I rated the three players the following.

Lebron James = 100
Kevin Love = 35
Kyrie Irving = 40

Because of these numbers, I am constrained on how I would value players on another team. For example, I think Steph is pretty much equal to Lebron in value, so I would assign Steph Curry 100.

Steph Curry = 100

I think D. Green + K. Thompson is slightly better than Curry and I think Green has more value than Thompson. so the reasonable numbers for them would be

D. Green = 55
K. Thompson = 50

Accordingly, I would rather have D. Green and K. Thompson over Lebron (close though) but I would surely have Lebron and Love over Green and Thompson. So once I assign values to a single player (Lebron in this case), all the arbitrariness goes away as the system has to be consistent both qualitatively (e.g. I think Green is better than Thompson) and quantitatively (e.g. Green = 55 and Thompson = 50).

[laika]

Lebron: 100/$23 million = 4.35/ million
Love: 35/$19.5 million = 1.79 / million
Irving: 40/$14.7 million = 2.72 / million
Thompson: 20/$14.2 million = 1.41 / million
Wiliams: 15/$2.1 million = 7.1 / million

So you see that if we look at the value/cost, then we have something deceiving, which states that Williams (7.1) is more valuable than Lebron (4.35) because he is so much cheaper. This intuitively does not make sense but this happens a lot when you just look at the rate. An easy solution to this problem is to multiply the rate by the value. So again,

Lebron: 4.35 * 100 = 435
Love: 1.79 * 35 = 63
Irving: 2.72 * 40 = 109
Thompson: 1.41 * 20 = 28
Williams: 7.1 * 15= 106

So here it is reasonable, and what I would call the true value index. We have Lebron having much more value than everyone else. But it is possible that a "steal" like Williams can have more value compared to Love given his very very low salary. And someone like Thompson can have very low value due to him being overpaid. I suspect that we can do this for different teams as well to see the values of each of these players in a more meaningful way.

Ratios don't make sense in this context. Absolute values are what matters when deciding best contract or best player. You should just subtract total value from total cost and not divide at all.

[PizzaSteve]

My thought is to normalize the value by limiting a 15 man roster to 100 total point shares. In this case the maximum value would be 100-1x4=96. This would be a team with one ultra superstar, no bench and 4 min players. The player would have to be so good that he was worth having no bench and any random available players of NBA quality and still win (prime Wilt in his early era?).

Most likely all teams want a full 15 man roster making the top practical score 100-14 = 86. I know 100 is a popular score (re: wine reviews, etc.), but normalizing on 100 as the max for the sum of all full roster spots makes the comparative scores closer to the actual $ decisions "real GMs" have to make. Then that value could be multiplied by the year's max cap, then divided by 100 to form a "laypersons" explanation of base salary expectation (absent exceptions).

I could see this as a simplistic way to explain cap room decisions to someone unfamiliar with the concept.

Q:"Why does Steph get $25/yr and Andre $10M, but Rush only $2M?"

A:"well, imagine a GM has $100M to spread among 15 players...Steph is one of 5 key starters, but is worth more than average (20)...but we also need a bench, so our starters have to average below 20, so 25 is set as a maximum....etc."

In this system a 30-40 would be about as high of a "value share score" as one might expect a player to pragmatically reach. So perhaps LBJ a is worth 40% of payroll, but capped at 25% of payroll. In this case the score-actual might make an interesting derivative value, the "Cap Gap". One could argue that LBJ recognizes this and uses his annual negotiation to minimize his "cap gap" underpayment by leveraging cap exception rules and annual renegotiations to get as close as possible to his true value score.

[Time for Change]

Your formula is simply rating squared divided by salary, so of course it weights the rating more.

LeBron: 100^2 / 23 = 435
Irving: 40^2 / 14.7 = 109 and so on.

Why not simplify it more and just say LeBron is rated 10000 and Irving 1600, Thompson 400, etc.

[zimpy27]

It seems like your initial assessment is a self-fulfilling prophecy of the result.It's arbitrary in assignment.

Only thing you accounted for was the value/cost ratio but it doesn't take into account the salary cap. You can't say Mo is more valuable than Kyrie in the context of price when you need to spend a minimum of 60m regardless.

Also, I know it's just an example but surely Mo would be rated below Shump and JR.

It is not arbitrary as the initial numbers should be additive. As an example, in my first post, I rated the three players the following.

Lebron James = 100
Kevin Love = 35
Kyrie Irving = 40

Because of these numbers, I am constrained on how I would value players on another team. For example, I think Steph is pretty much equal to Lebron in value, so I would assign Steph Curry 100.

Steph Curry = 100

I think D. Green + K. Thompson is slightly better than Curry and I think Green has more value than Thompson. so the reasonable numbers for them would be

D. Green = 55
K. Thompson = 50

Accordingly, I would rather have D. Green and K. Thompson over Lebron (close though) but I would surely have Lebron and Love over Green and Thompson. So once I assign values to a single player (Lebron in this case), all the arbitrariness goes away as the system has to be consistent both qualitatively (e.g. I think Green is better than Thompson) and quantitatively (e.g. Green = 55 and Thompson = 50).

It all comes down to your initial estimate though. You use your perception to assign value. Maybe you should call this stat "Perceived Calculations of Players" or PCP.

[24istheLAW]

You want a metric that does away with "arbitrary numbers" (by this, you are speaking of metrics based on actual plays that occur within a basketball game I presume), so you create a stat whose foundation is built 100% on your arbitrary opinion of how productive you perceive them.

How is this not being laughed at by everyone here?

I'm not gonna laugh at someone who gives it a go
That said my big beef with this is that the units (Value^2/USD) don't have any physical meaning. What do you measure in Value^2/USD? Its a cost of a quantity squared.
IMO measurements should measure something. OP, consider asking that question. What am I trying to measure here? And why does my mathematical formulation of measuring it have logical or physical meaning?

[old rem]

You want a metric that does away with "arbitrary numbers" (by this, you are speaking of metrics based on actual plays that occur within a basketball game I presume), so you create a stat whose foundation is built 100% on your arbitrary opinion of how productive you perceive them.

How is this not being laughed at by everyone here?

I find that you really can never fully Math nerd the whole game. It's like fast paced chess with human variables. Each player has to PROCESS a fast changing sitiation. Each player then has to physically execute it. Further..the TEAM has to be on the same page.

I'm a GSW (as many of you know) and I'd have difficulty putting "number value" on Dray Green, Klay, Bogut.. and several others. Part of that is that there's not a lot of Stats that define DEFENSE.. or aspects of teamwork. You don't get a "stat" off setting perfect picks,screens, for getting open at the right moment. There's shots that are points..and there's shots that are IMPACT.
Green can have 12 pt and be a DOMINANT factor. He's doing point 4/5, he's everywhere on D, can hit some 3's but he ALSO has an infectious energy/fire. Bogut? He's at the top of the key doing his pick + pass stuff as GSW runs your D in circles ..then...omg.. he sneaks in for a lob dunk. Meanwhile he's rebounding,is rim defender. Mo Buckets ...comes in as C. You have to get he's opposite of Bogut. His trademark on D is taking a charge..not blocked shots. Unlike Bogut he pops jumpers...10 ft...3pt. Mo can go point a minute. 15 pt may not look big.. but if he gets it in 12 min.. do the math. Livingston won't do 3's. It often seems he can hit a 15 ft J any time. Solid PG game but 6-7. Good D.

Curry is GSW's big Star...any team facing GSW knows he's broke most any record for "pure shooter". If you fail to D him.....Boom.. he's scored 40. However.. the NEXT BEST 3 guy is Klay. GSW has several more guys who can drop 3's.

Curry puts a PRESSURE on any D. When you OVERCOMPENSATE..... you're screwed. Steph does TEAM too....so... he may get 10+ assists and OTHER guys get the points. Steph is the point guard.....officially..but Dray does point about as much and Iggy will do some point. Sometimes Curry-Livingston.-Dray are all in the game....a whole BUNCH of PG guys. It's almost like an NBA team based on Hoosiers. Move, share the ball. Play D.

Analytics can't really assign a number value to everything happening.