RealGM

I've been messing around with this a bit. It's not fine tuned on how to create production functions that accurately capture a player, but I've used some just as examples to show the model.

I'm working on the assumption that there are diminishing returns on offensive production with increases in USG%. So, if you can create a function to describe how a players offensive production varies with USG% then you can calculate the rate at which their efficiency diminishes. For the time being I've made up some functions for 5 players.

What I'm using for the general form of the functions is: Y=A*USG^B

Y- Production

A- Co-efficient representing how efficient the players total offense is.

USG- The usg%

B- Exponent that represents how well the player can create for themselves. If they can create well then the exponent is higher, therefore their offense diminishes at a slower rate.



My thinking is that once you have functions describing your players production, marginal production, and average production all using the variable of USG, then you can do a few things with it. You could determine what each players USG% should be on the team to maximize overall team offensive efficeincy (ORTG). That could help aid a coach in determining how to set up his offense. Additionaly, it could help determine rotations, and which lineups maximize their offensive effiency together.

Anyways, here's charts depicting the production, marginal production, and average production as they cary with USG% for 5 players. And below is a little bit about constrained optimization to determine the optimal USG's each player would use to optimize team ORTG.







So once you have functions for each player, and their respective diminishing rates of marginal production you can determine the optimal USG %'s for each player that would result in the highest possible ORTG for the team. So for the above players I ran the constrained optimization problem and the optimal usg%'s for this team is shown here.



From there I asumed that the higher a player's USG% is the worse their DRTG would be, and that would should really be optimized is the margin between ORTG and DRTG rather then just ORTG. But I'm not sure if that would really be worth it as I have no idea how you would determine at what rate DRTG would diminish with increases in USG%.

Anyways. Thoughts?

What you're working through is basically a more complex form of what Dean Oliver brought up in Chapter 19 of his book (Basketball on Paper). Bob Chaikin put together a basketball sim that tried to work through these types of questions at roughly the same time. Both of these guys were major contributors to the APBR metrics forum before a lot of guys were snatched up by franchises to head up statistical teams a few years back. There were a lot of very detailed conversations in those days regarding these concepts and a lot of details emerged that didn't refute the work of either, but it did raise more questions than were answered. In the end, the APBR metrics guys basically conceded that there is no definitive proof that efficiency declines with usage.

Why the lack of proof? A few reasons.

One is that all players have different usage curves. It's obvious that at some point for everyone, efficiency will decline with increases in usage, but by how much? Some guys drop off a cliff after a few touches (a Korver type). Some guys seem to be pretty flat for a long time (a James type). And the decline for each player is not a simple linear function.

The next problem is that players typically see an increase in efficiency as their touches increase from zero to some positive number. Intuitively, this makes sense. If you're playing in a pickup game and you can get 5 or 6 shots in a half, you can get into some sort of rhythm. If you never see the ball and then are asked to hit an open look from 16 feet once or twice a half, you're going to struggle. Pros aren't like us, so the impact isn't as great, but it is still there.

Problem #3: Which is the cause and which is the effect when you try to develop the usage curves for each player in the first place? If I'm Chris Paul and Steve Nash is trying to guard me, my usage will be a lot higher than when Deron Williams is guarding me. I'll also be a lot more efficient when Nash is guarding me. If a good defender is on me and he can take away a couple of my favorite spots, I'm going to shoot less. And when I do shoot, it will be in places where I won't be as efficient.

I'm not saying that there's not value in this type of optimization, because there is. It's just that there will be a lot of noise in the #s. As a general rule, if you can't find something that is completely out of wack, then tinkering with the usage distribution is probably better served in a context specific way: we need to run screens for player X on the right wing because he's really good at knocking down shots from there, etc.

I think you're on to something when you mention Ortg-Drtg in aggregate as the true measure of how to optimize the offense. Players have motors that are tuned a bit differently. Some guys can run all day while others need to pick their spots, so it follows that expending a lot of energy on offense comes at a defensive cost. Let me just say, I have no idea how to measure this, but there are a few things to consider:

How discretionary is the offensive usage of the player in question? Opposite extremes among well known players of the recent past: Reggie Miller and Allen Iverson. Miller took relatively few shots and was extremely efficient. Truth be told, he should have taken more shots in his career. Jordan himself told him so after his second interim retirement. Miller ran off screens left and right expending energy offensively that way to score most of his points from the perimeter, but he passed up a lot of good shots in favor of resetting the O that he probably should have taken. In the postseason, he took more of these opportunities v. better defenses and was roughly as efficient at higher volume. He ran off the same number of screens and probably didn't work any harder to produce greater results. Iverson on the other hand had to have the ball in his hands to increase his usage, and more often than not, he had to get to the basket more to increase his production. This requires more work.

Secondly, how much of a motor does a player have? Certain guys can run all day, while others can't.

Outside of calculating individual game Drtgs and regressing the delta there vs. the delta in USG, I don't see how you can get a trend. Maybe from there you can see some trends to develop a general formula based upon FTA/FGA and 3PA/2PA and how these contribute to incremental usage on a macro scale. I would suspect that the higher the 3PA/2PA ratio and the lower than FTA/FGA ratio, the lower the defensive cost associated with higher USG. This doesn't address the motor factor, but it might be enough to create a general rule to better optimize USG.

Thank you for the detailed response.

Chicago76 wrote:What you're working through is basically a more complex form of what Dean Oliver brought up in Chapter 19 of his book (Basketball on Paper). Bob Chaikin put together a basketball sim that tried to work through these types of questions at roughly the same time. Both of these guys were major contributors to the APBR metrics forum before a lot of guys were snatched up by franchises to head up statistical teams a few years back. There were a lot of very detailed conversations in those days regarding these concepts and a lot of details emerged that didn't refute the work of either, but it did raise more questions than were answered. In the end, the APBR metrics guys basically conceded that there is no definitive proof that efficiency declines with usage.

Hmmm... I didn't know any of this. I suppose I should perhaps read this book for starters.

Why the lack of proof? A few reasons.

One is that all players have different usage curves. It's obvious that at some point for everyone, efficiency will decline with increases in usage, but by how much? Some guys drop off a cliff after a few touches (a Korver type). Some guys seem to be pretty flat for a long time (a James type). And the decline for each player is not a simple linear function.

This is very true, they are not linear functions. For example with the general form of the function I used Y=A*USG^B. 'B' represents how well a player can create for themselves, so a guy like James would have a higher value of 'B', thus his 'Y' (production) would diminsih at a slower rate then a guy like Korver who would have a lower value for 'B' (thus Korvers production would diminsh quicker).

For example. The players I did make I loosly patterned their functions to replicate Toronto Raptors players. So player 1 is Bargnani, and player 3 is Amir Johnson. Amir has a higher value of 'A' compared to Bargnani because Amir plays closer to the basket and plays a game that lends itslef to higher efficiency shots. However Bargnani's 'B' value is higher, representing that he can create his own shot better then Amir, thus his production diminishes at a lower rate.

The next problem is that players typically see an increase in efficiency as their touches increase from zero to some positive number. Intuitively, this makes sense. If you're playing in a pickup game and you can get 5 or 6 shots in a half, you can get into some sort of rhythm. If you never see the ball and then are asked to hit an open look from 16 feet once or twice a half, you're going to struggle. Pros aren't like us, so the impact isn't as great, but it is still there.

In all honesty this doesn't make intuitive sense to me. I would think that at low usg%'s a player would be more likely be partaking in high efficeincy shots. So at 5usg% a player probably has a lot of dunks, wide open 3's, layups etc... in there. Where if a player has say... 12usg% then they may start having to take some hook shots a little futher from the basket that are lower efficeincy shots (relitive to dunks, open threes, etc..).

I suppose there could be something similar to substitution, and income effect in economics, where you can get substituation effect, and income effect working against each other, but the substituation effect dominates the income effect leading to an increase in overall effect. So paralleled here to basketball.... A player would see diminishing returns by increasing the difficulty of their shots with higher usg%. However that may be offset to a degree by increasing returns by getting comfortable shooting the ball. However the total effect I still think would be diminishing production.

Problem #3: Which is the cause and which is the effect when you try to develop the usage curves for each player in the first place? If I'm Chris Paul and Steve Nash is trying to guard me, my usage will be a lot higher than when Deron Williams is guarding me. I'll also be a lot more efficient when Nash is guarding me. If a good defender is on me and he can take away a couple of my favorite spots, I'm going to shoot less. And when I do shoot, it will be in places where I won't be as efficient.

I had some similar thoughts, and difficulties actually. Not so much with defenders because I think this should normalize over a large sample. But rather, how you work in the cause and effect of players that help increase your ORTG. Like say, Amare's ORTG is higher with a PG like Nash, then with Felton as his PG. How would you attribute that? A co-efficient that also measures the passing ability of teamates?

I think you're on to something when you mention Ortg-Drtg in aggregate as the true measure of how to optimize the offense. Players have motors that are tuned a bit differently. Some guys can run all day while others need to pick their spots, so it follows that expending a lot of energy on offense comes at a defensive cost. Let me just say, I have no idea how to measure this, but there are a few things to consider:

Yeah, I think that would be the way to go. I mean a business man cares about profit, not necissarily revenue. so in basketball the goal should be to worry about margin between ORTG-DRTG rather then simply maximizing ORTG.

How discretionary is the offensive usage of the player in question? Opposite extremes among well known players of the recent past: Reggie Miller and Allen Iverson. Miller took relatively few shots and was extremely efficient. Truth be told, he should have taken more shots in his career. Jordan himself told him so after his second interim retirement. Miller ran off screens left and right expending energy offensively that way to score most of his points from the perimeter, but he passed up a lot of good shots in favor of resetting the O that he probably should have taken. In the postseason, he took more of these opportunities v. better defenses and was roughly as efficient at higher volume. He ran off the same number of screens and probably didn't work any harder to produce greater results. Iverson on the other hand had to have the ball in his hands to increase his usage, and more often than not, he had to get to the basket more to increase his production. This requires more work.

Secondly, how much of a motor does a player have? Certain guys can run all day, while others can't.

Outside of calculating individual game Drtgs and regressing the delta there vs. the delta in USG, I don't see how you can get a trend. Maybe from there you can see some trends to develop a general formula based upon FTA/FGA and 3PA/2PA and how these contribute to incremental usage on a macro scale. I would suspect that the higher the 3PA/2PA ratio and the lower than FTA/FGA ratio, the lower the defensive cost associated with higher USG. This doesn't address the motor factor, but it might be enough to create a general rule to better optimize USG.

Well I think you identified a lot of the considerations that would have to be put into developing a function that describes an increase in DRTG with increases in USG%. However it seems like a real bitch, lol.