APBRmetrics

[hoopster101]

Came across this blog post today. I don't know if anyone has already done similar work, but I thought the unintuitive conclusions were interesting.

[HoopStudies]

Looks like "skill curve" stuff in Basketball on Paper... Some people here don't buy the concept. I, having written the book, do believe it. Those curves do vary by player and that makes analysis quite tricky...
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Dean Oliver
Author, Basketball on Paper
The postings are my own & don't necess represent positions, strategies or opinions of employers.

[Crow]

This post comes at a good time and is relevant to the Andre Miller discussion.

Skill curves are a part of the picture but really I'd like to see more attention to the full network pathways and the optimum set and sequence given the defensive responses to the chosen pattern.

A play doesn't get an average FG% I don't think based on shots taken. I think it gets a FG% on the quality of the network pathway and the timing and frequency of that pattern given the defensive response.

At a minimum the player skill curve should be paired with the associated curve for all teammates while he is on the court to complete the picture, especially for PGs but probably everyone. The player's skill curve is only part of the picture, ultimately it is the total team offensive efficiency that matters and then again the the total net efficiency including defense.

Ideally the analysis should move beyond the relative simplicity of skill curves to a fuller examination of the quality of the network engineering by the coach (and those who influence him) and the floor general (and those he works with, influencing each other in various ways).

I have previous spent more thought on the fact that Iverson was traded to Denver while Dean was a part of the organization. Perhaps more thought should go to Miller being dealt. The Nuggets may not have needed Iverson but maybe they needed to move away from Miller to rise above 45 wins? They moved up not long after he left and Iverson is generally discarded as the reason especially since they continued up after he was discarded. More comment on either player move & effect by Dean would be interesting but...(your choice or your restriction)

I called for a physicist to look at basketball (and apply calculus or other higher math) and perhaps we have a candidate.I left an invitation for the author and others there to stop by if they want. And a moment later I now see the author of the article is already here- good.

(My last invitation to the only findable person associated with the complex networks presentation at UNC drew no response.)

[Mike G]

The name of the blog -- Gravity and Levity -- is great. The writing is lucid.

Part of it confuses me:

[Ben F.]

[Mike G]

OK, my bad.
I guess all they lose is the 'option' of playing to their max potential.

There's still an odd assumption in there. If Patrick cuts his shooting from 44% to 21% of all shots, his FG% is supposed to rise from .450 to .600 . At the same time, his teammates each put up 42% more shots (from 14% to 20%) ; yet their FG% holds steady at .450 .
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36% of all statistics are wrong

[erivera7]

Interesting post, thanks for sharing the link.
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@erivera7
I cover the Orlando Magic - Magic Basketball

[Ben F.]

[gravityandlevity]

It was quite a pleasant surprise to find my little write up of "Braess's paradox in basketball" discussed here. Whenever you put forth an idea in a field outside your area of expertise (and this is way outside), there is always the fear that someone who really understands the topic will immediately see some glaring flaw. So in that sense it's awfully nice to have confirmation from "professionals" like yourselves that this is an idea worth discussing.

I'm glad to join discussions here at APBR metrics. I've been a lifelong basketball fan and have only recently begun to think that maybe my training in math and physics can be useful for basketball. Crow, thanks for the heads-up.

In a moment I'll try to explain what I think is the value of this "price of anarchy" approach, but for now I just wanted to introduce myself. It's a pleasure to be here.

By the way, Mike G, I'm glad to hear you approve of the blog name. It was almost "Let's Get Physical"!

[HoopStudies]

Gravity -

I, for one, am glad to have you here. I saw that you cite the Feynman Lectures in a blog post. I went to Caltech, had my frosh Phys class guest lectured by him, and my grandmother knew him quite well. Anyway, I come from the math/science background and find it quite useful in sports. Feynman diagrams don't do much good in sports, but network theory does have some relevance.
_________________
Dean Oliver
Author, Basketball on Paper
The postings are my own & don't necess represent positions, strategies or opinions of employers.

[bchaikin]

feynman diagrams for the nba would be great - think about the concept. while many think of quarks and gluons and intermediate vector bosons as simply mathematical constructs, to physicists they are real (and to anyone who understands or believes the math). feynman, like einstein and hawking, could visualize reality and what the math represented better than most, and express it in such a way that all could understand...

treating an nba player as a point particle with a number of attributes - each player the same number of attributes, but with various values in limited ranges - in a system with definitive rules makes for a predictive model, and takes away alot of the perceived subjectivity...

[gravityandlevity]

Thanks for the welcome!

Let me try to break down what I think can be done with this "price of anarchy" primitive network approach.

First of all, I should make the assumptions of the method clear. They are highly questionable, but sometimes when the problem seem intractable you have to start with questionable simplifications.

1) I assume that every player has a definite "skill curve" (Dean, I apologize for not using your already-established terminology in the post. Sometimes in the excitement of a "new" idea you forget that someone else did it first).
2) I assume an extremely simplified "offensive network": namely, the only thing that matters for the probability of a shot going in is the person who took it. There are definitely more complicated "non-linear" effects (someone who makes their teammates better); I'm ignoring those.
3) There is no accounting for defense.

These are severely limited assumptions, but the exciting part is that they allow for definite predictions of the proportion of shots that each player should take, and the resulting "best possible" field goal percentage. You can also predict the "Nash Equilibrium" point: the proportion of shots that each player is likely to take if the team just takes the highest percentage option each time down the floor.

The math is pretty straightforward. If the shooting percentage of the five players is f1(x1), f2(x2), ... f5(x5), where x1, x2, ... x5 is the fraction of the team's shots taken by each player, then the total field goal percentage of the team is:
F = x1*f1(x1) + x2*f2(x2) + ... + x5*f5(x5)

Of course, the fractions x1, x2, ... x5 are subject to the condition
x1 + x2 + ... + x5 = 1.

The point I'm calling the Nash Equilibrium is the point where all five players are shooting the same percentage:
f1(x1) = f2(x2) = ... = f5(x5)

The global optimum is the point where the total field goal percentage F is optimized with respect to each player's shooting fraction. i.e.
dF/dx1 = dF/dx2 = ... = dF/dx5 = 0.

If you know the skill curves for each player, then this is an exactly solvable problem. Your "price of anarchy" is F(ideal) - F(Nash). In the example from my original post, it was 3.5% of shooting percentage.


The problem, of course, is that I can't see any reliable way to extract skill curves for an arbitrary player. The only reasonable way I can think of is to look at trends for "field goal percentage in a season" vs. "number of shots taken that season", as I did in the original post. Unfortunately, the prohibits you from making reliable conclusions except for player who have had long careers with varying degrees of offensive load.

As an example, here are linear fits for "skill curves" for a hypothetical starting five of Allen Iverson, Kobe Bryant, Ray Allen, Kevin Garnett, and Shaquille O'Neal:

A couple observations:
1) Shaquille O'Neal, as a general comment on his career, is an offensive monster.
2) Kevin Garnett was born to be a team's secondary offensive option.
3) Kobe Bryant is at all times more efficient than Allen Iverson (...no big surprise there)

The approach I outline above yields the following estimates:
at the Nash Equilibrium
Iverson takes 0%
Bryant takes 6%
Allen takes 3%
Garnett takes 26%
O'Neal takes 65%
--> the team (and each player) shoots 51%

The optimized strategy yields:
Iverson takes 5%
Bryant takes 19%
Allen takes 13%
Garnett takes 18%
O'Neal takes 45%
--> the team shoots 53%

My skill curves here are questionable, but you can see the main point. An optimized team distributes its shots much more evenly, and as a consequence gains a few extra points of field goal percentage.

[Ryan J. Parker]

Glad to see this discussion come here to the forum. I've only done very basic analyses of FG% with respect to say usage rates or % of shots taken while on the floor, and I haven't come up with much in this regards.

Dean's USG vs ORtgs gives us evidence there is something there with respect to what a player is asked to do on the court, but I'm not yet convinced it's specifically tied to FG% from specific locations on the floor.

The work I've done shows that when a player actually takes a shot from a given location on the floor (in whatever parameters he may have), I haven't found evidence that his teammates are "raising" his FG% from that location.

The evidence suggests that teammates affect a player's distribution of shots. As an example: some players may do a good job of giving their teammates good looks from behind the arc or perhaps close to the rim that in turn are raising their teammates effective FG%.

I'm excited to work with this stuff in an optimization class I'm taking in the fall, where we constrain some of this, such as maybe it's only reasonable that Shaq takes at most 40% of the lineups shots; anything over that and he's getting crushed by the defense. I know the curves you present try to figure that out, but there is still a max # of shots I think any one player can take before things like turnovers grind things to a halt.
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I am a basketball geek.

[Mike G]

A practical adjustment that shouldn't be any harder than FG% vs FG-frequency, but would yield more plausible results, would include free throws. Iverson's always gotten lots of FT and made a high %, thus boosting his scoring efficiency quite a bit. Shaq doesn't make his FT, so his high FG% overstates his case for shooting the lion's share.

"True Shooting Percent" is:
TS% = Pts/(FGA*2 + FTA*.88)

This gives credit equivalent to 1.5 'baskets' for a made 3-pointer. The .88 multiplier results from (on average) .88 possessions used for each 2 FTA.

If you include turnovers, you have to dig to find those TO associated with scoring attempts. Ignoring those, 'true scoring attempts' are just 1/2 the denominator in the above equation.
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36% of all statistics are wrong

[gravityandlevity]

Good point, and my favorite type of suggestion: one that's easy to implement.

I think what Ryan is saying is that my "linear extrapolation" of the skill curve to shooting fractions above 0.4 is highly unlikely. I tend to agree.

Any idea how we can extract something like a skill curve from single-season data?