The Value of Shots Taken

Tomi,

That's true. But if you think about it, the REASON that those shots draw defenders is that they are good shots, and defenses by their very nature try to prevent good shots. Good defenses actually try to let teams take certain bad shots (like 22-foot jumpers).

173 days ago

Brett Gunter

Patrick,
The last of your bullet points reminds me of an old Wages of Wins argument in the comments of a post, concerning the non-productive players (in a WP48 sense) who had the talent to be 'coached up.' I'm all for coaching, but I'd like for everyone to stop equating physical talent--whatever that is, exactly--with productivity. If you CAN do something, but DON'T, that might be stupid, or it might be evil--but either way, it's measurable.

The argument we often hear, touting the value of 'any shot is better than none,' relates to the high value of offensive rebounds--which only result, of course, from missed shots. I will allow that if your only 2 choices are the worst shot ever taken, or no shot at all, by all means take the shot. What I will NOT accept is using that logic to absolve players who spend the last 10 seconds of the shot clock trying to 'create' a good shot by going one-on-one (or one-on-FIVE) rather than passing to a less-covered teammate--or (here's a radical idea) CONTINUING TO RUN THE OFFENSE. I do not know if this is true, but I am willing to theorize that, when every player on the defense KNOWS Melo or Nick or Russ is going to take the shot, both defense AND rebounding become simpler and easier; if you're not on the ball, or doubling, then your main task is to block out your man. If I'm correct, this would surely negate any small advantage of just 'getting a shot up.' Additionally, abandoning this flawed heroball strategy might improve things like team chemistry, scoring balance--oh, yeah, and FG%; since that means MORE POINTS, it might come in handy, too.

173 days ago

Will VanderWyden

What a fantastic post, thanks Patrick.

173 days ago

Steve Dickinson

Very nice post Patrick.

Slightly unrelated, one thing that interests me is the correlation between usage % and efficiency. For low volume, high efficiency guys, do they tend to maintain their efficiency as their usage increases, or does it tend to decline? And conversely, if high volume, low efficiency guys took less shots, would their efficiency increase?

Are you aware of any research into this area? Love to read some.

173 days ago

Frederic Bush

So, what do you think about this paper? It argues that NBA players are very good at aligning the EV of their shots with the shot clock -- they pass up poor shots early in the shot clock but take the shit shots with the clock winding down when that's the best they're likely to get. http://econ.ucsd.edu/~mrgoldman/HGGT6.pdf

173 days ago

Jack Noble

One thing that get's at my intuitive understanding of "creating" a shot is that a player who takes an unassisted shot created that shot in a way a player who takes an assisted shot generally doesn't. E.g. Perhaps the reason most people agree with Wins Produced about Lebron James but not about Tyson Chandler is that part of why Chandler is hyper efficient is that his shots are usually assisted while Lebron's are not.

Wins Produced already discounts assisted baskets. But I wonder if it isn't still overvaluing players who rely on assisted shots. One way it might be: assists don't get recorded when players draw fouls.

173 days ago

Steve,

I know Dave Berri has done research in this area. There are not a huge amount of players to use as a sample that go from low usage to high usage, but generally, and increase in FGA from one year to the next does not decrease efficiency.

Recent examples are Kevin Love, who's FGA skyrocketed in 11-12 but whose TS% only declined a little (and is largely explained by his 3FG% -- i.e. variance) and James Harden, who isn't at his lofty totals from last year but is still highly efficient (and here I would argue variance again -- look at his 3FG% on exactly the same number of attempts).

Frederic,

I won't argue this point; obviously defenses sometimes play well and the shot clock runs down. I would argue that a) this doesn't happen that often (a simple perusal of the average time left on the shot clock in the NBA confirms this) and b) the 'penalty' of these shots evens out over time, and those bad shots are going to be pretty evenly spread out over lots of players (similar to end-of-quarter heaves, etc). People claim that guys like Melo, Westbrook, etc take many bad shots because they are the ones who end up with the ball in those situations but a glance at the data easily proves this wrong; some players take lots of "bad" shots early in the shot clock.

173 days ago

Steve Rosenblatt

Good case against players that shoot too much, but could wages of wins be making the opposite mistake, overvaluing players that shoot very little but efficiently? Tyson Chandler as an example....

173 days ago

Jon Midget

Another example of going from small role to big role: Paul Millsap. Specifically from 2007-08 season to 2009-10 season. Variations in usage and role (18% usage off bench in 2007-08, 22% usage and starter in 2009-10, with variations in between).

The result? His lowest TS% was when his role and usage were lowest, in 2007-08. The other three years, with were the same regardless of minutes, usage, FGA, etc.

173 days ago

I think you will be hard pressed to find examples of increased shot attempts that result in the "expected" decreased shooting percentages simply because coaches and players won't be super illogical in their shot selection. The guys who take bad shots generally have good enough skills that it isn't a disaster (there are exceptions) and the guys who WP loves because of percentages (see Reggie Evans) but who have limitations, just never will have an offense run through them. Coaches and players are intuiting at least some of WP's formula and applying it.

My only problem with WP formula is that it doesn't acknowledge usage levels at all. This has got to be a mistake. Would the results of WP be different if we assumed that untaken shots went to a hypothetical volume scorer (who presumably on most teams is a guy who scores inefficiently). So Reggie Evens's low shots doesn't leave shots for an "average" scorer instead it leaves shots for volume shooting guards.

Also, as a player I know that I have to take some bad jumpers from time to time to set up my pump fake and drive (which is my most effective move). It doesn't take a lot, but you need to have some diversity to your game to set up other moves. If you show your best move to a defender again and again it won't be as effective.

173 days ago

Mostly holds water and is a simple argument, but WP will always be flawed in ignoring the fact that guards shoot more, and score more than might look right because in doing so they create better shots for their teammates. It's a tradeoff, but it works. That's why WP will always undervalue players like Westbrook and overvalue players like Durant - I would happily argue all day that Westbrook is of more value to Oklahoma than Durant.

172 days ago

Thomas,

You clearly do not understand WP. It does not, in fact, undervalue players for those reasons at all -- the position adjustment means *precisely* that as a shooting guard, you need a lower TS% to get a "good" WP48 than at any other position.

And if you are arguing that Westbrook is more important than Durant...all I can say is that I wish we were both NBA gms, you'd be on my speed dial.

172 days ago

Jon,

Interesting that you chose Reggie Evans. His shooting is positively NOT why WP evaluates him highly.

It's furthermore yet another myth that WP cares more about percentages than totals -- all other things being equal, a player with 60% TS who shoots a lot will have a higher WP48 than a player with 65% TS who rarely shoots.

What's interesting about guys with low usage and high efficiency (like Chandler, not Evans) is that it's on the team to get them more shots. In Dallas Chandler got about 50% more FGA than last year in New York. Doesn't seem like a big leap to me to think that maybe creating plays that get Chandler easy shots (and Dallas demonstrated that this is possible) is a better idea than drawing up "Melo Isolation Variant 54-A".

I'll repeat myself: WP48 does not try to explain WHY players are efficient shooters.

172 days ago

Patrick, don't patronise, of course I understand WP, it's not exactly complicated. The positional adjustment helps in this instance, but it doesn't model interaction, and that's a flaw. It doesn't matter that you don't think it's a flaw, it's not your opinion that decides the truth.

Don't get me wrong, Durant is awesome, and I don't think there's much in it, but I still think his lack of versatility makes him less valuable.

Oh, and if I were a GM and had Durant on contract then I wouldn't be trading him away.

172 days ago

I doubt westbrook missing jumpers is what helps kd be so effective. Unless hes repeatedly showing him how not to shoot. im wondering how russels veesitility makes him more important. how is he versital exactly? i think westbrook runs fast and jumps high but that distracts the fact his production is almost interchangeable with mario chalmers. much like wp doesnt tell y a player is ineffecient it doesnt have to explain interaction. it tells u who is responsable for creating wins. the thing is alot of the players that r fun to watch are not creating wins (see a. iverson)

172 days ago

Actually, to predictively explain wins it is important to model interaction effects. The most important interaction effect on offence is probably that between assists and points, where the geometric mean of assists and points gives a far better idea as to the value of a player in creating shots for others than simple assists alone. In this statistic Westbrook is much better than Durant, and as such the apparent disparity between them according to WP begins to evaporate.

172 days ago

Patrick,

I didn't mean that Reggie Evans gets help in the WP model from his high TS%. He doesn't shoot enough for that to move the needle. I know that it is his crazy rebound rate that gets him his All-Star WP rating. But implicit in the WP model is that shots untaken can be distributed to an "average" NBA shooter. When Evans is on the court, there are going to be many more available shots for his teammates (as opposed to when Lopez and, inexplicably Adray Blatche (who seems to view himself as a first option offensive player) fill the center spot). I'm not sure it is correct to assume these additional shots will get picked up by an average player producing at an average level with this extra scoring load.

Since the assumption is that untaken shots end up taken by an average scorer, WP doesn't penalize Evans for his below average scoring output. I hypothesize that one should assume that the shots get soaked up by a volume scorer and not an average scorer. So when we look at Evan's 3 FGA per 48 (I'm using your AWESOME player rater) we should model in that he is pushing 12 shots off to a less than average shooting player. So Evans should take a hit for that in the model.

172 days ago

Joseph Maurice Koudsi

To Patrick's point, WP does not explain how or why a player shoots well, rebounds well, etc... - one reason why you always have to take it with a grain of salt & use it as a directional metric.

I think it would be nice to be able to find the underlying causes of variation of WP from game to game & lineup to lineup. WP, in my opinion, is the best metric for evaluating players, though basketball is a complex game of interactions, randomness, & harmony.

Explain to me why Antwan Jamison is averaging so many rebounds & shooting so efficiently? If you watch Laker games, you'll notice that a lot of his rebounds are a result of D12 altering shots, & a lot of his open 3s/layups are coming off pick and roll play involving Kobe & Howard/Gasol. I believe that who a player is playing with will have an impact on how well he performs (a hypothesis I would like to test).

WP is the best metric for measuring player performance - let's now use it to model some other interesting questions.

172 days ago

1. most of these questions have been answered at wagesofwins. 2. wp has a truth that missing shots is bad therefore pkayers shouldnt be rewarded for just shooting or penalized for having discretion not to. 3. Players and teams dictate the vast majority of shot distribution ie gameplanning

172 days ago

Jon,

The idea that shots that Reggie does not take would be taken by a below average shooter does not make sense to me. First, not all volume shooters are inefficient ones (see Durant, Kevin; James, LeBron, Martin, Kevin), and second, it is not clear to me that volume shooters fill this gap.

In Reggie's case, think of all the times he gobbles up an ORB and passes out to the wing, and the offense resets. Whether or not a poor shooter ultimately takes the shot is a factor of the offense and the other four players on the court, not necessarily that Reggie not shooting puts pressure on the other players. Also consider that Reggie (or Kevin Love, or Kenneth Faried, etc) usually keeps a defender "honest" even when they are not a threat to shoot, simply because his defender has had a coach shouting in his year all day that you have to always be near him to put a body on him and block him out.

172 days ago

Thomas,

You ask me not to patronize, then you tell my opinion does not change the truth...which is apparently dictated by...your opinion.

I'm finding it difficult not to patronize.

You've basically spouted a lot of buzzwords and make statements like "The most important interaction effect on offense is probably that between assists and points" with no evidence to back it up, or even an explanation of the thought process that led you to this conclusion. I'll write your words back to you: your opinion of what the most important interaction is, or how important those interactions are, does not influence the truth.

172 days ago

Drew Miller

It seems totally intuitive that a low-shooting center's untaken shots would be replaced at less than average shooting. I assume they would be at roughly the same percentage as the average shot taken by a non-center. You'd maybe want to do some kind of pace adjustment to make sure you're not penalizing a player for a generally slow offense (although does anything like this happen for any other stats in wins produced?). Seems like an interesting thing to throw into the model and see if it has any explanatory power.

Thomas - build your model and let us know how well it explains historical wins and losses. I'm going to guess it will be worse than wins produced.

172 days ago

Idk the value of not taking a shot, but I know a miss is worth -0.034. Westbrook has a lot of -0.034's to his credit.

172 days ago

Russell Degnan

Interesting post Patrick, which got me thinking. If we look at a possession cycle (the points between shooting and your next possession), rather than a single possession, then the value of a made shot is the points made minus the points the opposition makes from being guaranteed the ball from a missed shot. At average efficiency (52.5% 2pt, 35% 3pt shooting), that translates to:
2pt: 1.05 - (0.475x1.05) = 0.49875 points
3pt: 1.05 - (0.650x1.05) = 0.68250 points

Given equal shooting efficiency, three point shooting is better because it gives the opposition undisputed possession less often for the same number of points.

Okay, but there all these disputed possessions. If a team never gets an offensive rebound, then the points value of disputed possessions are -0.49875 and -0.6825 respectively, cancelling out the earlier gain. But if a team can get offensive rebounds, then the value of the shot, irrespective of whether it goes in, are those two numbers multiplied by the ORR%. (or perhaps more reasonably, the change in that number over an "average" shot, as the value falls to the rebounder)

Which raises some interesting questions. Do some times types of shots generate more offensive rebounds? If so it could offset a surprisingly large amount of inefficiency. All things being equal, two point shots need to be rebounded at a 36.8% higher rate than three point shots to generate the same number of possessions. Do some players get rebounded at much higher rates? If iso-shots got rebounded at a much higher rate [plausible, but not guaranteed, a scrambling defence might have worse position], that might actually matter. Assuming of course that all possessions are equal (they probably aren't).

172 days ago

also evans ts% isnt as good as the average C so theres no indication his shots are being taken by less efficient shooters also the forgotton point is shot distribution is primarily a funtion of the offensive system and its goals. avery isnt planning for each player to post 20% usage so theres no way to indentify exactly how many shots evans should be taking/passing up

172 days ago

Patrick,

I never claimed that the truth is dictated by my opinion, I just happen to have done the legwork on this problem already and found that that particular interaction is an indicator of player value which can increase the value of high-assisting high-scoring players in a way that better predicts outcomes. At no point have I spouted any buzzwords, I know you're not statistically trained but to just ignore completely valid terminology as buzzword usage is a rather preposterous thing to do. If you would like to learn about these things rather than bury your head in the sand and ignore them (like any good scientist would, of course) then here's a good place to start: http://pages.uoregon.edu/stevensj/MRA/interaction.pdf

But hey, maybe one of us needs to ring the guys at CERN and tell them not to worry about bothering to model interaction effects because they don't matter?

Drew,

I have built my model(s) and continue to think on and improve them. They are far better predictors of future results than wins produced, which is the way a model assessing player importance and value should be measured. If I wanted a model that just explains past results then I can do that myriad ways with just the same correlation to wins as wins produced has. Even a rating that is just player points scored minus player points conceded (pro-rated from minutes played and opposition points) 'explains' past wins perfectly in terms of correlation.

172 days ago

pardon us lamen for evaluating players based on there production rather than the predicted stats. your all knowingness please tell me the score of heat-spurs next thursday and if wade will be back to his regular production. you should write a book like berri and have it peer reviewed but remember to put your predictions n or how woyld we judge u

172 days ago

"I know you're not statistically trained"

Once again, you state opinions as facts. I hate to break it to you but that is not true.

How does a term being valid exclude it from being a buzzword? It's how you string them together that matters.

The fact that you claim that explaining wins in a model is easy, and therefore not a necessary component of a model, tells me just about all I need to know about your ability to evaluate my knowledge of statistics.

172 days ago

Patrick,

Point differential near-perfectly maps to wins (looking back in time) which is why wins produced maps well to wins, but any metric which also maps to point differential will also map near-perfectly to wins.
The words were put together just fine. I'm sorry to hear you claim to be statistically trained, because if you were properly trained then you wouldn't just ignore my arguments.

Anyway, you've taken no effort to tackle any of my points, instead hoping to build lots of straw men, so it's pretty clear there's no interest in a genuine discussion about the usefulness of modelling interaction effects here, or how they might relate to good play, in which case I'm off.

172 days ago

Interesting discussion. By the way, Reggie Evans was awesome in last night's game against the Knicks. Fourteen rebounds in 18 minutes! On one possession he got three consecutive offensive rebounds which were kicked out for resets of the offense. Nets eventually scored with their fourth attempt.

I may be wrong that the high volume "shot creator" types have to carry a heavier load when playing with an extreme player like Reggie Evans. And Patrick you are certainly right that Evans has to be "guarded" at all times in that his defender must be near him to box out. But I think Drew is on to something when he points out that playing Reggie Evans means having one less big on the floor that provides scoring and that generally means you miss out on a higher percentage shooting player. So "average" shooting for that team becomes average for non-centers.

By the way, in case I'm misunderstood, I want to make clear I'm not saying Reggie Evans isn't playing great. This rebounding rate makes up for everything and then some. I'm going to write Brett Yormark, CEO of Nets, and suggest he gets some Reggie Evans jersey's into the Nets Store and that the video guys get more replays of Reggie rebounding on the big screen at the games. Reggie is quickly becoming a fan favorite.

172 days ago

Ty Hicks

I'm trying to follow this argument, but can someone tell me exactly what this sentence means, "WP will always be flawed in ignoring the fact that guards shoot more, and score more than might look right... " I'm a bit baffled.

172 days ago

Thomas,

Am I avoiding your arguments or knocking them down with straw men? Pick one. By the way, I'd argue the former, since you haven't actually presented an argument with any evidence (hint: an interaction that you have privately modelled in a model that you are not sharing with us is not 'evidence').

I'm well aware of the fact that point diff correlates to wins -- that's precisely the point, isn't it? We don't know if your model does as well (since you seem to be keeping it secret).

I'm well aware that a sentence like "the geometric mean of assists and points gives a far better idea as to the value of a player in creating shots for others than simple assists alone" makes grammatical sense. But you saying it doesn't make it true. Forgive me if I don't just take your word for it.

I'm not ignoring your claims on the basis of my stats training, I'm ignoring them on the basis of my scientific training.

171 days ago

Ty,

That's simply a claim that Thomas made, but did not provide evidence to back up.

171 days ago

Joseph Maurice Koudsi

Patrick, does WP essentially give the same value to all shots taken? If so, is it not taking into consideration that missed shots don't necessarily mean loss of possession (let's say there is a 20% chance of getting an offensive rebound when a shot is missed vs 0% when the shot is made)?

Also, has any analysis been done on how turnovers vs missed shots vs made shots impact the other teams offensive efficiency? I would imagine that turnovers lead to an increased offensive efficiency for the opposing team on average vs shots (though this is just a hypothesis).

171 days ago

Paul Müller

@ Patrick
Someone mentioned that you are being penalized in WP for making an assisted shot. As I understood your calculation, the penalty is shared between the 4 players who haven't made the assist. Isn't that right?
That would mean he is penalized by only 1/4th of the average efficiency increase through assists for the entire team. And if you take into account, that players who make almost exclusively assisted shots are likely to be much worse in unassisted shots than the rest of the team, he is penalized even less. The only unassisted shots Chandler is doing are put backs from rebounds, which obviously is also like an assist, just that he should get full credit for it. In any case he is not able to create a shot on his own (despite of rebounds, which cannot be forced). Thus the player who assists him could also get a much bigger share of the players efficiency. Ultimately how to spread the value of an assist between assisted player and passing player is a question to debate, but WP uses 1/4 of the lower boundary to penalize the assisted player (If I understood the calculation of WP correct).

170 days ago

Frank Alejano

I've done no more than a cursory search of The NBA Geek and Wages of Wins (both awesome sites, btw- this is my first post, hi!), so sorry if this is just basic knowledge and I'm just blathering.

A while ago it occurred to me that missed shots shouldn't real factor into shooting, but rather should be treated closer to turnovers, rebounds, steals, etc.- in other words, missed shots make you lose possessions. I figured that you should count a possession as one in which the team scores a basket. Once you've shot the ball, you've either finished a possession (scored a 2-pointer) or missed, losing the possession. Rebounding gives your team a possession, steals not only give your team one, but take one away from your opponents, etc.

Mixing missed and made FGs implies that a certain number of misses is fine (Tyson shooting 80% is great!!!) when in reality every single miss hurts. You can see it pretty clearly when you look at my beloved Mavs- we've got a bunch of players that have reasonable shooting percentages but burn possessions up, while guys like Chandler are giving his teams all sorts of extra opportunities and not exhausting many himself.

170 days ago

Paul Müller

@ Patrick
About your discussion with Thomas. Don't you think that the most important part of a model is it's predictive power? Thomas just made the case that it is easy to find a model which explains the past, thus being good in explaining the past is a nice property which might be of no use. If you cannot predict the future (better than other measures), your explanation of the past is likely to be wrong.

When you introduced the diminishing returns for Def. Rebounds, the explanatory power of WP was reduced, but it's predictive power was improved. I would argue it was an improvement. Don't you agree?

170 days ago