A simple floor spacing formula

[Dr Positivity]

I wanted to see if I could find a way to quantify floor spacing. The first place to start was with average shot distance on basketball-reference. I tested on the Raptors rotation players with their average shot distance divided by 23 (representing the length of the 3pt line). Lou Williams leads the team at 17.9 average shot distance, which divided by 23 is 0.78.

Lou Williams: 0.78
Terrence Ross: 0.77
Patrick Patterson: 0.72
Greivis Vasquez: 0.71
Kyle Lowry: 0.67
DeMar Derozan: 0.58
James Johnson: 0.29
Amir Johnson: 0.25
Tyler Hansbrough: 0.21
Jonas Valanciunas: 0.19
Chuck Hayes: 0.17

The big problem I have with this is floor spacing in my opinion also depends on how much you have the ball. As a ball dominant player Lou Williams has the opposite style of play of Ross and Patterson. If Lou Williams has a play where he over dribbles the ball, draws a defender out to the 3pt line, then shoots a 3 in this defender's face - it counts as much in the above shot distance measure, but I don't feel it's nearly as "floor spacing positive" in regards to making the rest of the team better as a player where an off ball role player such as Ross and Patterson stand at the 3pt line without the ball and draw a defender away, creating space for a teammate.

So the next strategy I had was to adjust this by assisted/unassisted %s. Here the % of each players FGs that are assisted (rounded):

Chuck Hayes: .95
Amir Johnson: .87
Patrick Patterson: .80
Terrence Ross: .75
Tyler Hansbrough: .72
Jonas Valanciunas: .67
James Johnson: .56
Greivis Vasquez: .54
DeMar Derozan: .48
Lou Williams: .44
Kyle Lowry: .36

This reflects how players like Lowry and Williams who did well in the shot distance measure, are much more ball dominant players than the spot up shooters on the team. Next I simply multiplied this number by the first chart (average distance/23 chart) and got:

Terrence Ross: .58
Patrick Patterson: .58
Greivis Vasquez: .38
Lou Williams: .34
DeMar Derozan: .28
Kyle Lowry: .24
Amir Johnson: .22
James Johnson: .16
Chuck Hayes: .16
Tyler Hansbrough: .15
Jonas Valanciunas: .13

I thought this was pretty satisfactory results for both taking into account shooting range and playing off the ball with the two players who feel the most to me like floor spacing specialists easily ranking top 2

Here is the same method used on the 2013-2014 Spurs

Average shot distance/23

Danny Green: .84
Matt Bonner: .82
Patty Mills: .79
Marco Belinelli: .73
Manu Ginobili: .61
Kawhi Leonard: .54
Cory Joseph: .50
Boris Diaw: .47
Tony Parker: .43
Tim Duncan: .39
Tiago Splitter: .17

Assisted %:
Marco Belinelli: .90
Matt Bonner: .89
Danny Green: .84
Tim Duncan: .67
Tiago Splitter: .66
Boris Diaw: .66
Manu Ginobili: .64
Kawhi Leonard: .62
Patty Mills: .58
Cory Joseph: .48
Tony Parker: .37

And multiplied together:
Matt Bonner: .73
Danny Green: .71
Marco Belinelli: .66
Patty Mills: .46
Manu Ginobili: .39
Kawhi Leonard: .33
Boris Diaw: .31
Tim Duncan: .26
Cory Joseph: .24
Tony Parker: .16
Tiago Splitter: .11

Once again I find these results to be fairly satisfying for a purely numerical way to measure floor spacing. Once again the formula is simply (Average shot distance / 23) * (% of FGs assisted).

My first thought for possible flaws would be a Josh Smith 13-14 situation where his volume of long distance shooting doesn't reflect his real skill. He rates as .54 on the distance /23 chart and .63 on the assisted FGs chart for a total of .34, which is still a pretty middling number compared to the above players and around Kawhi Leonard's level, so it's not dreadfully off base. This season's Kyle Korver by the way, is at .97 on the distance chart (22.2 ft average) and .95 assisted for an total of .92, how far that is ahead of last season's Danny Green (.71), helps show his freakishness in that area.

The other issue is this doesn't adjust for position i.e. Matt Bonner and Patrick Patterson play a position where floor spacing is more rare than at Green's. However that big men tend to have a high assisted % helps make up for this. The reverse of them would be PGs where it's a lot less likely they do well in the assisted % category, but can get that back by increasing their % of 3s attempted by having the ability to create their own. Stephen Curry rates as a .75 in the distance/23 (17.2 average feet) and .43 assisted % for a mediocre .32 overall, which would be a possible way to criticize this formula by saying it doesn't give him enough credit for floor spacing. Unless shooting so much off the dribble makes him less of a floor spacer, and his real value in terms of "making his teammates better" is drawing double attention as a volume scorer? Maybe Patrick Mills spaces the floor more than Curry because he's a great 3pt shooter who doesn't hold the ball much? On that note Curry doesn't need to be credited as an elite floor spacer to be rated as a superstar player statistically anyways

Edit - I also see now that Andre Iguodala is sort of in the sweet spot of taking a high % of his shots at 3 but at an average rate and having a high assisted percentage, thus he actually rates higher in this formula than Curry, Klay, Barnes or Draymond. Assuming that he is left open more than other players, this "less respected shooter" factor may be something the formula misses

[Crow]

Interesting start. Different ways to try to get at it.

Distance of defender to shooter at time of shot is something of an indicator of effective spacing. Shots at rim help spacing too. Maybe instead of distance from rim it could be absolute distance from avg. defender distance from rim? That might be around 12 feet. Spacing is out or in. Not sure how to incorporate these things but those are my first thoughts fwiw.

[Mike G]

Nice approach. But I don't see how stand-and-shoot guys are 'better' at spacing the floor. Five such players on the floor would find few good shot attempts. They might even have to shoot from further on avg, increasing their "value" in this metric.

Don't the Tiagos and Amirs also spread the defense by drawing attention toward the basket? This prevents the D from crowding the arc, making those shooters more effective.

And don't the 'ball-dominant' guys also draw defense to them, wherever they are? A player who can dribble in traffic and pass out of it (or drive) is essential to make use of the options on the floor.

If a player never gets an unassisted FG or anything inside the arc, he's not an effective 'floor spacer' unless he (a) can regularly get open for a shots, and (b) makes a good % of these shots. Neither factor seems to be incorporated into this version of the formula.

[Dr Positivity]

I agree that finding a way to include efficiency would improve things, but have some issues on how to do it as I wouldn't want to just include 3P% or 3PM in there because while it may work fine for PG/SG/SF where all floor spacers take 3s, it would run into some problems with big men. For example Anthony Davis average shot distance is 9.2 to Amir Johnson's 5.8 as he is much more of a midrange shooter and presumable floor spacer, but Amir has taken 33 3PA this year at 42% while Davis has taken 9 at 11.1%, so using any of 3P%/3PM/3PA would favor Amir as the floor spacer. And can't fix the problem by saying for PFs and Cs it's FG%/FGA/FGM on 16-23 jumpers that'll count the same as what 3P%/3PA/3PM do for perimeter players, as there's enough PFs and Cs who are really shooting 3s and some of them aren't shooting much from 16-23 feet at all, so there has to be a way to credit them more than 16-23 feet shooters which would require some arbitrary weight in there. Not to mention rating PF/Cs differently than PG/SG/SF from the outset, would also run into the major classification issue of some players being SF and PF tweeners.

[Mike G]

I agree that players' alleged position should not be part of a formula. But their function in the offense should naturally show up and be counted -- a 7' player or a 6' player might play the same role.

When Orlando had prime Dwight + (4) 3-point shooters on the floor, would you say Dwight was part of the 'floor spacing'? He commanded double teams, and often there was a guy wide open at the arc. His presence made the 4 shooters practical and profitable.
If he doesn't command extra attention, they don't get the luxury of having 4 shooters out there. They'd have to use a lineup slot on a pick-setter, board-crasher, perhaps.

[Dr Positivity]

Yes I guess creating a separation between the word floor "spacing" and floor "spreading" could restrict it more to the shooters who drag defenders out

My idea was to use this as part of a bigger stat and in that stat players are given credit for volume of possessions in a separate part of it. Thus in your example that Dwight Howard draws the attention of the defenders more than a role player, would be given credit for it via his higher possession usage

[EvanZ]

Position can have a dramatic effect on floor spacing. A big who can pull the opponent's big away from the basket creates more useful space near the rim (i.e. for his teammates to attack) than a wing doesn't he?

[nbacouchside]

Position can have a dramatic effect on floor spacing. A big who can pull the opponent's big away from the basket creates more useful space near the rim (i.e. for his teammates to attack) than a wing doesn't he?

Yes, I believe Height*3PA is a statistically significant predictor of O-RAPM, for this very reason. You can also use DReb as a proxy for height and get the same result.

[Crow]

The data apparently exists from SportsVu to show all player positions at time of shot. So now or eventually some have / will have exact data on spacing and won't need proxies for that. They will still need estimates of effective spacing play by play or overall including defender response based on general threat level not just threat on that specific play based on that specific positioning.

[NateTG]

The formula that's described here (i.e. average shot distance * assisted rate) is elegant, but the approach is rather unscientific: Let's say, for example, that someone else comes along and suggests something like (average shot distance * assist rate * assisted rate * unblocked shot rate) as an alternative 'simple floor spacing formula'. (It's pretty easy to make an argument that those other factors also align with 'floor spacing') How do we test which formula is a more appropriate notion of 'floor spacing'?

With the understanding that other people may see things differently, I tend to think of things this way:
When a player on one team draws a player on the other team away from the ball or the low post, then that first player is 'spacing the floor'.

Because the box scores are extremely focused on the ball, and - for me - the notion of 'floor spacing' is all about things that are happening away from the ball, I wouldn't expect any simple box score calculation like this to capture what I think of as the 'floor spacing impact' that a player provides.

The data apparently exists from SportsVu to show all player positions at time of shot. ...

With the raw data, we could also look at how the defense reacts to the offense well before the shot is taken. That said, I don't think proles like us
are all that likely to get access to said data.


Edit: This seems like an example of a player not 'floor spacing'

http://www.basketballanalyticsbook.com/ ... invisible/

[Dr Positivity]

The formula that's described here (i.e. average shot distance * assisted rate) is elegant, but the approach is rather unscientific: Let's say, for example, that someone else comes along and suggests something like (average shot distance * assist rate * assisted rate * unblocked shot rate) as an alternative 'simple floor spacing formula'. (It's pretty easy to make an argument that those other factors also align with 'floor spacing') How do we test which formula is a more appropriate notion of 'floor spacing'?

Can you elaborate on the argument for assist rate and unblocked shot rate connecting to floor spacing? I assumed unblocked shot rate is being used to show a player shoots less at the rim, though since the distance measure accounts for players shooting farther from the rim, this feels already accounted for. In terms of players getting blocked less when they are "wide open" on jumpers, although this may at times account for floor spacing, does it go the other way when since a player is left wide open because teams are playing off a weak shooter, not getting his shot blocked is a sign that he's not spacing the floor as much (since they are playing off him).

However for example I could see the argument that using a players ORB vs DRBs could be an avenue to explore, since player with a low ratio of ORBs to DRB, could have that difference partly because they're stretching the floor on offense

I agree it's a simplistic measure of floor spacing since as mentioned it's such a non boxscore friendly value to the game. My main reason for liking this method is when trying it on players and teams, it feels like the the most "floor spacer"-centric spot up outside shooters fairly reliably end up rated the top of the list. I do think there's an "Andre Iguodala problem" where for example Iguodala's mediocre 3P% and 3PA does not hurt him in comparison to Curry, Klay and Barnes in judging how much of a floor spacer he is. So agree it's be far from exact and the SportVu solution may end up being far better, but perhaps a workable number for me in the same way I don't see DRAPM as exact measure of defense, but still not a bad number to use if you have to take one for defense

[NateTG]

Can you elaborate on the argument for assist rate and unblocked shot rate connecting to floor spacing? I assumed unblocked shot rate is being used to show a player shoots less at the rim, though since the distance measure accounts for players shooting farther from the rim, this feels already accounted for.

It comes down to the idea that floor spacing is a team effect, so both parties in the assist should get floor spacing credit, and that floor spacing should create open looks.

[steveshea]

I once ran a study to measure the influence of Miami's floor spacers on the shape of San Antonio's defense in the 2013 NBA Finals. Here are the metrics I used:

1. To understand the total stretch of the defense, I took the area of the convex hull of the defenders. The larger the area the more stretched the defense. (The convex hull of the defense can be described as the resulting polygon when stretching an elastic band around the defenders in their position. It's also the colored polygons that move around in NBA.com's movement animations.) The same idea can be used to measure the spread of the offense.

2. To understand each individual's impact on the floor spacing, I first computed the average position of the defenders (avg x, avg y). I then computed each defenders distance from the defense's average position. I did the same thing for the offense to see each offensive player's distance from the offense's center.

I found that as Miami added 3-point shooting (e.g. replaced U. Haslem with M. Miller) San Antonio's defense stretched (in regards to the area of the convex hull of the defense). I also found that certain Miami players had a much more significant impact on that stretch than others. For example, Ray Allen's defender was much further from the defense's average position than Dwyane Wade's defender. Finally, I found that Miami's offense was far more efficient when the defense was stretched.

The details of my study are public. Anyone that is interested can read more in Chapter 5 of Basketball Analytics: Spatial Tracking.

[AcrossTheCourt]

You have a problem with a linear assumption. A shot from 10 feet does not have half the spacing effect as a shot from 20 feet. And, of course, shots from behind the line have a much greater spacing effect than short jumpers.

And yeah, you can't ignore position. It's really powerful. Height*3PA is too conservative in my opinion.

Like my piece here:
http://www.gotbuckets.com/2014/04/22/pa ... ful-is-it/

I've tried a spacing measure using the defender distance on catch-and-shoot attempts. I can't tell how useful it is now, but I think it'll ultimately be an improvement over 3PA's purely for spacing.

[EvanZ]

I've tried a spacing measure using the defender distance on catch-and-shoot attempts.

Would a player with a quicker release and creates greater space look worse in this metric?