Proposed method to track performance of our starters

Maybe you want to check this out: http://stats-for-the-nba.appspot.com/

It has adjusted +/- stats, following a method similar to what Dan Rosenbaum describes in that article.

 

I don't find it useful because of the data/math needed, but I think it does reveal how well a player improves his teammates because it's a representation of how much the team improves when that person is on the floor.

I've been playing around with a different idea just based on boxscore and extended stats available on basketball-reference, but when I ran the numbers I keep coming up against really startling results. So I'd like to just throw out my methodology/equations to see if anyone can help me troubleshoot.

The basic idea is that defense is a complicated team effort that involves a lot of subtle positioning and angles adjustment that isn't counted because there's so many, sometimes very minute, and it goes by so quick. Because of these constant split second decisions, TEAM decisions (esp for things like pnr), flat scores for defense from the raw box scores doesn't really show defense.

However the results themselves show up, in the final scores, in the FG%'s.

Using eFG because it takes into account 3pt shots, which can be defended, and doesn't include FT's.

So:

eFG% = made/attempts = 100 * (FG + 0.5*3PT) / FGA

(defense affectable pts made against team) = (total made points against team) - FT​

And also:

(opponent game eFG%) = (defense affectable pts made against team) / attempts

(opponent average eFG%) = (opponent normal average makes) / attempts​

Thus, for the amount of opponent effectiveness reduced by team's defense:

(opponent game eFG%) / (opponent average eFG%)
= (defense affectable pts made against team) / (opponent normal average makes) = change in opponent eFG%

1 / (change in opponent eFG%) * (defense affectable pts made against team) = the opponents normal point production if there was any other team defending them per total game time​

Thus:

1 / (change in opponent eFG%) * (defense affectable pts made against team) - (defense affectable pts made against team)
= team Defense Points Difference (ie. teamDPD)

teamDPD / 48(min) = Points effected per min = teamDPD48

However to calculate, say, a team's opponents against league average I'd need to shift the scale somehow so that those teams who are below average aren't negative. I'm playing around with either a flat number or to use the league's worst defender.

teamDPD48*ADJMPG of player = net Defense points difference effected by Player in game, with a ramping weighted scale of player's minutes (ie. if a player is kept in the game for longer, they are 'worth' more despite playing with fatigue and with bench/rookie players)​

Final equation for teamDPD48:

(1 / (opponent game eFG%) / (opponent average eFG%) - 1) * (PPG-FT) / 48​

Thoughts? Critique? The huge drawback imo of this method is that it's heavily team dependent, even when Adjusted Minutes Played is involved, and while one player might have great contributions it might get shadowed in the event of a loss. Perhaps by balancing against the other elements in the box score? Hmmm. I think I just need to start applying the formula just to see if it returns plausible numbers.

 

ohhhh good point! I like that, and probably factor in Fouling too.. I sort of did that with a semi-flat "events per game" figure that tallies all good 'event's together and counts misses against makes.

What you've additionally put about the different defending tactics makes me think of this article.

Specifically this image:
Flash is the opposite of a Cut, but otherwise all the plays on the vertical axis should make sense. And the darker it is, the better the FG%


OPEN (no defender within 5 feet of player)
GUARDED (defender within 3 to 5 feet)
PRESSURED (defender within 3 feet but no hand up)
CONTESTED (defender within 3 feet and hand is up in front of shooter)
ALTERED (defender within 3 feet, hand is up, and shooter is forced to change shooting angle or release point while in air)
FOUL (defender fouls shooter)

Maybe somehow incorporate blocks/fouls and perhaps even separate out 2pt fg% and 3ptfg% because sometimes those change independently enough that at this point I'm still toying with scrapping the use of eFG% because it's not subtle enough. Also if the team reduces 3pt attempts and % while not increasing fouls on 2pt shots, that would be an indication of defenders forcing players into less efficient shot locations. Hmm. Back to the drawing board.:grin:


If you're curious about the adjusted minutes weight I'd give to the DPD, it's based on that a coach would trust a player with more minutes if, when he's on the floor, the points differential maintained or increased, thus it means more talent even if some of the factors are unquantifiable.

It's corroborated by this:

What’s the average career length for NBA Players in various rotation roles?

Minimum of 41 games played in a career = 6.18 seasons.

Less than 12 minutes per game for a career = 2.01 seasons.
More than 12 minutes per game for a career but less than 20 = 5.01 seasons.
More than 20 minutes per game for a career but less than 25 = 7.59 seasons.
More than 25 minutes per game for a career but less than 30 = 9.21 seasons.
More than 30 minutes per game for a career = 10.88 seasons.
NBA All-Star at least once = 11.36 seasons.​

Which is basically the ratio of how I'm scaling it.

 

If you don't want to use opposition FG% or eFG% to try to hammer down defensive impact, you could either use a PPP Allowed figure per Synergy, or go with the more traditional TS% (which would happen to incorporate good and bad fouls).

And yes, trying to hammer down defense is especially hard as it's more of a holistic thing.

Synergy is nice enough to break down PPP allowed by scenario such as Isolation, P&R, Roll man, etc, but once again is problematic in capturing the full range of defensive prowess given the impact or non-impact of Help Defense.

For example, if you contest a spot up shooter and they make their shot it negatively impacts your Spot up defense on Synergy, but if someone doesn't even bother trying to close out, they take no hit at all (not an ideal situation).

It's similar to the problem with measuring TO's. All a person needs to do to lower their TOV% is take more shots. So, there is a perverse statistical relationship between TOV% and people who have bad shot selection.

No stats are perfect.

As for your interest in further exploring player chemistry and skills interactions, here's a really nice paper that was submitted at the MIT Sloan Analytics conference.

It had the very user friendly title Positive and Negative Synergies in Basketball.

http://www.sloansportsconference.com/wp-content/uploads/2012/02/MMS1-NBA-Chemistry.pdf

Hope that helps. Or at least didn't leave you muttering to yourself in a corner. :grin:

 

This. This so much. FIVE MAN ON A STRING. BUT HOW DO YOU MEASURE THAT STRING?

And yeah, I've looked at the Synergy due to all your interesting posts on it, but I can't help but feel that there should be a better way to quantify a situation that is so team-dependent, and yet isolating an individual player's impact in that same situation. Which is why I was poking at the idea of maybe weighting/merging two consolidated stats together.

And while I like the thoroughness of the idea of the Recursive method of +/-, I'm still making a face at the fact that it requires so much more data. Which makes it iffy in-season, in tracking game-to-game progress.

Thank you for the link to the paper! :grin: I hadn't seen this version of it, though I did see a short version where they parsed out player types and the most achieving sets... and it kind of disturbed me at the time because it pretty much said that the Knicks couldn't succeed really. Though that was partly because of the logjam with Tyson, Stat, and Melo.

 

Well, I suppose one way you could address the help defense problem is you could try to analyze the opponent offensive side of it.

For example, on the one side you have the individual/isolation type statistics, and on the other side you could try to pick out more granular information in terms of shot selection by the opposing offense.

For example, most players have preferred spots on the floor and ranges. IF you are forcing those players to shoot outside of those ranges or outside of those spots, then the defense is most likely forcing them to shoot from uncomfortable spots vs them choosing to shoot from those spots voluntarily.

A simple way would be to break it into shooting regions, the more advanced analysts are actually trying to parse them into very granular shooting cells.

Here's another fine paper from the MIT Sloan Analytics conference, with yet another friendly title of...

CourtVision: New Visual and Spatial Analytics for the NBA

http://www.sloansportsconference.com/wp-content/uploads/2012/02/Goldsberry_Sloan_Submission.pdf

The most interesting parts of the paper talk about the difference between good and great shooters, and how position on the floor and shot selection in terms of high efficiency shooting comes into play in actual spatial terms.

Now, in terms of addressing your Man on a String, I suppose you could take THAT offensive data, then line it up to the particular defensive match up (IE, when the person is switched), then allot some sort of base score depending on how far or close that person's shot is to their favored areas, whether the shot is contested or not, etc.

If you extracted out the FG% on contested vs non-contested FG%, you could use a generalized average +-, then you could start looking at positional data and assigning +- to your adjustments based upon spatial location when shooting.

I personally wouldn't suggest using 1,284 cells like those analysts (unless you already have access to the data), but it might not be impossible to compile or acquire some less specific locational shooting data.

Finally, as per the Melo/STAT/Chandler trio, well, I've already voiced my opinions on that on the PSD boards regarding their inability to function as an elite unit due to spacing, preferred scoring methods, location, and imbalances in defensive match ups.

As expected, it received mixed reviews. :grin:

Anyway, hope that helps.

 

But then you that the bit which, what if the opponent is voluntarily choosing to make inefficient shots anyways? Then there would be a lack of defensive pressure which would encourage the shooter to shoot... and miss. That would be a correct defensive decision as a team (because it takes the shot out of a better/more efficient shooter's hand) but it won't show up even as a differential on a case-by-case basis.

OOO. If I dig backwards through that html would it link to more of these?

Haaaah, nope, I don't have that data.

If I'm understanding you right, you're suggesting to take a defensive rating based on how much the defense distorts the offensive movement. But then that falls into the issue of a team having (already) multiple offensive looks that may or may not be driven by the defense. Or position that has been distorted by the opponents own internal issues (say, injury causing a player to have slightly reduced mobility and their teammates covering for them) rather than the player's defensive abilities.

Also, it wouldn't factor in defense on the fastbreak and the like.

...holy cow I wonder if you were one of the posts I saw back then about that.

 

In those cases I would probably just treat that as a general Team Defensive decision (scouting report) vs an individual defensive decision. There are times when it's clear that you should sag off or not close on a 3 point shooter if they are sufficiently poor.

That of course is NOT the same as Not closing out on a legitimate 3 point shooter, which in that case I would file under defensive lapse.

Since teams HAVE scouting reports, I would consider a fail to contest on any decent 3 point or jump shooter an individual break down in help defense, which you could either allocate to a single player, or partially allocate to the closest players.

No idea. Never tried to dig through it. :grin:

Players that are shooting from non-favored spots are nearly Always being distorted by the defense. Either in general (through shading/hedging) or specifically (through funneling/backing down). How you choose to assign a +/- would be up to you. For example, a 2nd player moving up to shade/hedge correctly could be assigned a value. A player funneling or backing down an individual player could be assigned a larger value.

Just some ideas.

No, it wouldn't. You'd have to examine that specific aspect of defense separately. Yes, I know... another data set. However, if extracting defense was so easy, then everyone would already know how to do it.

No idea. If it was, you have my deepest condolences. :grin:

 

The link I provided above updates those adjusted +/- stats fairly regularly. It's generally no more than a few days behind. I think it would be useful for assessing player's defensive contributions in the context of the lineups they are a part of.

 

Just occurred to me Re:news of Gasol sitting out, what happens with your method when there's an injury with the starters?

 

Yeah, but then I'm curious to know what the margin of error is, and I've looked but they didn't seem to post that.

 

Thank you for your thoughts! They give me much to think over!

Why? because of all the (melo)drama?:grin:

 

Because he uses a "regularization" method, the errors tend to be much less compared to the conventional adjusted +/-. Probably you can check the www.apbr.org/metrics board for discussion on the errors he got.

Here's a good review of adjusted +/- stats in general:

http://godismyjudgeok.com/DStats/2011/nba-stats/a-review-of-adjusted-plusminus-and-stabilization/


By the way, Joe Sill was the first to apply this "regularization" method for adjusted +/- stats, and he won a best paper award at Morey's 2010 MIT Sloan conference on it. Unfortunately, I don't think his paper is online. You can read Sill's review of his "regularized" adjusted +/- method here (I'm using the web archive, because his website has since gone offline):

http://web.archive.org/web/20100308...allAnalysisView?analysis=RAPM&discussion=True

 

ah neat! thanks!

 

Maybe this would be useful to you as part of your analysis:

http://www.82games.com/1213/BYPOSL10.HTM

I gives team PER and opponent PER for each position.