NBA: Why Don't Rebounds Eliminate the Heat? Score the Four Factors

[Latrinsorm]

Everyone knows you can beat up the Heat on the boards. Chicago, Memphis, Indiana, Boston (pre-trade) - the Heat can't handle those big bodies, and that'll pay big dividends come the playoffs... except when it comes to the actual playoffs the Heat are 2-0 against Chicago, Indiana, and Boston since 2011. The only series they've actually lost in that span came against a team that was worse at rebounding than they were: the 2011 Heat went 25.2 and 75.5 on ORB% and DRB%, the 2011 Mavs went 24.1 and 74.8, and in the actual Finals the Heat out-rebounded the Mavs by the tune of 27.2% to 24.8%.

"Okay smart guy," you may be saying, "so how'd they beat your precious Messiah?" First of all, LeBron isn't the same person as Obama. That's racist. Second of all, by out-shooting them. The Mavs beat the Heat in eFG% by 51.3% to 50.1%. We can sort out the Heat's 12 playoff series in each of the four categories...

won eFG, won ORB
2011 1R (5)
2012 ECF (7)
2012 Finals (5)
2013 1R (4)

won eFG, lost ORB
2011 ECF (5)
2012 1R (5)
2012 2R (6)
2013 2R (5)
2013 ECF (7)
2013 Finals (7)

lost eFG, won ORB
2011 Finals (6, loss)
2011 2R (5)

lost eFG, lost ORB
none

The Heat are really good at shooting and defending shots, and compared to winning the eFG% battle the ORB% battle seems irrelevant. Category one's average length is 5.25, category two's is 5.83: a whole half a game if you can punish the Heat on the boards. Is this because LeBron is just that much of a clutch winning closer, he makes the shots when they count?

.

Dean Oliver came up with the Four Factors:

Shooting (40%)
Turnovers (25%)
Rebounding (20%)
Free Throws (15%)

That is to say, shooting is more important than anything and specifically twice as important as rebounding. How did Dr. Oliver come up with these weights? I have no idea. Another fellow named Ed Kupfer has made it even more complicated by assigning different weights depending on which side of the ball you're on:


Off Factor Def
22.4% Shooting 19.5%
9.2% Rebounding 7.8%
6.5% Free Throws 8.7%
13.2% Turnovers 12.6%Summing across for convenience gives us:
Shooting (41.9%)
Turnovers (25.8%)
Rebounding (17.0%)
Free Throws (15.2%)
How did he come up with those weights? I have no idea, but it's probably a good sign that the two metrics agree.

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Then I figured, why not just weight them myself? What if I took every NBA team over the past 9 years, charted out their relative Rtgs and factors, and looked for cases where two teams had (to the hundredths place) the same value for three of the four factors? It would look like this, where O = offense, D = defense, E = shooting, T = turnovers, R = rebounding, F = free throws:


O+ oE+ oT+ oR+ oF+
0.99 0.97 1.02 1.04 0.98
0.99 0.97 1.02 1.19 0.98

0.97 0.97 1.08 1.00 1.05
0.97 0.97 1.08 1.00 1.10

0.99 0.98 0.95 0.99 0.94
1.00 0.98 0.95 1.00 0.94

1.02 0.98 0.95 1.08 1.01
1.01 0.98 0.95 1.08 1.08

1.02 1.01 0.93 1.00 0.89
1.03 1.01 0.93 1.00 1.12

1.01 1.01 1.03 1.07 1.09
1.01 1.01 1.03 1.08 1.09

O+ oR+ oF+ oE+ oT+
1.01 0.92 0.99 1.01 0.92
1.00 0.92 0.99 1.01 0.99

0.95 0.93 0.94 0.96 1.04
0.98 0.93 0.94 0.99 1.04

0.99 0.93 1.06 0.99 1.01
1.00 0.93 1.06 1.00 1.01

0.97 0.99 0.94 0.95 0.95
0.96 0.99 0.94 0.95 1.00

D+ dE+ dT+ dR+ dF+
0.94 0.95 0.99 1.04 0.82
0.95 0.95 0.99 1.04 0.96

1.01 0.99 0.92 0.98 0.92
1.00 0.99 0.92 1.01 0.92

0.99 0.99 1.04 0.98 0.95
1.00 0.99 1.04 0.98 1.10

1.00 0.99 1.04 0.98 1.10
0.99 0.99 1.04 1.00 1.10

0.99 1.00 0.93 1.04 0.81
0.99 1.00 0.93 1.04 0.91

1.01 1.00 0.94 0.99 0.92
1.02 1.00 0.94 0.99 0.96

1.00 1.00 0.95 1.02 0.98
1.01 1.00 0.95 1.02 1.15

1.00 1.00 0.96 0.99 0.81
1.01 1.00 0.96 0.99 1.09

0.98 1.00 1.08 1.00 0.97
1.00 1.00 1.08 1.00 1.12

1.02 1.01 0.95 0.99 1.07
1.02 1.01 0.95 1.00 1.07

1.01 1.01 1.00 1.01 1.01
1.01 1.01 1.00 1.01 1.18

1.02 1.01 1.03 0.97 1.10
1.03 1.01 1.03 0.97 1.20

1.04 1.03 0.98 1.00 1.10
1.03 1.03 0.98 1.00 1.16

1.03 1.03 1.03 0.98 1.05
1.02 1.03 1.03 0.98 1.06

1.04 1.04 0.99 0.97 0.99
1.05 1.04 0.99 0.97 1.11

1.04 1.05 0.98 1.00 0.96
1.05 1.05 0.98 1.00 1.08

D+ dR+ dF+ dE+ dT+
0.99 0.98 1.10 0.97 1.06
0.97 0.98 1.10 0.97 1.13

1.02 1.00 0.94 1.02 0.92
1.00 1.00 0.94 1.02 1.02

1.01 1.01 0.92 1.03 0.98
1.00 1.01 0.92 1.03 1.09

1.00 1.01 1.05 0.97 0.88
1.02 1.01 1.05 1.01 0.88

1.02 1.01 1.17 1.00 0.96
1.00 1.01 1.17 1.00 1.07

1.00 1.02 0.96 1.00 0.99
1.00 1.02 0.96 1.01 0.99
Which isn't a heck of a lot of data, only 32 samples. Still, we can calculate out and get:
O D
E 1.00 0.40
T -0.17 -0.18
R 0.06 -0.33
F 0.00 0.05
Rebounding is a little tricky because values are listed for ORB%+ and DRB%+ respectively, so to preserve ratio levels I weighted DRB%+ at /3, as teams generally get offensive rebounds at a third of the rate of defensive rebounds. This is also why it's the only value with different signs: getting more offensive rebounds makes a higher (better) ORtg, getting more defensive rebounds makes a lower (better) DRtg. Summing across we get...

Shooting (71.1%)
Turnovers (17.6%)
Rebounding (8.6%)
Free Throws (2.7%)

Like I said this is with limited data so far but I always prefer an empirical method, and even if this method is an overestimation it agrees in form with the other two analyses: rebounds don't eliminate the Heat because the Heat are great at shooting on both sides of the ball, and that's way more important. Currently the top 5 in difference of eFG ratio go Spurs (.110), Heat (.104), Rockets (.092), Clippers (.084), Pacers (.080).

[Ker_Thwap]

I'll need the numbers on superstar name recognition vs. lower paid lesser known opponents who get within x inches and are called for a game changing momentum foul (or what I like to call the Greg Kite factor.) Then let's factor in the officials and the home and away differential on garbage fouls. How about a nice survey on how many microseconds a defender must have his feet set for in order to draw a charge if his last name is James? Compare that to how many minutes a defender must have his feet set, outside of that circle, if his last name isn't James?

In short, the NBA is a small step above professional wrestling and sports involving Russian judges.

[Latrinsorm]

It's difficult to do objective analysis on "game changing momentum" because there is no such thing, "garbage fouls" because the definition usually means "calls I remember that I don't like", and block/charge because it's a subjective call by definition.

With that said I do think it's helpful to demonstrate that free throws have by far the least impact of the four factors, although "helpful" implies that you base your analysis on data rather than visceral impressions. You can't take the standard deviation of "WHAT KIND OF CALL WAS THAT???"

[Ker_Thwap]

It's difficult to do objective analysis on "game changing momentum" because there is no such thing, "garbage fouls" because the definition usually means "calls I remember that I don't like", and block/charge because it's a subjective call by definition.

With that said I do think it's helpful to demonstrate that free throws have by far the least impact of the four factors, although "helpful" implies that you base your analysis on data rather than visceral impressions. You can't take the standard deviation of "WHAT KIND OF CALL WAS THAT???"

Yes, subjective like sports that involve Russian judges. Your statistics won't determine much of anything until you're willing to factor in some squishy human factors. Surely you can establish a criterion for a bad foul, that isn't subjective, and from there it's a simple matter of applying the numbers. I can recognize when my superstar of choice is the recipient of a foul call. All the "easily measurable" statistics in the world aren't going to explain why certain people/teams win in sports. The popularity contest portion of the game does matter.

[Latrinsorm]

Yes, subjective like sports that involve Russian judges. Your statistics won't determine much of anything until you're willing to factor in some squishy human factors. Surely you can establish a criterion for a bad foul, that isn't subjective, and from there it's a simple matter of applying the numbers. I can recognize when my superstar of choice is the recipient of a foul call. All the "easily measurable" statistics in the world aren't going to explain why certain people/teams win in sports. The popularity contest portion of the game does matter.You say "much of anything"? Give me a % figure for how often the model has to predict the winner of a series, and we'll see how important your squishy popularity contest is.

[Ker_Thwap]

Why is there a home court advantage if not for the squishy?

[Latrinsorm]

Why is there a home court advantage if not for the squishy?There is a quantifiable home court advantage, but every NBA team plays the same amount of home and road games so it doesn't matter over the course of a season. Obviously the same applies to any series decided in an even number of games, and for 5 and 7 games it would be worth 0.7 and 0.5 points per game respectively. There is also no evidence that some homes are disproportionately favored over others.

See? Objective analysis, data, done. Now you can give me that %, and we can go from there.

[Ker_Thwap]

There is a quantifiable home court advantage, but every NBA team plays the same amount of home and road games so it doesn't matter over the course of a season. Obviously the same applies to any series decided in an even number of games, and for 5 and 7 games it would be worth 0.7 and 0.5 points per game respectively. There is also no evidence that some homes are disproportionately favored over others.

See? Objective analysis, data, done. Now you can give me that %, and we can go from there.

42. You said yourself that certain players are allowed a 3 step travel every time. Just because you don't feel like tracking this phenomenon doesn't mean it doesn't exist. When I own the NBA someday, I'll be having robot officials.

You didn't say "show your work."

[Drew]

LeBron had his nose broken and didn't even get a foul call. The guy is like Shaq where if they called the game fairly for him it would break the game. So we all let him get beat up because no one would pay to see LeBron shoot 85 free throws a game. It's the same reason Shaq didn't get to (miss) tons of free throws, the guy was so good we'd accept that he had an extra level of difficulty over the average player.

[Latrinsorm]

42. You said yourself that certain players are allowed a 3 step travel every time. Just because you don't feel like tracking this phenomenon doesn't mean it doesn't exist. When I own the NBA someday, I'll be having robot officials.

You didn't say "show your work."42%? Sheesh, I'll crush that. You sure you don't want to set the bar a little higher?

I never said subjectivity doesn't exist - I'm the one who brought it up. What I heavily implied was that it is insignificant on scale of a season, and I stand by that unless and until someone wants to demonstrate it with data. If you want to keep believing your various conspiracy theories, I can't stop you, but I also can't stop publicizing data that offer alternative explanations. Why? Because what would Miley Cyrus do.

[Ker_Thwap]

42%? Sheesh, I'll crush that. You sure you don't want to set the bar a little higher?

I never said subjectivity doesn't exist - I'm the one who brought it up. What I heavily implied was that it is insignificant on scale of a season, and I stand by that unless and until someone wants to demonstrate it with data. If you want to keep believing your various conspiracy theories, I can't stop you, but I also can't stop publicizing data that offer alternative explanations. Why? Because what would Miley Cyrus do.

But, the NBA season is insignificant. Anyone not trying to tank makes the playoffs. I'd say that neither of us has proof that your "insignificant" or my "significant" is more likely. I haven't really followed her career.

I am not a conspiracy theorist! People acting like people is not a conspiracy theory. A conspiracy theory requites aliens, robots and ninjas or I won't even consider it.

[Latrinsorm]

Playoffs? We're talking about... playoffs? My only point in this thread is that shooting trumps rebounding. If I can find correlations without paying your alleged cause any heed, your cause must be insignificant (even if it really annoys you).

[Ker_Thwap]

Playoffs? We're talking about... playoffs? My only point in this thread is that shooting trumps rebounding. If I can find correlations without paying your alleged cause any heed, your cause must be insignificant (even if it really annoys you).

Oh, was that your point? Your topic heading seemed to think you were trying to answer the question of how the Heat can get out-rebounded and still win. I was merely courteous enough to give you one extra reason to consider, albeit one which didn't have a ready database.

[Latrinsorm]

Okay, you guys, fasten your seatbelts for this one...

Defensive rebounding hurts defenses!!!!!

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First off, this analysis has all been predicated on the notion that the four factors are relevant to ratings, or equivalently that two teams with (nearly) all the same factors will have (nearly) the same ratings. It turns out that from 1981-present there have only been two sets of teams to do so, and that only on defense:


dE+ dT+ dR+ dF+
1.03 0.97 1 0.91

1.04 1.01 1 1.08The first couple are the 1997 Phoenix Suns (1.018 DRtg+) and 1988 Philadelphia 76ers (1.021) - about 0.3% difference. The second are the 2005 New York Knicks (1.026) and 2002 Chicago Bulls (1.030) - about 0.4% difference. I'm satisfied with <0.5% difference. I was kind of hoping the couplets would be further apart chronologically, but that's how it goes.

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Okay, constant factors make for constant rating. But maybe the methodology is flawed for different factors in general, not just for rebounding. Here are the coefficients determined for shooting, turnovers, and free throws:



O D
E 0.691 0.698
T -0.242 -0.199
F 0.077 0.065


Strong agreement across the ball, and offensive rebounding's value alone is .108. If we double that we get relative weights of:



E 63.5%
T 20.1%
R 9.9%
F 6.5%


Which agrees well with the order of other publications... so what's the deal with defensive rebounding? If you allow more offensive rebounds (higher ORB allowed), your defensive rating should be worse (higher DRtg). Yet...

http://img.photobucket.com/albums/v456/johnnyoldschool/DRBsWTF_zpsbc5dbbf2.png

...dudes, this is intense. It's not some fluke, it's 32 couplets with excellent fit. How can this be? Well, consider the Ibaka/Love dilemma: you can challenge a shot or you can obtain rebounding position, but not both. Ibaka always goes for the block, so his rebounding is very modest (45th this year in DRB%) but his blocking is exceptional (2nd in BLK%). Kevin Love does the opposite, so his stats are the opposite (2nd and T86th). Thus, allowed ORB% and eFG% aren't independent variables, and pursuit of the former at the expense of the latter is a loss for the defense. This isn't the case on offense, because the shots that maximize offensive rebounds are near the rim and 3s, both of which are good for eFG%.

Another step is transition: not going for a defensive rebound can mean an easy opportunity at the other end (+own eFG%), not going for an offensive rebound can mean stopping one (-allowed eFG%). Thus if your team goes hard for defensive rebounds and/or the other team doesn't care to go for offensive, your transition game goes to pot.

.

So that's why you can't beat the Heat with defensive rebounds... doing so plays right into their hands.

[Latrinsorm]

Just to tie a bow on this, here are all the graphs:

http://img.photobucket.com/albums/v456/johnnyoldschool/NBABrute4oe_zpsbed78f89.png
http://img.photobucket.com/albums/v456/johnnyoldschool/NBABrute4ot_zpsaad3ddc5.png
http://img.photobucket.com/albums/v456/johnnyoldschool/NBABrute4or_zps1a1a8aae.pnghttp://img.photobucket.com/albums/v456/johnnyoldschool/NBABrute4of_zps0ca2ebe5.png

[Latrinsorm]

And defense:

http://img.photobucket.com/albums/v456/johnnyoldschool/NBABrute4de_zps6c0064bc.png
http://img.photobucket.com/albums/v456/johnnyoldschool/NBABrute4dt_zps1c4d6837.png
http://img.photobucket.com/albums/v456/johnnyoldschool/NBABrute4dr_zpsf7c59a65.png
http://img.photobucket.com/albums/v456/johnnyoldschool/NBABrute4df_zps4fdd5e19.png

[Latrinsorm]

Bump.

So the weights I determined for shooting, turnovers, rebounding, and free throws were...
Offense .6867, -.2379, .1018, .0767
Defense .7005, -.1938, -.2874, .0620

If this analysis is worth a damn, then I should be able to plug in these weights to the 2014 season results (which were not included in the original sample) and get very good agreement. Do I?

http://img.photobucket.com/albums/v456/johnnyoldschool/NBA4Brute2014O_zpsd6ab7e24.png

http://img.photobucket.com/albums/v456/johnnyoldschool/NBA4Brute2014D_zps5b34582b.png

Come at me, bro. Now, the equations should ideally result in a trendline of y = 1*x + 0. If we do that, the R^2 values we get are .9538 and .9832, not as good fits as the unconstrained regression but very very very nearly as good. Dudes, I'm pretty happy about this. :)

[Latrinsorm]

Okay, so I figured out what was wrong with the rebounds. If you do 1 - 75%, you get 25%. If you do 1 - 75, you get negative 74.

Whoopsie daisie!

However, this just means that I was doing a slightly offset regression of defensive rebounding percentage, so the theory still works. With that corrected, we can get weights of...

Offense .6867, -.2379, .1018, .0767
Defense .7005, -.1938, .1280, .0620

Put another way, the value of each factor on offense and defense is:


Factor Off Def
Shooting 62.25% 64.60%
Turnovers 21.57% 17.87%
Rebounding 9.23% 11.80%
Free Throws 6.95% 5.72%


Or, for convenience of memory: 65%, 20%, 10%, 5%.
Or, shooting is more than half again as important as every other category put together.