APBRmetrics

I was just revisiting Jermias' not-so-recent presentation of ten seasons' worth of coaching RAPM (http://stats-for-the-nba.appspot.com/coaches) and I could not recall whether these striking results have been discussed.

What these data show is a net negative input into the basketball production function. And one cannot argue that the explanation involves some positional confusion, a la PGs, as a result of short coaches being swapped for tall ones, or some such.

Three quick points of summary:

(1) The median coach by this account contributes -1/-1.1 per 100 possessions.
(2) Most of this subtraction of value must comes from making offenses less efficient, what with only 15 coaches out of 97 having posted positive values.
(3) The net contribution on defense isn't clear on cursory examination, with 47 coaches having shown positive contributions and 50 negative.

I don't know if anyone has the data at hand to weight these estimates by possessions to come up with averages. Regardless, the exercise wouldn't turn the position of "head coach" into a net positive position.

A basic question is why this is so? A reasonable interpretation, and probably the correct one, is that coaching changes are disruptive, presumably disproportionately so on the offensive end, as new schemes are but slowly implemented. So what you get, on average, is the new boss, same as the old boss, but with significant transitional costs.

Another issue, not related to the results from the overall distribution, is how to improve the point estimates. It seems clear to me that taking into account player-aging effects are extremely important when appraising coaches, as those who disproportionately have post peak players will have their rating impacted negatively. I am supposing that this would go a long way toward explaining why Greg Popovich is only a -0.4. But then this factor would probably also explain part of the positive contribution of the best coach of the decade, Tom Thibodeau and his stand-out 2.4 rating.

Acknowledging that RAPM crops the extremes (though the coaching numbers aren't the extremes being cropped, right?) is the concept of a superstar coach simply an oxymoron? And might anyone have a sense of whether coaches, on average, are paid approximately the same amount as -1.0 RAPM players?

I processed that chart just a bit. Made the names sortable and entered 'games coached' from b-r.com
Thinking the coaches with few games might upset the averages schtevie reported, I broke them roughly into quarters, based on their games coached. No apparent advantage by coaches with more games.
And of Lenny Wilkens' 2487 games, not that many were in the previous 10 seasons.

Weighting all coaches' RAPM by their games, I get an average of -1.12 on offense, +0.08 on defense, and -1.06 total.
I think it should be at zero.

Should be at zero? But the point is that it is not.

P.S. I guess my short term disruption theory isn't supported by the averages shown, unless coaches, regardless of total games coached, have approximately the same number of games per gig.

Doesn't your disruption theory also have to suppose that after a year or two, coaches will tend to be better than average with the players they have?

And wouldn't a league have zero net influence by coaches, just as by players?
The defensive impact is close enough to zero. But how can all coaches over all years make their teams an avg of 1 PPG worse on offense?

They can't be allowing 1 PPG more than they're scoring.

Perhaps I misunderstand Jeremias' regressions, but I thought that the coaches are in the same pool as the players. That is that the combined sum of players' + coaches' RAPM "should" sum to zero (not that this constraint is formally imposed) but that doesn't obtain for coaches as a sub-group, any more than it obtains for any positions 1 through 5. (Similarly, Eli Witus' results - http://www.countthebasket.com/blog/2008 ... lus-minus/ - showed PGs and SGs to be net negative contributors).

If this is correct, coaches indeed could be net negative contributors and it could all show up in offense. (And the possible explanations are far more limited than with Eli's results.)

I think you're right.

Averaging the salaries of all players having RAPM = -1.0 since 2009-10 (inclusive of the current season) this equals $4.1 million. Nineteen in all, these range from a high of $13.36 for Antawn Jamison to a low of $0.64 for Jarron Collins, both last year.

So though the bad news is that head coaches on average subtract value, the good news is that on average they are a bargain (their average salary being distinctly lower than $4.1 million, according to what I infer from various sources)!

schtevie wrote:... head coaches on average subtract value...!

Incorrect. They add less value than 48 mpg of average NBA players.
The median player may be around -1.0, but more than half are below avg.
And of course, 4 million dollars doesn't get you a (48X82) 4000 minute player, either; perhaps half that, on avg.

Mike, I don't understand what you are claiming is incorrect. By your calculation, the average contribution of coaches is -1.06 per 100 possessions (per RAPM). That is a negative contribution. I called it a subtraction of value. And what that implies is that the non-coach (i.e. player) contributions, appropriately defined and averaged across five positions, should sum to something close to +1.06. How this latter number is sliced and diced is beside the coaching point.

But, I do take the implicit point about coaches being there for all minutes/possessions per game. This, of course, just makes their negative contribution a greater (relative) value still, as to buy 48+ mpg worth of a -1.0 player costs, as you note, would cost considerably more than $4.1 million.

Here's a modest, thought experiment. Let's put a potted plant on a (former) head coach's chair, channel Bill Russell, and assume a player-coach. Would such a team expect the same -1.0 per 100 possession decrement? Or, more precisely, if the $3 or so million saved, were redeployed on other resources, what might the effect be?

Such idle speculation aside, there remains the fundamental question: how does one explain that the average contribution of coaching is negative?

P.S. And, please, no introduction of the concept of VORC - value over replacement coach.

Good topic and good analysis by both of you. Especially on the aging question. I had taken note of the stronger results for coaches on the defense side, especially from the strongest coaches. I would definitely strongly favor hiring a defensive-minded, defensive strength biased Head Coach.

Only two coaches have a better offensive impact than McHale. Of course it is based off limited data. Is that what the Rockets needed most? I don't think so.

If the Bobcats are averaging a -15 ppg point differential, then they're averaging -3 from each position.
If a player (or 48-min platoon) is functioning at -1.0, they're adding about 2 ppg, not subtracting.

You can't just waive all your below-NBA-avg players and magically have a .500 team.
An average player, who holds his own against NBA average lineups (0.0), is quite a valuable player; market value something like $4-6 million per 2000 minutes. There's no team so good and deep that he doesn't improve the team's point differential.

The same is basically true of the -1.0/100 contributor, whether coach or player.
But when we use negative numbers to denote "below average", confusion is common.

Mike G wrote:If the Bobcats are averaging a -15 ppg point differential, then they're averaging -3 from each position.
If a player (or 48-min platoon) is functioning at -1.0, they're adding about 2 ppg, not subtracting.

You can't just waive all your below-NBA-avg players and magically have a .500 team.
An average player, who holds his own against NBA average lineups (0.0), is quite a valuable player; market value something like $4-6 million per 2000 minutes. There's no team so good and deep that he doesn't improve the team's point differential.

The same is basically true of the -1.0/100 contributor, whether coach or player.
But when we use negative numbers to denote "below average", confusion is common.

Yes, confusion is common, and it tends to arise when folks deviate from the most commonsensical definition of average in the context of a zero-sum game: 0. And this last comment about the contribution of coaches illustrates this point.

To begin, I was being a bit facetious about comparing the average (RAPM) value of coaches to that of players. Not in the sense that -1.0 doesn't equal -1.0 (it does) but in terms of how perfectly these factors can be substituted for one another in the basketball "production function". Rather highly imperfectly is the answer, unless you wish to seriously entertain something like the thought experiment I noted above.

This mischief aside, coaching input being independent of player input, you could get all VORCy and argue that the average coach has positive value because the next Tom Thibodeau waiting his turn actually is likely to have a worse effect on the scoreboard. That would be what? -1.5 points? -2.0? Someone could come up with some estimate, and majorities could agree upon it as a standard? The point is that this would remain an absolute, negative contribution on the scoreboard.

Yes, if your reference point is the worst team in the league, substituting someone who is still below-average (according to the beautiful, immutable zero standard) but less bad will improve competitive performance, but the Bobcats are an arbitrary baseline. Why not the Wizards? Why not the average of the Wizards and the Bobcats? Why not a weighted average of the worst and second worst teams in the league over the last seven years, with weights 0.6 and 0.4, respectively?

Sadly, I realize that this exercise in persuasion is futile and the malign influence of baseball will forever leave basketball VORPed, but I maintain that it is useful to have accounting structures in place where reference points aren't approximate ranges and cannot change as the wind blows, or as there are better or worse classes of incoming college seniors, or as the rules of the game change, influencing the effect of existing talent pools, etc.

But let's drift back to the original point.

The RAPM estimates cited, based on ten years of data (and 97 coaches) show an average coaching contribution of about -1.0. For context, Aaron and Stephen's six year APM estimates for individual players showed standard errors of only about 1.5. Given this, what's the chance that the true value for the coaching average is non-negative? And if negative, what is the possible story to explain this?

Then finally, what is the chance that the distribution of coaching contributions is much different than what is shown? And if the distribution is shown is correct (never mind the accuracy of individual estimates) how should we mark our views to market, in the sense of how we think of coaches having influence on game outcomes?

Both the median and the games-weighted average for coaches is about -1.0
This is below the avg NBA player-minute, but probably close to the median.
So you could trade an above-avg coach -- -0.5 for all -- for 2 below-avg (but above median) 24 mpg players, and you could break even.

... the beautiful, immutable zero standard...

But it's not immutable. If the league expands, bench players become rotation players, or starters. What was average becomes exceptional.

If the league should contract to 8 teams, current all-stars would be struggling to be "positive contributors", relative to the zero-standard. It's the most arbitrary standard you could find.

In an employers' market, an apple orchard owner can fire everyone who is below average in bushels per day picked. He can tell you something like, "You are one bushel per day below average, so we consider you to be a -1 picker. You're fired."

And by weekly firing everyone below average, he may progress toward elite picking standards.
But should there not be an unlimited supply of people willing to work incredibly hard for a paycheck, he may have to revise his standards, and only fire the bottom 10% of his pickers.

The range of apples per day picked may be only a few percent, in fact. In the NBA, just a few ppg in scoring differential can differentiate a .300 team from a .700 team.

Like a moth to a flame, despite the thread drift, I cannot resist further comment on the wackiness of VORPiness.

The beauty and immutability of zero being the reference for defining average performance has everything and only to do with the fact that we know that this is in fact the average performance, league wide. Always has been. Always will. What is the direct consequence of basketball being a zero sum game, from a league perspective.

The beauty and immutability of zero being the reference for defining average performance has nothing to do with league expansion or contraction, the number of players allowed per team, rule changes, the adoption of new strategies and relinquishing of old, the expansion or contraction of the talent pool, or anything else. Whatever impact such things have on zero as a reference point, they have on VORP as well. Always have. Always will.

At the end of the day, there is no problem with VORP as a convention IF people know what the value of the RP being used is AND understand all the conditions and assumptions embodied in determining that number, that in the case of NBA basketball is necessarily imprecisely estimated. But the fact is that people most typically don't.

Instead, what happens is the title VORP drops majestically from on high (from a baseball diamond in the sky, where given the rules of that game it has much greater value as a convention) and deference is granted. As such, in a basketball context, VORP tends not to abet clear thinking but obscures it. Not a good convention to have.

But never mind.

I recant.

I think I like the idea of VORC.

What Jeremias' RAPM numbers show is that RCs, those with fewer than 100 games, are actually about 0.3 less bad than all others. So, instead of adding 3.2 or 4.6 or 5.1 points, or however many, depending on the particular estimation procedure, to establish VORP, now we get to subtract 0.3 points from the existing scores. So, Greg Popovich really costs his team 0.7 points per 100 possessions not 0.4. That's better.

What's good for the player is good for the coach. VORC it is!

Greg Popovich really costs his team 0.7 points per 100 possessions

Of course he doesn't. You're probably about 2 points off the mark.