“Wins above Bench” measures true basketball value

Judge Smails: If you don’t keep score, how do you measure yourself with other golfers?
Ty Webb: By height.

When a team like the Bucks loses a player like Andrew Bogut, the cost of that loss is not equal to Andrew Bogut’s production minus the average center’s production.  In practical terms that kind of calculation grossly understates what Bogut meant to the Bucks, mainly for two reasons.

One because of the way talent is distributed among humans.  You’ve heard this story before.  In sports, as in most fields, the exceptional few queer the pitch.  Because of the LeBrons of the world, what is calculated to be “average” is actually well above average (or below average, depending on how you conceptualize it.)  Because of that, most teams can’t employ replacements that are as productive as the “average” at a given position.  Its too costly.

The second reason an “average player” value assessment is distorted is because of basketball’s substitution practices.  In basketball, an injured starter’s replacement is only level one of damage assessment.  To get the entire damage, you have to account also the replacement for the replacement (Kurt Thomas replaced Andrew Bogut, and Dan Gadzuric replaced Kurt Thomas).  That second level is often the costliest.

To account for both those things, I came up with a “useful fiction”.  Instead of assuming or attempting to measure a class of “replacement players” like you would in sports that don’t involve frequent substitutions (think: backup first baseman), I instead assumed basketball’s “replacement class” is made up of composites I more generically call “the bench average”.

The bench average is simple to calculate and pretty simple to explain.  The “bench average” equals 67% of the a.) average win production of the average second string player at a given position plus; b.) 33% of the average win production of the average 3rd string or “emergency” player at a given position.

Here’s the rationale I used to come up with that.

Each basketball team is made up of about 11 to 12 actual contributing players, plus about 4 extras who the coach never wants to play except in practice  and in dire emergencies.

Ty Webb: You’re not, you’re not good, Al. You stink.

An Average “Bench Team”

Given ideal circumstances most teams would play their starters about 66-71% of the time and their “second string” or  “contributing” reserves about 33-29% of the time.  Those are rough numbers.

Now, if I wanted to put together the best team possible for the least amount of money (“freely available talent”), I should be able to pretty inexpensively hire a starting five made up of average second stringers (on the theory that I am offering the opportunity to upgrade to a starting role… Scott Skiles says  playing time is the most valuable thing in a coach’s arsenal), and I should be able to pretty inexpensively induce 5 to 7 more “key reserves” who are made up of players at least as productive as the average “emergency” (on the same “opportunity” theory).  Its like musical chairs.

Remember though,  these are average second string players and average third string players.  Not the  very best of each lot.  The very best second stringers, like Marcin Gortat and Lamar Odom, are not freely available and are expensive.  So I’m not assuming you can easily get those kind of players.  But if you can’t at least attract a Zaza Pachulia or a Channing Frye with a “Come here and play full time minutes” pitch, without having to pay him a fortune, then there’s something seriously wrong with your organization or with that player’s level of competitive integrity.  And the same logic applies to filling out your key reserve positions.

What does the “bench team” measure.  In practical terms, it measures baseline competence as an organization.  If your team didn’t post at least as many wins as a team composed of starters who are at least as a fictional “bench team” would have posted, there’s something wrong with your direction and your leadership.  It is the lowest acceptable level of success.  Its a baseline from which to judge.

How many wins could such a team expect?  Using the 2008-09 Marginal Win Score numbers found at 2009nbawincharts.blogspot.com, I calculated the expected number of games this fictional “bench team” would be expected to win.  Its about 28 games.  That’s 70% of  average, which, strangely enough, is just about the same as in football and in baseball. (Giving you some idea of how poorly the Wolves and Nets were assembled).

By position, expected “bench average” win production would be as follows:  1. SG (.409%); 2. SF (.384%); 3. PG (.358%); 4. PF (.333%); 5. C (.239%).

That is not a terribly surprising win distribution, given the duties of the different positions.  The point guard position requires specialized skill, so although height is not an issue, there is a higher barrier than the perimeter spots, while the big man positions require rare height ( or so teams believe.  Most teams would be far better off employing “heavy” power forwards as backup centers rather than guys like this Mbenga of the Lakers or Fran Elson of the Bucks.  Those guys are wasted space.  But teams insist on seven footers, regardless of  production).

Ty Webb: A flute without holes, is not a flute. A donut without a hole, is a Danish.

Bogut’s True Value

So, what does this mean for the new value calculation for a player like Andrew Bogut?  Well, first my old calculation “Wins Above Average”.  By “Wins Above Average”, Bogut’s estimated 7.9 wins and 1.3 losses produced this season would put his value WAA at +3.3 wins, implying the Bucks were something like a .500% team without him.

But “Wins Above Bench” puts his value at +5.7 wins, implying the Bucks were something like a 37 win team without him. (I think that’s what they were actually).

Ty Webb: I guess you’ll just have to keep beating yourself.

SUMMARY of  “Wins Above Bench”

I think “Wins Above Bench” gets closer to a player’s true value to his team, and gives a better indication of how much resources they ought to expend on him (Bogut’s value seems better reflected.  His +5.7 is best on the Bucks, indicating his relative value on the team, but low compared to other team’s “key” stars, mainly because Bogut has what Packers coach Mike McCarthy refers to as “availability issues”.  Being there is half of life, and if you’re always injured, well your WAB isn’t going to look as good as it should.)

As I roll out the 2009-10 NBA team Win Charts, the column entitled “Wins Above Bench” will give you an easy and pretty reliable method of evaluating each player’s true value to his team, and whether he’s “worth the dough”.

Footnote:   Neither the term “Wins Above Bench” nor the concept of valuing players according to a fictional replacement level are in any way novel and I want to make that clear.  Each is as old as the sabermetric hills.   But I think the concept of a (67/33) bench team basketball-specific calculation might be.  If its not, who cares?  I wouldn’t get credit anyway.

I think Basketball Prospectus has a Wins Above Replacement Level calculation but I couldn’t tell you how they calculate or the rationale behind the calculation.  I think its  just an across the board arbitrary baseline, but that’s a guess.


4 Responses to ““Wins above Bench” measures true basketball value”

  1. palamida Says:

    Great work, Ty. I think the whole “replacement level” thing is somewhat overlooked – and it really shouldn’t.
    I played with Hoopdata numbers a little bit. At a glance what I found reinforces your findings. I do wonder how they allocate positions over there…. I’ll just throw some numbers out there, perhaps something will pique someone’s interest 🙂
    Again, all the caveats in the world, it’s really shallow work and I don’t think their positions are to be trusted anyways….

    I looked at Pg, SG and Center. All these numbers are from this season:

    23 PG’s played over 30 minutes – Let’s call them – starters. Naturally the 30 min. mark is arbitrary. Jameer nelson for example (a clear starter) played a little less, but those things do not really matter here anyways as this crude by definition and made only to give a general idea.

    Those starters (per 40 mins) posted 6.44 WS.
    29 players played 20-30 mins and posted 5.1 WS. (those would be your 2nd string players). An additional 28 players played 9/10-20 mins. (I excluded the ones who played less, many of whom did not play in many games, as well as playing very few mins). These 3rd string PG’s posted 3.78 WS.
    Quite similar to what you reported.

    The SG’s – Here there were more “starters” – 27, who posted 5.8 WS.
    23 “bench” players posted 4.97 (this drop-off is indeed less meaningful)
    24 more, the 3rd stringers, posted 3.72. (again only looking at players who played at least 8-9 mins a game, I think this is best, since sample size becomes an issue with some of them and I think that when doing something this crude – it’s best to exclude them).
    I suspect there are more “starters” here since some SG’s see some PG mins, more so than the other way around.

    Lastly Centers:
    Only 16 played “starter” mins, which is expected since I used the same cutoff and Centers due to physical limitations and the tendency to commit more PF see less mpg as a group; These starters posted 11.94 WS. Impressive….
    BTW did you know David lee led this group in minutes playing 37.3 Mpg? that’s remarkable. I guess not even trying to defend helps you stay out of foul trouble and reserves energy at the same time….:)

    25 “benchers” posted 10.17 WS – not all that bad.

    The 3rd string Centers though are (as you argued many times) where the real damage occurs. To start with, there were 35 different players fulfilling this role, and that’s when I exclude all the 2 MPG Pops Mensah Bonsu types.
    They posted a 7.39 WS mark, which is not that far removed from the Starting PG’s production – That’s just nasty.
    That’s that, crude as they come, But I think that it’s safe to say this season’s data (used in a far less accurate method) reinforces your results, premises and conclusions.

  2. tywill33 Says:

    Good work by you! I appreciate your interest in my work, and the fact that you take my work seriously enough to critique it.

    I have an issue I’d like you to examine, but I can’t put it into words. It has to do with who coaches are willing to use at each position.

  3. Jerbil Says:

    Hey, guys- impressively learned- but what about the crucial question: Would Milwaukee have beaten the Hawks with a healthy Andrew Bogut?

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