APBRmetrics

jburchen · Joined: 23 Feb 2010 Posts: 9 Location: Vermont

I am currently working on an Economics Thesis and I was wondering if anyone has created or thought about the best way to create a dollar value of the statistical output of a player. Just so that I had numbers to plug into my model right now, I am using:

((League BRI)/(Sum(PER*MP) for all players with greater than 500MP))*((PER*MP) of individual players))

Its really crude and I'm looking to develop it. My thoughts were something along the lines of translating PER in Extra Wins Added and then figuring out the dollar value of a win for a team. Then,

(($ Value of Win)*(Extra Wins)) - (cost of replacement player) = ($ Value of Player)

Seems simple enough, but that's just my thoughts. I would love some feedback. Thanks.
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jburchen · Joined: 23 Feb 2010 Posts: 9 Location: Vermont

Just to clarify, my goal here is to quantify the value of the output of a player. I do not want to use actual salary data because I want to be able to compare it to actual salaries.

I see a ton has been done to quantify the statistical output of a player in a single metric, but has anyone thought about ways to translate statistical output into a $ value to the team they play for?
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herbal vaporizers

ARucker · Joined: 10 Feb 2010 Posts: 34

DLew · Joined: 13 Nov 2006 Posts: 224

Hollinger already has an estimated wins added measure based on PER. You may want to look into that, though as ARucker mentioned, it comes with all the flaws of PER.

jemagee · Joined: 05 Nov 2005 Posts: 129

kjb · Joined: 03 Jan 2005 Posts: 865 Location: Washington, DC

Win Shares is a stat at basketball-reference, which is derived from Dean Oliver's work.

David Berri's stat is Wins Produced. His simplified version is Win Score.

I took a look at translating stats into dollar values. I used a linear approximate value metric similar to PER, and calculated a player's percentage contribution to the team's overall production. Then multiply that percentage by the salary cap (or actual team salary, or average team salary, or the luxury tax threshold) and voila -- production translated to salary.

I thought it was an interesting toy, and I used it to write a couple articles. The concept might be useful to you, though.

HoopStudies · Posted: Thu Feb 25, 2010 2:54 pm Post subject:

ARucker · Joined: 10 Feb 2010 Posts: 34

I wouldn't rely on anything Berri has done without very carefully scrutinizing his methodology. No interest in igniting or restarting the flamefests that have already taken place regarding his work on his site and elsewhere...just wanted to throw the caveat out there.

See eg. http://dberri.wordpress.com/2009/12/22/the-rockets-surprise/ (with some good comments/analysis by Italian Stallion)
Or my personal favorite: http://gladwell.typepad.com/gladwellcom/2009/11/pinker-on-what-the-dog-saw.html (with some excellent replies by Steve Sailer, dignified despite Gladwell's complete lack of courtesy/class)

Crow · Joined: 20 Jan 2009 Posts: 812

You could look at this article

http://dberri.wordpress.com/2009/08/04/the-underpaid-and-overpaid-in-2008-09/

with its assumption that a win was worth $1.755 million (on average, not marginal).

And this is handy pre-existing, regularly updated tool for getting a quick read on performance value vs. actual salary:

http://realgm.com/src_playerrankings.php

You may or may not agree with all of the weighting of Floor Impact Counter but you can narrow-in on who to study further.

jburchen · Joined: 23 Feb 2010 Posts: 9 Location: Vermont

Wow, that was a great help.

I will be sure to evaluate (and discuss) the merit of whichever metric I choose. It is pretty clear that there are varying opinions on the merit of each metric. "The Underpaid and the Overpaid in 2008-09" does a great job of what I am trying to do in terms of player rating. Thanks for the heads up. If time permits, I might try to create a weighted average of several metric-to-$ values of players to try and limit the effects of any one metric. That is probably a little ways out though.

In terms of the which dollar metric (however you would like to put it: salary cap, BRI, gate revenue, etc...), why do people think that BRI is a bad idea?

I understand the constraints of the salary cap, but the cap does not constrain the amount of revenue a player can generate. My thoughts were, that if I could quantify the revenue generating ability of a player and subtract his contract value, I would have a surplus value of a player. That is, the revenue he generates above and beyond his salary. This surplus value of a contract is really what a profit maximizing (whether or not teams are actually profit maximizing is irrelevant at this phase) team would seek. Thus, when they make trades, they are acquiring a 'player contract,' not just a player, that has an expected surplus value:

((expected $ value of player per year)*(contract years remaining))-(Salary Remaining) = (expected surplus value of player contract)

Using salary cap would help to capture what value a player SHOULD get paid, but that is not my focus. It is his revenue generating ability less his salary.
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Renntech

Crow · Joined: 20 Jan 2009 Posts: 812

True marginal revenue production will vary by player and player level and certainly market and will not necessarily in line with current stat production or actual win production (variability / timing of stat production matters).

Wins are important but this is an entertainment product- or really a set of them (ticket sales, other arena revenue, merchandise, local and national TV contracts, etc.) with many co=producers with different distributions of player impacts and simple current player win production of course won't explain everything accurately.

Past wins, player contribution to entertainment value beyond the stats and wins and other things matter (arena size, amenities and quality of experience; team marketing, pricing strategy, area disposable income, pro and other sport competition; division or conference rank, fan expectations, etc.).

But know what you are looking for / testing, do it and, if you want, let us know what you get from it.

Crow · Joined: 20 Jan 2009 Posts: 812

Using the real GM tool it is interesting to see one cut at who and where the bigger "outperformers" are overall and to me specifically in the minimum or near-minimum salary band. Identifying, getting and effectively using guys who are better than replacement level (distinct tasks) but still cheap is an important part of the moneyball game (more valuable and important in some places and situations than others).

ARucker · Joined: 10 Feb 2010 Posts: 34

jburchen · Joined: 23 Feb 2010 Posts: 9 Location: Vermont

I really like the idea of using the real GM tool. After creating a broader model, that may be a great way to show the robustness of my findings and that, those GMs that are able to recognize cheap assets may create the best teams (the Spurs, without the Richard Jefferson trade, come to mind).

With regards to which portion of the BRI isn't player related, that is the real challenge right now. I plan to use controls like demographic measures of the host city, population, age of arena, past championships, previous season wins and 'star power' much in the same that Berri and Schmidt did it in "On the Roach with the National Basketball Associations Superstar Externality."

In terms of coaches, entertainment, and fan base, my thoughts are that wins (as created mostly by players, thought coaches could play some smaller role) trump all those other attributes. I may explore the economic reality of this statement before simply stating it in my paper, but I find it hard to believe that in the NBA something other than the on-court product plays a significant role in generating revenue (with all controls imposed). Let me know if there are examples of this being proven or disproven, otherwise I will be sure to post something after I do some work on it.

Finally, I also need to find a way to address the TV revenue sharing problem. My thoughts were to subtract out TV revenue from team's BRI (if that data is available) and then redistribute it to teams based on the team's proportion of non-TV revenue generated by the NBA as a whole. This seems logical given that teams ability to generate fans should not be terribly different between TV and other revenue generating streams. I'd love feedback on this idea though.
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vapir oxygen

Crow · Joined: 20 Jan 2009 Posts: 812

You can refer to the pages off this starting page at Forbes

http://tinyurl.com/y994kcb

to get estimates for a lot of the data you are interested in.

Dividing the national tv revenue the way you suggest might not be a bad way to do it. Probably fairer than dividing it equally. Maybe the big markets should get even bigger shares though. Depending on how far you want to go you could look at market-based nba tv ratings and use that to help guide estimates of how much national tv revenue markets are generating.