*“In the beginning God created the heavens and the earth. ^{2} Now the earth was formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters. *

^{3} And God said, “Let there be light,” and there was light. ^{4} God saw that the light was good, and he separated the light from the darkness. ^{5} God called the light “day,” and the darkness he called “night.” And there was evening, and there was morning—the first day.” _Genesis 1 to 5

We make assumptions about understanding in life all the time. We assume things are clear and well explained because for us at this point they are. Because for most of us, it’s easy to forget the moment of confusion before we understood something, the dark, or to translate that moment of understanding, the eureka moment, the light to something transferable to other people. At this point, I take understanding of the Basics for granted and I really shouldn’t. One of the reasons I started this blog was to take a lot of the hard math and put it in understandable, practical terms in a fun way (or try to). Partly for my sake (because I enjoy writing and it helps me process and think) and partly for the sake of broadening the audience while trying to amuse them. Today, I’m going to get back to that (and I’m stealing a bit from an old post)

Reader Casey Hopkins asks:

*I’m reading “The Wins Produced Calculation” which uses Bob Lanier’s 77-78 stats as an example.*

*I am trying to understand the difference between League Average Adj. P48 and*

* average player WP48 that are used in steps 4 and 5.*

*The overall (not by position) League Average Adj. P48 is given as 0.304*

*The average player WP48 is 0.099.*

*Aren’t these conceptually the same value? I understand the calculations for each are different and cannot be expected to produce identical results, but the difference seems too large for these to be the same value.*

*What am I missing?*

*My apologies if this has been asked and answered elsewhere, but I searched for it and could not find it.*

*Thanks*

My response was:

Casey,

Ok. It confused me at first too. Let me try to put it simply

ADJP48 is player total raw win production per 48 minutes but for wins we only care about marginal win production thus we have WP48 to measure this.

WP48 is equal to : Player raw win production per 48 minutes – Average Player raw win production per 48 minutes @ same position + Expected Win production of average player per 48 minutes

Expected Win production of average player per 48 = 41 wins / (5 players on court)/ (a little more than 82,think Overtime)

Casey Hopkins then asked:

*Arturo,*

*Wow, thanks for the quick response.*

*I still have some confusion, I will try to explain it a little better.*

*In the Bob Lanier example, there is a table that gives Average Player raw win production per 48 minutes @ each position. The values are C/PF = 0.420, SF = 0.286, G = 0.196. In the text associated with this table , the Average Player raw win production per 48 minutes @ all positions is given at 0.304.*

*In a different calculation later, Expected Win production of average player per 48 is calculated at 0.099.*

*Here is my question:*

*In theory, should Average Player raw win production per 48 minutes @ all positions be equivalent to Expected Win production of average player per 48 minutes because they are describing the same thing?*

*In theory, it seems to me the answer to this question should be yes.*

*In practice, I realize that we are estimating using two different calculations and that the results will differ. However, the magnitude of the difference (0.304 to 0.099) seems so large that they must not be equivalent and so I believe I do not understand the underlying meaning of the two values.*

*Thanks for your time, I know you are busy.*

I started to write my response but I figured this would be better as a long form post. I know I’ve covered bits and pieces of this before but here goes, my full 100% walkthrough of the Wins Produced calculation.

**Part I: Player Win Production**

Now the first thing Prof. Berri did was build and equation relating Box Score statistics to win production using regression. I’m not going to go through that but the equation for a players raw win production look like this:

**PROD = 3FGM*0.065 + 2FGM*0.032 + FTM*0.018 + FGMS*-0.034 + FTMS*-0.015 + REBO*0.034 + REBD*0.033 + TO*-0.034 + STL*0.034 + FTM(opp.)*-0.018 + BLK*0.018 + AST*0.022**

and taking it to per 48 minutes is dead simple:

**PROD48 = [PROD/Minutes Played]*48**

Now the next part is a bit tricky, basically we work out defense and production of assist and block shots for each team and adjust to bring it back to the average. So if a player plays with Steve Nash on the Suns or Kevin Garnett on the Celtics it gets accounted for. This look like:** **

**Raw Player Win Production per 48 minutes: ADJP48= PROD48 – MATE48 – DEFTM48**

No here I go off script. If I want to project team wins what I do is work out:

**Team Raw Win Production= Sum of ADJP48 for every player times (the Minutes Played by every player divided by 48)**

**Team Projected Wins = ****Team Raw Win Production – Avg Team Raw Win Production for the League +41 wins**

So projected wins for the team work on the assumption that an average team wins 41 games (.500 ball) and it’s marginal wins produced that matter.

For the players what we want to do is compare apples to apple. This is because productivity varies by position. The average productivity of opponents in the calculation is fixed and for 2010 it was something like this:

So we use the Production of the average player at the position as the second term and we assume that a team of average players wins half it’s game.

**Player Raw Win Production= ADJP48 for player times (the Minutes Played by player divided by 48)**

**Player Wins Produced = ****Player Raw Win Production – Avg Player Raw Win Production @ position +(.500)/(a little more than 5, again games got to overtime)**

**Player WP48 = Wins Produced/ (total Minutes played/48)
**

So for an NBA team, much like a fantasy football team, a player’s true value is really a function on their net productivity (i.e how much more they can produce than their opponent).

The .100 (0r .099) term means that if you break even on average you’ll win half your games.

Hope that covered everything.

*Uncategorized*

Man of Steele

12/01/2010

bringin it Old Testament again; I like it !

brgulker

12/01/2010

I had similar confusion at first, and it was caused by the word “average.” When I hear that word, I tend to think “mean,” but “mean” is not what we … mean … when we say “average player.”

I think we can all do a better job of explaining that, and this post is an excellent way of doing so.

dberri

12/01/2010

Now explain the same idea in a book (say we call it “The Wages of Wins”) without any math at all 🙂

arturogalletti

12/01/2010

Dave,

You should totally write that book. I would read it and buy copies for all my friends. 🙂

Casey Hopkins

12/02/2010

Arturo,

Thanks for the post, it has helped. I’ve also read Wage of Wins and it helped as well.

But I’m still stuck and I’m pretty sure it is because I don’t understand ADJP48 and I don’t understand ADJP48 because I don’t understand raw wins.

As I fool around with the numbers, for Boston last season (regular season only), I summed each player’s Raw Wins (Raw Wins = ADJP48 * (minutes/48)) to get a Team Raw Win Production of 139.394. So the sum of the player’s raw win scores exceeds the number of games played? How can that be?

What is a raw win? What information does this number convey about a player?

I suspect I may be missing something so basic that it is assumed everyone understands it.

arturogalletti

12/02/2010

Casey,

You’re almost there. Let me walk you through the end bit. Boston as a team produced 139.394 Raw wins last year. The average team last year produced 129.894 Raw wins. So you would expect Boston to be 139.4-129.9 = 9.5 wins over .500 or 41+9.5 = 50.5 wins.

In essence raw wins tell you exactly how much production the player generated. Wins produced translates that into wins by calculating marginal wins vs a position average baseline and assuming .500 level (or .100 WP48) production at the average. You can set different baselines (search this blog for Wins over replacement player for example).

So Boston was expected to win 50.5 games out of 82 = .616 Winning % which is the same as .616/5 = .123 avg team WP48 or .023*5*82 =9.5 wins over .500. See all the math adds up.

Casey Hopkins

12/03/2010

Eureka!

Thanks,

Casey