FAQs and Position Averages

Posted on December 13, 2007 by


In recent weeks the number of comments has increased dramatically at the WoW Journal.  This is a good thing since it tells us that people are interested in the conversations we are having in this forum.  But I have noticed one downside.  It appears that we frequently have the same questions being raised. And this forces someone – generally Jason Eshleman or Owen Breck (and others)- to answer the same questions over and over again.  

Given that I am an economist, and occasionally like to think like one, I thought it might be more efficient to create a page with Frequently Asked Questions (FAQs).  And for that, I think I need some help.  What I would like people to do is the following:

1. Think of a question you have seen raised repeatedly.

2. Find the answer.  Owen argues that with more than 500 columns posted at the WoW Journal, virtually all questions have had to be answered at one time or another.  So an answer should be out there someplace.

3. In the comments section, report your question and where you found the answer.

My hope is that with the participation of the growing WoW community, this should yield a FAQ page fairly quickly. Then again, you might all tell me that you come here to be entertained (slightly); not to be do my work (a perfectly fair response).

Getting the FAQ Started

To get us started, I thought I would address a question I know was asked in the comment section by someone (not sure who anymore) that I never got around to answering. 

What is the average level of productivity at each position?

In evaluating individual players I often do more than just report Win Score, PAWSmin (Position Adjusted Win Score per minute), Wins Produced, or WP48 [Wins Produced per 48 minutes].  Often I also report what a player does per 48 minutes relative to the average at the player’s position across all the statistics tracked for players.

Sometime ago someone asked if I could post all the position averages in one place. With players at every position now analyzed (I think), averages have been posted separately in one place or another for centers, power forwards, small forwards, shooting guards, and point guards.  But now – in Table One – you can see all these averages at once.

Table One: Position Averages

Hopefully Table One can serve as a handy reference.  Keep in mind that this is based on data from 1993-94 through the 2004-05 season.  Also, you should note that in calculating WP48, the position average for that season is calculated.  So a player’s Wins Produced depends upon what a player did at his position during the season being examined.

Okay, that was easy.  Not sure if people have picked up on this tendency, but virtually every column in this forum goes for more than 1,000 words.  So far I have only written about 500 words, so we have time for another question.

Here is one that was discussed earlier in the week:

If a player shoots less than 50% from the field, is he below average according to the Wages of Wins measures?

When we look at the averages from Table One we learn something about how shooting efficiency impacts player evaluation according to the Wages of Wins metrics.  Before I get to that, let me just briefly note how I calculate shooting efficiency.

Typically when I measure shooting efficiency, I like to use Points-per-shot.  This is calculated as follows:


The measure is taken from an article written by Rob Neyer (yes, the ESPN baseball guy) back in 1996.  For those interested, here is the citation:

Neyer, Rob. 1996. “Who Are the ‘True’ Shooters?” In STATS Pro Basketball Handbook, 1995-96 (pp. 322-323). New York: STATS Publishing.

This statistic is actually just Adjusted Field Goal percentage multiplied by two.  My sense is that Adj. FG% is more widely known, so Table Two reports both PPS and Adj. FG%.

When we look at PPS for an average point guard, we see a mark of 0.948.  This works out to an Adj. FG% of 0.474.  If you look down the column for point guards, you will see that this level of shooting efficiency – along with all the other statistics an average point guard would post per 48 minutes – results in a Win Score per 48 minutes of 6.3. 

We can take this measure and calculate both PAWSmin and an estimate of WP48.  PAWSmin is Wins Score per minute minus the average Win Score per minute at the player’s position.  Because we are looking at the average point guard in Table One, PAWSmin must be zero.

From there we can estimate WP48 with the following formula:

Estimated WP48 = 0.100 + 1.614*PAWSmin

We must remember this is just an estimate of WP48. But as noted previously, there is a 0.99 correlation between PAWSmin and WP48.  So it’s a pretty good estimate.  And given a PAWSmin of zero, our equation produces an estimated WP48 of 0.100.

Now why is this important? An average player will post a WP48 of 0.100.  From all our calculations we see that an average point guard – with an adjusted field goal percentage of 0.474 – will post a 0.100 WP48.

What if our point guard shoots 50% from the floor? Table Two reports that result.

Table Two: Average Performance at Different Levels of Shooting Efficiency

A point guard who converts 50% of his shots has a positive PAWSmin and an estimated WP48 of 0.127.  Looking at the other positions, you will see that the value of a point guard shooting at this rate exceeds the value of any other position shooting at 50%.  This is because point guards, across this time period, had the lowest average Adj. FG%.  So the return to getting to 50% from this position is higher.

What if players are below average in shooting efficiency?  Table Two also reports the production we see from players when they shoot 45% or 40% from the field.  Not surprisingly, if you are average at everything, but below average with respect to shooting, then you are a below average player. 

Okay, let me summarize.  What the Wages of Wins metrics tell us is that average levels of productivity in each area result in an average level of wins production.  Above average performances yield above average wins production.   And finally, below average performances yield below average wins production. All in all, pretty simple.

So there are two entries for the FAQ page.  If you have the time (and after reading all this you may not) feel free to add additional questions and answers in the comments section.

– DJ

Our research on the NBA was summarized HERE.

The Technical Notes at wagesofwins.com provides substantially more information on the published research behind Wins Produced and Win Score

Wins Produced, Win Score, and PAWSmin are also discussed in the following posts:

Simple Models of Player Performance

Wins Produced vs. Win Score

What Wins Produced Says and What It Does Not Say

Introducing PAWSmin — and a Defense of Box Score Statistics

Finally, A Guide to Evaluating Models contains useful hints on how to interpret and evaluate statistical models.