# Measuring the Value of Replacement Level in the NBA

Posted on 08/13/2010 by

As a sports stat-head,  one of the great joys of summer is when I get my hands on the Football Outsiders Football Almanac. It’s a fantastic analysis of the in and outs of a complex sport. It also affords amateur statisticians like myself  a window into the construction and evolution of a a statistical toolbox and model to  properly understand and analyze a sport.  Every summer, I am amused, inspired and intrigued by reading this tome and this summer is no exception. So as I was reading the almanac my mind went back to a question raised by one of the readers of this blog in a previous Post .

The questions were raised about what the zero point (or basis for comparison should be for WP48)  should be,  by reader BPS. Here’s the full quote (highlights are mine):

The core of the issue is ‘what is the right way to break up the zero point?’

When you add up the production of an average team without re-zeroing, you get 129 wins. But you know that the average team wins 41 games, by definition, so you have to subtract out 88 games to get the proper zero point, team-wise. Similarly, if you don’t re-zero the team WP48, you get 1.573, but by definition you know it’s 0.500, so you have to subtract out the difference.

Now in order to assign value to the different players, we need to, in this case, break down the 1.073 WP48 that is subtracted to re-zero the function between the players.

In the traditional WP48 model, this is broken down as a position adjustment, so that the average player at each position has a WP48 of 0.100; this makes it easiest to understand at a glance, since every player’s score is being compared to the same positional average. It’s not quite the basketball equivalent of value over replacement player, instead being value compared to average player. This basis makes it very easy to see who is under or over performing at their position, which is what you want for analyzing team strengths.

But a key insight is that it doesn’t actually matter how you break up the adjustment between players for the purposes of calculating total wins. Each team is always going to have the same positions, so the sum of the adjustment is always going to be the same, no matter how you break it down. So you’re free to pick any basis you want, as long as the sum is the same you’ll get the same team wins.”

So borrowing on the work done for both Football and Baseball WP48 and Wins Produced represent Value over Average Player (VOAP) and not Value over Replacement Player (VORP). Value assigned by the model is based on the marginal value from the average and this is well and good but this does not account for the scarcity of resources. The average value of a replacement player is not a fixed quantity and this could make a significant impact in how player value is assigned. So the obvious question is can we figure out what the value of a replacement player is by position in the NBA? I sure aim to find out.

Finding the Replacement Level

So now that we have a goal, the first question is how to get this done. Football Outsiders uses the value delivered by the player who make up the bottom 10% of passes or runs. Here i’m going to use a reasonable assumption of player availability based on minutes played. After some trial and error,  I’m going to:

• Sort player by years and minutes played by position.
• Calculate the productivity of the players that account for just over 20% of the minutes played at each position (or just about 10 minutes per game)
• Set that as the replacement level for each position.

I toyed with 10% & 20%  as the percentage of minutes played but 20% (or slightly less than 10 minutes played in a game) . I modeled the projected wins  for both scenarios (See graph below):

So if we use 20% of the minutes played at each position,  a win total for a team composed solely of replacement level players fluctuates between 10 and 20 wins. At 10% , the fluctuation is between 0 and 15 wins. Given that no team in the NBA has won less than 11 games, the results at 20% seem more in line with reality . So we will calculate replacement level for NBA players based on the bottom tier of players based on minutes played at each position up to the point where 20% of all player minutes at the position for the season are accounted for.

Replacement Level by position

The table & graph below illustrates the results for our replacement level by position:

The chart is below:

But these graphs are not very illustrative. Let’s turn them around a bit.

What I did next is work out the win difference by position of an average player vs. a replacement level  player. This is Basketball Wins over replacement by position (well call this WOR).

This one actually made me giddy when I first saw it. Average Center and Point Guards have over time been much more valuable to teams than any of the other positions. Over the last 5 years the difference between an average center and a replacement level one  is 4.3 more wins than the same at shooting guard. The short supply of tall people is really not a surprise however the short supply of ball handlers is.

The next steps are to start talking about WORP for individual players but you’ll have to wait to a future post for that.

Click Here for Part 2 (Where I refine the algorithm and publish a full list of replacement players for 2010)

Ain't I a stinker?

Click Here for Part 2 (Where I refine the algorithm and publish a full list of replacement players for 2010)