Mar 17, 2015; Houston, TX, USA; Houston Rockets guard James Harden (13) reacts after making a basket during the fourth quarter against the Orlando Magic at Toyota Center. The Rockets defeated the Magic 107-94. Mandatory Credit: Troy Taormina-USA TODAY Sports
Freelance Friday is a project that lets us share our platform with the multitude of talented writers and basketball analysts who aren’t part of our regular staff of contributors. As part of that series we’re proud to present this guest post from Jeff Feyerer. Jeff is a school financial administrator during the day, but on the side he fulfills his love of sports through coaching and copious amounts of writing and research. He currently writes at his College Basketball analytics site The Transition Game and dabbles in football as an NFL Draft Scout at Our Lads. Follow him on Twitter at @jfey5.
For those not familiar with my concept of Playing Time Efficiency (an introduction to the metric from earlier in the season can be found here and here), I set out with the idea of establishing a unifying metric to answer the following questions:
- Which players that are given too much/too little playing time given their efficiency numbers?
- Which players hurt or help their teams by playing more or less?
- Which players provide more or less value to their teams based on the amount they are used?
- How do these numbers translate across the entire league?
To answer these questions, I used the following variables:
- Playing Time Percentage – expressed as a percentage of total team minutes available to a player
- Offensive and Defensive Efficiency – figures taken from Basketball-Reference.com based on points produced per player (via Dean Oliver), rather than other efficiency numbers which use points scored/allowed during time on the floor
- Usage % – amount of possessions used by a player on offense whether it be a FGA, FTA or turnover
The initial equation I came up with was:
PTE = PT%*((IOE-TOE) + (TDE-IDE)), where:
PTE = Playing Time Efficiency
PT% = Individual Minutes Played/Team Minutes
IOE = Player’s Individual Offensive Efficiency
TOE = Team Offensive Efficiency
IDE = Player’s Individual Defensive Efficiency
TDE = Team Defensive Efficiency
This first iteration didn’t include usage percentage, but was instead presented along with it. The resulting metric was useful in addressing what I wanted to address within the team about playing time and efficiency, but it still failed to adjust for usage percentage directly. How the efficiency translated to the league and not just the team, was still a question as well.
Over the course of the last few months, I’ve attempted to address the questions that remain and what has resulted is what I believe is ALMOST what I was looking for and something I will believe is valuable to anyone trying to measure overall player value. The following will describe how I got to the final (or at least current) PTE number.
Usage Percentage – Valuing/De-Valuing Based on Offensive Importance
The purpose of presenting usage alongside PTE initially instead of incorporating it into the equation was to hammer home the understanding that high-usage players are valuable, especially if they are efficient, but can be extremely damaging as they continue use possessions if they’re missing shots and turning the ball over. The most valuable thing in basketball will always be a high-efficiency, high-usage player.
For this article, in order to examine the data, I am using individual player statistics as of 3/11/15 for all of those players that played at least 20% of minutes for their teams (from Basketball-Reference). This left me with 309 players available for the analysis. As one would expect by looking at my initial equation, putting simple math to use, and seeing the efficiency data of players across the league, a number of low-usage/high-efficiency players graded out well. In the table below, there are five players that fit into that category.
While Anthony Davis, Jimmy Butler, James Harden and Chris Paul seem to fit my goal of pinpointing the top players in the league based on efficiency, Ed Davis and Gorgui Dieng are huge outliers. Looking at the bottom 10, players like Kirk Hinrich and Kendrick Perkins have performed poorly, but are they really the worst players in the league if they don’t play or aren’t used as much as others? As a Bulls fan, I would say yes, but I’m biased.
Though PTE is an offensive and defensive statistic, adjusting for defensive usage is something that’s more difficult (I’m working on it). Therefore, when trying to involve usage into PTE, I will only be speaking to the offensive part of the equation. The relationship between offensive efficiency and usage has been drilled down and analyzed by numerous people since the advent of advanced analytics in basketball (summarized nicely here by Justin Williard). Do they have a linear relationship? Is it inverse? Here is the data set plotted with usage % on the x-axis and offensive efficiency on the y-axis with the x-axis set at the league average efficiency of 105.4.
With five players in a basketball lineup, an assumption would be that a perfectly balanced lineup would have all five players with a usage percentage of 20% and that the league average would be the same number. In the graph, that point is justified as the data points become more concentrated around the 20% mark. With our goal being to adjust PTE to weigh how much a player is used, I incorporated an adjustment based on a player’s usage above or below the 20% mark.
The adjustment used was not a positive adjustment for those that are used more and a negative adjustment for those that are used less. Instead, the following rules seems to apply based on the adjustment to the equation I made. Players that are high-efficiency/high-usage and low-efficiency/low-usage saw their PTEs go up, while those that are high-efficiency/low-usage and low-efficiency/high-usage saw their PTEs go down. I didn’t want to totally rule out those players that are having obscenely efficient seasons despite low-usage, but instead wanted to adjust to reflect their true role and value. Below are the resulting Top 10/Bottom 10 along with those players that were affected positively and negatively by the adjustment:
Anthony Davis and James Harden jump to the top of the board now while Gorgui Dieng jumps completely out of the picture. As stated before, those players that are aided by this change can be separated into two categories: the high-usage/high-efficiency players (Harden, Davis) and the low-usage, low-efficiency players (Perkins, Hinrich). Also, those hurt by the change can be separated into two categories: the low-usage, high-efficiency players (Korver, Jordan, Chandler) and the high-usage, low-efficiency players (Rose, Bryant).
As a result, I have a metric that measures a player’s value relative to the rest of his team based on his offensive role. With the first three goals at the beginning of my research solves, the one that remains is whether this data can be translated to compare player’s across the league.
League Efficiency Baseline
Bringing forward the new equation with the usage adjustment, we can now incorporate a standard, league efficiency baseline instead of each’s team’s offensive and defensive efficiency. From Basketball-Reference, I was able to get the average NBA team’s efficiency which is 105.4 as of March 11th. The assumption by putting the league average efficiency into the equation as opposed to each team’s numbers is that the result will be good players from good teams and those players that are performing well (relative to their teammates) on bad teams will be bumped out. Sure enough, that’s what happened. Below are the top and bottom 10 along with the biggest changes as a result of the new baseline efficiency.
The players with the largest positive change are all members of teams with the four largest efficiency margins in the league, while the largest negative changes came from those on the bottom four. This was anticipated and desired.
The result is a metric, Playing Time Efficiency, that goes a long way in determining which player is having the best season relative to the rest of the league.