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Saturday, July 13, 2013

Player Impact Estimate

Story on stat used to evaluate NBA and WNBA players....

PIE In the Sky

Tamika Catchings is the reigning WNBA MVP. She's a versatile forward that can score, rebound and distribute the basketball. LeBron James, the 2012 NBA MVP, can claim the very same.
And in the past, the comparisons between these two superstars would have stopped there.
For the 15-plus years that the WNBA has been in existence, drawing parallels between WNBA and NBA players ended up as an exercise in subjectivity. The styles were different. The rules were different. Maybe above all, thegame clocks were different (the NBA plays for 48 minutes and the W goes for 40). So, when you wanted to measure an NBA player against one in the WNBA (or vice-versa), you had to use some imagination. Until now. has developed a new rating called the Player Impact Estimate, or PIE, that calculates a player’s impact on each individual game they play. Because the formula accounts for a player’s influence relative to each specific game, it eliminates statistical biases created by league, style of play or even era.
And now, thanks to PIE, we can make a definitive link between Catchings and James.

The PIE formula compiles everything a single player does in a game -- points scored, rebounds, blocks, missed free throws etc. -- and weighs that number against the same stats generated by everyone in that same game. For the mathematically-minded, the individual player’s stats are the numerator (top) of this equation and the cumulative stats of everyone in the game are the denominator (bottom). The formula then computes a percent value for each player which gives us, in laymen’s terms, the percentage of positive things attributable to that player in that game. Below is the PIE equation.
PIE charts
Since entering the NBA nine years ago, James, who has taken his Miami Heat team to back-to-back NBA Finals appearances, has arguably been the most dominant player in the NBA, just as Catchings has been in the WNBA. But quantifying individual excellence is something that is not easy to do in a team sport such as basketball. The PIE equation, however, does just that. And utilizing this formula to look at the past 10 seasons in both leagues, Catchings and James appear to be virtual matches in terms of overall effectiveness.
Using the PIE formula, analyzed every individual season from an NBA or WNBA player since 2001-02 and James and Catchings -- big surprise -- clearly rose above the rest of their contemporaries. That said, not only did Catchings and James lead their leagues with eight seasons ranked in the top 100 of PIE overall apiece, but these two perennial All-Stars have accounted for 16 of the top 79 seasons (20.25 percent) in the NBA and WNBA over the past 10 years.
So why PIE?
This statistical measurement is called PIE because the sum of every player in a certain game will add up to 100, thus allowing us to sort these values in a pie chart. See below for two example PIE charts for recent games for both Catchings and LeBron. Also, click on each image to get a full PIE breakdown of those games.
LeBron PIE chartTamika PIE chart

Above you will see PIE charts for James' Game 6 performance in the Eastern Conference Finals against the Boston Celtics on June 7 and Catchings' game against the Atlanta Dream on May 27. Click on the images for a complete PIE breakdown.
In all of her regular season games in the past 10 years, Catchings’ PIE percentage amounted to 16.63%. By comparison, James checked in with a PIE percentage of 16.32%, or only 0.31% points lower than Catchings’.
Once you remove two outlier seasons -- James’ rookie year as an 18-year-old kid directly out of high school and Catchings’ injury-riddled 2008 campaign -- the difference becomes even more miniscule. Discounting those seasons, Catchings’ PIE percentage jumps to 17.1%, whereas James’ improves to an identical 17.1%.
The only difference here is in the decimal points. James’ precise total of 17.11903% is ever so slightly ahead of Catchings’ total of 17.06901% -- a mere 0.05002% difference. To grasp how insignificant that gap is, Catchings’ total would exactly match James’ if she were to have grabbed 20 more defensive rebounds -- for her career. That’s right, Catchings, who has grabbed 2,429 rebounds over her 11-year career, is only 20 rebounds shy from having the exact same mathematical impact on the games she's played in her career as James has for his.
PIE averages
Above is a season-by-season look at the PIE averages for Catchings and James. Once again, if you take out James' rookie year and Catchings' injury-riddled season in 2008, they were never more than 4.1% apart in parallel years.
Another common theme for Catchings and James -- and one that’s not hard to see -- is that when they step on the court, they are often the best player on it. In 689 regular season games, James had the top PIE rating 375 times, or in 54.4% of his appearances. In Catchings’ 322 regular season games, she was the top PIE player 121 times, or 37.6% of the time. While that number may seem to favor James considerably, it is noteworthy to consider that since the WNBA has only 12 teams -- versus 30 in the NBA -- that means that Catchings was more likely to face one of the league’s truly elite players on a nightly basis, thus skewing the amount of times she earned the top PIE rating.
Translation: Catchings and James are good. We all already knew this, but now we’re finding out just how good via the PIE ranking. And what makes PIE so noteworthy and telling for a player’s overall worth is that it correlates significantly to winning. The PIE formula generates a R2 value of .9084 which -- to the rest of us that dreaded the math portion of the SAT -- means that if you help your team generate a higher PIE rating than your opponent, then you are more likely than not going to win the game. In fact, when a team leads a game in PIE, they win 93.7% of their games.
So, with that information in hand, it’s easy to deduce that no players in their respective leagues have helped their teams win more games in the last decade than Catchings and James have respectively. Which is why it is no surprise to see that Catchings has led her team to seven consecutive postseasons and one WNBA Finals, while James has also led his team to seven consecutive playoff appearances (including three NBA Finals) and is now only one win away from his first NBA title.
Catchings and James may be of different genders playing in different leagues, but PIE gives us the methodology to compare their merits. And no matter how you slice it, they are truly elite. While watching their greatness with your own eyes is the real treat, the proof is in the pudding, er the PIE.
All stats are as of June 20, 2012

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