There are players who score and only score, and there are players who score and make players around them better. There is value in a player who not only scores, but also makes others around him better by distributing and facilitating. How do we separate a great all-around player who has an impact on his whole team from a guy who’s just known for his scoring ability? Introducing the harmonic mean between points and assists.
The harmonic mean between two variables is simply (2*A*B) / (A + B), where A and B are any two variables. In this case, A and B are points and assists. The harmonic mean was first introduced in sports by Bill James, when he developed the Power-Speed number in baseball. In his formula, home runs and stolen bases were the two variables. To do well, you need a lot of both. This makes sense because the numerator in the formula grows at a much faster rate than the denominator.
The same applies in the points-assists harmonic mean (PAHM). In order to have a high PAHM, a player must have a lot of points and a lot of assists. In other words, one would expect point guards to infiltrate the top of this list and for Carmelo Anthony to not fare too well.
After running the results the first time, I noticed that players who had played more games naturally had a higher PAHM because they had more opportunities to get points and assists. In order to avoid this problem, I divided their overall PAHM by games played to get their Per Game PAHM.
2012-13 Per Game PAHM Stats:
A few observations when we look at this table:
- As expected, the list is filled with point guards. In fact, 24 of the top 28 are point guards. This is again no surprise because point guards generally rack up assists and aren’t afraid of taking a shot. Also, the league is filled with stellar point guards today and this table reiterates that notion.
- Chris Paul, like his fictional twin brother Cliff, is in fact great at assisting others as portrayed in the State Farm commercials.
- Rajon Rondo is a bit of a surprise at No. 2. He didn’t play a full season but he made his way to the top of the list because of his high assist total. Just imagine how great he would be if he had a better scoring touch.
- Kobe Bryant is 11th on this list (first among all shooting guards). So next time someone on Twitter or Facebook posts a “Kobe doesn’t pass” meme, you can swiftly respond with this stat. (More on Kobe in a bit.)
- LeBron James is a freak, but we already knew that. He’s not only third overall in Per Game PAHM, but he’s a power forward! The next power forward on the list is Josh Smith and he’s ranked No. 40.
- No surprise but Carmelo Anthony is not on this list. He was actually ranked No. 84 in the stat – no surprise from a guy who was criticized all year for not passing the ball.
PAHM and the Lakers
The Lakers ranked in the middle of the pack as a team in PAHM at No. 15. Four Lakers were in the top 100 in the stat – Kobe, Nash, Pau Gasol, and Steve Blake. Gasol is an interesting name in the list. He was ranked No. 45 overall and third among all power forwards. This fits his description as a finesse big who can distribute. Here are the rest of the Laker rankings:
The main takeaway from this table other than the fact that Kobe is dominating in a stat most people wouldn’t think he could dominate is the limited help the team received from Chris Duhon and Darius Morris. Once again, the 2012-13 story cannot be told without first talking about injuries. Nash and Blake missed almost half the year and were not backed up well by their third and fourth stringers (nor were they expected to be.) Nash was also 5th in the league in 2011-12 in PAHM, but he fell to 21st last year.
But let’s talk about Kobe. He recorded the highest PAHM of his career this season at 9.86 and he has a career PAHM of 8.01, which is excellent for a shooting guard. One may attribute his high PAHM to his 31,617 career points, but the fact that he’s averaged near five assists per game throughout his career definitely has a lot to do with his high PAHM. If you cut Kobe’s assist by 60 percent, it lowers his PAHM to the low 5’s.
This is intriguing because as mentioned before, most people don’t look at Kobe as a distributor, when in fact he’s been fairly good at getting his teammates involved. And when Kobe gets his teammates involved, the Lakers win games.
We’ve seen the numbers regarding Kobe, assists, and Laker wins. This year when Kobe recorded three or fewer assists, the Lakers were 2-17, but were 23-10 when he recorded at least seven assists. A regression run between Kobe’s game-by-game PAHM with Laker wins reiterates this notion. Kobe’s game-by-game PAHM was statistically significant in the regression meaning it was a factor in Laker wins and losses.
In short, PAHM has several good uses:
- It’s a great way to evaluate point guards. The higher a point guard’s PAHM, the more versatile they are in terms of scoring and distributing.
- It’s also interesting to look at players that play other positions pop up at the top of the list because it shows that they are not only good scorers, but solid facilitators.
- It’s a number that separates great players from great scorers. For instance, it says a lot that LeBron has a higher career PAHM (11.08) than Allen Iverson (10.0) even though the former is a power forward and the latter is a point guard.