## Thursday, May 10, 2012

### Steve Novak vs Tyson Chandler

The 2011-2012 season of the NBA has been one of the most memorable seasons, at least for this former and now renewed fan of the NBA. I stopped following the NBA after Michael Jordan's second retirement from the Chicago Bulls, partly because I didn't connect with any player or team. I'd catch a few games every now and then, but I haven't cared about any player or any team for quite some time... until Linsanity. The rise of Jeremy Lin has been a joy to witness. The impact of it all, especially on the Asian or just the Taiwanese community, will have to wait for another post. Today, we'll focus on a math question.

One thing about watching Jeremy Lin is that I also got to watch many of his teammates on the New York Knicks. Two players who had an impressive statistical season are Steve Novak and Tyson Chandler. One for having a league-leading 3-point field goal percentage and the other for league-leading field goal percentage. They were both very impressive, but who had the more impressive achievement (statistically speaking)?

To answer the question, we can choose to compare them with players from any time or just with players in this season. I've decided to compare them with the latter, it seems more reasonable to compare them to their peers. Rules of the game do change and player abilities also evolve over time.

A little digging and I find an great site for basketball statistics at basketball-reference.com. It took a little time to clean up the data and combine the stats for players who were traded mid-season. One other issue that popped up were outliers, players who had 0% because they attempted low number of shots and missed all of them and players who had a very high percentage because they made most or all of the few shots they had attempted. I decided (arbitrarily) to set the minimum number of attempts to 66 (the number of games in this shortened season) which is equivalent to about 1 shot attempt per game. Doing this eliminated these outliers and left a histogram that is approximately normal.

From the histograms above, Tyson Chandler seems to be further away from the pack than Steve Novak. In Statistics, there's a useful measure of the distance from the mean in terms of standard deviation that is useful here. It's the z-score. It gives us an idea about how typical or how extreme a value is relative to peers. Z-score is given by the quantity of the value (x) minus the mean (mu), divided by the standard deviation (sigma).
\begin{align*} z &= \frac{ x - \mu }{\sigma} \end{align*}
Calculating the z-score for Steve Novak's 3-point field goal percentage, when compared to his peers, we get
\begin{align*} z_{novak} &= \frac{ 0.471631206 - 0.351442150 }{0.051557762}\\ &= 2.33115347 \end{align*}
Calculating the z-score for Tyson Chandler's field goal percentage, when compared to his peers, we get
\begin{align*} z_{chandler} &= \frac{ 0.678873239 - 0.441181706 }{0.060831197}\\ &= 3.9073953 \end{align*}
While both achievements are impressive, Chandler's field goal percentage is almost 4 standard deviations above the mean while Novak's performance is slightly higher than about 2 standard deviations. Chandler wins. It's not even close. One thing to keep in mind, even as we draw this conclusion, is that players who attempt a large number of 3-pointers are typically pretty good at it. Whereas, it's reasonable that even poor shooters will attempt 2-pointers so Tyson's "peers" may have a larger proportion of poor shooters thus lowering the average.

Now, if only I could get my hands on the data for the points scored in the first 5 career starts of a player. :)

PS: Apparently, Tyson Chandler's .679 field goal percentage is second (third?) only to Wilt Chamberlain's .7270 (1972-1973) and .6826 (1966-1967) on the all time list for highest field goal percentage in a single season. Unfortunately, Chandler did not meet the rate minimum requirements to show up on that list. For field goal percentage, the requirement is 300 FG. Chandler had 241 FG.

PPS: Chandler could also have made the true shooting percentage list. Once again, unfortunately, for true shooting percentage, the requirement is 700 PTS. Chandler had 699 (missed it by 1).