## A Response to "Myth Busting the NBA: Is Deron Williams really a better shooter than Chris Paul? "

### Introduction

First, let me be clear, Amar's article is EXCELLENT. I really think he's captured the heart of this question and explored it in impressive detail--far clearer than I could. But, as I have a little background in econometrics that has laid utterly dormant in law school, I was hoping to indulge myself and weigh in on a few of the metrics from Amar's article. In doing so, I recognize Amar's impressive body of statistical work on this site, and I readily admit this exercise is more than a little like tugging on superman's cape.

### 8>3

The conclusion of Amar's article is that Deron is a better shooter than Paul--Deron scoring 7 points to Paul's 0 points (points determined by Amar's method of scoring). Deron's 7 points were awarded for his significant advantage over Paul in three statistical categories: Threes Made Per Game (+3 pts), Percentage of all FGM that are 3PTM (+3 pts), and Relative Success Rate (+1pt). The four other categories examined were declared ties (0 points awarded). I will comment on the 3 categories awarded to Deron.

Deron clearly won out in this category making 1.158 three pointers per game to Paul's .878 (career).  However, while it's true that great outside shooters make a lot of three point shots, you have to be careful how much weight you place on this.

The number of threes made per game is simply equal to your three point shooting percentage multiplied by the number of three point attempts you make divided by the number of games you play (3PTM/game = (3PT% * 3PTA)/games played). Given that Deron and Paul have roughly the same 3PT% and  "games played" comes out in the wash, the variable that is really controlling here is 3PTA. Instinctively, do we feel that someone is a better shooter because he takes more three point shots? Don't three point attempts depend on anything from a coach's philosophy to player selfishness or even the Magic getting lazy in the fourth quarter of a losing game in SLC?

An Easy Example:

Take LeBron for instance. LeBron James is clearly a worse outside shooter than Deron or Paul. He shot 33.3% from three this past season. But while Deron made a higher percentage of threes last season, 37.1%, LeBron had more Threes Made Per Game--1.697 to Deron's 1.263. Why? Though they both played 76 games, LeBron attempted 387 three point shots to Deron's 259.

An Ugly Example:

Trevor Ariza's move to Houston last year catapulted him to the bottom of the league in FG% (39.4%). His Three point shooting certainly didn't help. Ariza shot 33.4% from three last season. Contrast that with Kyle Korver who shot a record setting 53.6% from downtown. And yet amazingly, Ariza made1.9 Threes Per Game to Korver's 1.1. What? Again, the difference here was in attempts. Ariza averaged 5.7 three point attempts per game while Kyle averaged only 2.1.

At this point you know what's coming next. Deron's advantage in Threes Made Per Game is sneakily due to the number of shots he's taken from beyond the arc. Deron has shot .647 more threes per game than Paul over their respective careers.

Recommendation: Eliminate this category from consideration. (-3 points from Deron)

### Percentage of all field goals made that are three point field goals made

Again, Deron took this category handily. What does this category mean? Simply that if Deron and Paul made pies representing their total field goals made and ate a piece from their pie representing the percentage of field goal makes that were three pointers, Deron would continue to be one of the heavier guards in the league and Paul wouldn't gain an ounce. In other words, three point shots are a much bigger part of Deron's game than Paul's. But does that make him a better shooter? Certainly if Deron was the better shooter it would entice him to take more threes. But that logic doesn't necessarily prove that he is the better shooter. Let's look at  some examples.

An Easy Example:

While in Philadelphia, 54.136% of Kyle Korver's made shots were three pointers. He essentially had free reign to do his thing beyond the arc.  However, since coming to Utah only 42.883% of Kyle's makes are three pointers. Thus it appears that Philadelphia Kyle is 26.2% better at this metric than Utah Kyle. Has Kyle become a worse outside shooter since coming to Utah? I would argue that he hasn't. He set the single season record for three point shooting percentage last season. It just happens that in Utah coach Sloan reins Kyle in a little on the perimeter and has designed a certain curl play that sees Kyle making a lot of easy elbow jumpers. Kyle hasn't gotten worse, he's just in a different system.

An Ugly Example:

BBj is the star of his church ball team called the "Half-Court Hookers." Before the season the team agrees to only take 3 point hook shots from half court for the entire season. After 8 games BBj has 2 FGM and both were three pointers. Thus, even if he's only made 3% of his field goals for the entire season, his "Percentage of all field goals made that are three point field goals made" is a perfect 100%. More than double Kyle Korver's percentage on the Jazz. For the 9th game, BBj invites his 7 foot Grecian friend to play on the team, let's call him "BBs!!". Unaware of the teams commitment to half court hook shots, BBs!! makes baskets from everywhere, gives the Half-Court Hookers their first victory, and scores 63 points! (Making 30 of 40 shots, 3 of those being 3 pointers.) However, his "Percentage of all field goals made that are three point field goals made" is only 10%. This is nowhere near BBj's perfect 100%.

As you can see, team systems, individual style of play, and whether you're the Orlando Magic will have a big impact on this statistic.

Recommendation: Eliminate this category from consideration. (-3 points from Deron)

### Relative Success Rate

Okay, this one is a doozy. The last statistic compares the percentage of FGA that are 3PTA's to the percentage of FGM's that are 3PTM's. Now, the intuition on this is definitely there, it would be great if you shot the same percentage from anywhere on the floor. But if you're like me on my first read of the article you probably spent less than 3 seconds trying to figure out what was going on, saw that Deron won the category, and just thought "sweet" and moved on. On my second read through, however, I took a stab at simplifying Amar's metric. This really helped.

Amar's ideal looks like this.

However, because not everybody reaches the ideal,  we have to allow for something less than the ideal (or more...see Kyle Korver). Below X represents a player's fraction of this ideal.

Now let's simplify the equation.

Now that we can actually see what's going on, it becomes much easier to see the limitations of this metric. Unfortunately, the metric can be skewed in weird ways.

An Easy Example:

Imagine a player, CJ2010, who shoots 45% from beyond the arc and also shoots an incredible 90% overall. (3PT% = 45%, FG% = 90%, both marks well above anything Deron's approached). CJ2010's "Relative Success Rate" = 45% / 90% = 50%, far below Deron's 77.5%. Why? The Relative Success Rate penalizes you for large differences between your 3PT% and your FG%

An Ugly Example:

Now, imagine a player, LakerFanBoy, that is consistently dismal wherever he shoots on the floor. In fact, his miserable 5% from beyond the arc is only rivaled by his unthinkable 5% within the arc (yes, this is also equal to Matt Harpring's lay up FG%, ba-dum-bum- pshhhhhh). Thus his 3PT% = 5% and his FG% = 5%.   LakerFanBoy's Relative Success Rate = 100%, the ideal.

The Ugliest Example:

Last season, Trevor Ariza's 3PT% = 33.4% and his FG% = 39.4%. His Relative Success Rate =  87.4%. (Ariza: plus 2 pts, Deron: 0 pts, Paul: 0 pts, the very soul of basketball: minus "far too many" pts)

Recommendation: Eliminate this category from consideration. (-1 point from Deron)

### Final Tally

Deron, 0. Paul, 0.

### Conclusion

As badly as I want to say that Deron is a better shooter than Paul I can't do it based on these statistics. In the categories that I believe have true statistical value, the guards come out roughly equivalent. Furthermore, if we include FT%--gulp--Paul would take the category under Amar's system and win the entire thing by 1 pt.

With that said, DERON WILLIAMS IS A BETTER SHOOTER THAN CHRIS PAUL. The quality of a shooter cannot be assessed without accounting for some things that are difficult to reduce to numbers. (i.e. team systems, defensive schemes, individual playing styles, etc.) Further, there is no metric to account for the fact that good shooters attract attention from the defense. It could very well be that Deron's career 3PT% of 36.672% would be much higher if defenses treated him like they treat Paul on the perimeter. If Deron didn't have to do this to get a shot off from deep. But whether or not Deron get's more attention beyond the arc can only be argued at this point anecdotally and not empirically. And where do I look for this kind of evidence? The scouts, the experts, those who have made their careers on absorbing this sort of information, whether consciously or subconsciously, and betting the farm on it. If most people think Deron is a better shooter than Paul, that might just mean something.

All comments are the opinion of the commenter and not necessarily that of SLC Dunk or SB Nation.

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