Sue Ogrocki/Associated Press

What constitutes a good point guard? Is he in the traditional, “pass-first” mold or the new type who also looks to score? And can Passer Rating illuminate anything on the conversation?

What is Passer Rating you ask? In the simplest terms, it should be understood as an estimate of the number of points a player provides for his team through passing.

Passing has always been a difficult thing to measure. The primary method is assists, which are recorded when a player passes the ball to a teammate who then shoots and scores. That is woefully insufficient, but it’s all that’s been available.

Assists are a lot like paper money. There’s a certain kind of commonality to them, but they can be very different. American bills all have identical size, are made from the same paper and have a uniform texture. But hand a blind man a stack of varying denominations, and he won’t know one from the other.

That’s the same sort of issue we've been dealing with in using the traditional box-score number. All assists have been treated the same, and conclusions about passers, primarily point guards, have been derived from them.

What my Bleacher Report colleague, Adam Fromal, and I set out to do, is come up with a way to metaphorically write denominations on assists. Our result was Passer Rating.

His ranking of the best passing point guards was already posted. My purpose here is to discuss how we got Passer Rating and what we can learn from it that we don’t see in assists.

The Inherent Problems with Assists

Assists are not all the same and they don’t count everything. There are six fundamental problems with them:

Assists don’t credit three-pointers differently. They don’t count secondary (hockey) assists either, meaning a second pass results in the basket. They don’t recognize when a player gets fouled on the shot and makes his free throws. Those points were effectively helped by the passer, but not awarded to him. They only factor in successful passes, not bad ones. Assist-to-turnover ratio attempts to resolve that, but it treats all turnovers the same whether they’re from passing, dribbling or offensive fouls. They don’t factor in pace. A team that plays faster gives a passer an inherent advantage. They don’t factor in team dynamics, which influence how an assist was obtained.

The last of those reasons requires more explanation.

Consider a hypothetical scenario where Player A catches the ball, sees a teammate cutting to the basket and lobs it up to him for an easy alley-oop. In another situation, Player B is driving to the hoop, collapses the defense and kicks it out to the three-point line for an open shooter.

Both are assists, but they varied in terms of how the points were generated. In the first play, the scorer set himself up for the bucket by cutting through the lane. However, the passer set up the second opportunity by drawing the shooter's defender away from him.

So, is there a way of determining when the passer isn't just getting the ball to his teammate to score, but actually doing the work to get him open, too? That's the final thing we wanted to address.

How Passer Rating Resolves These Problems

Happily, with the addition of the SportVU tracking data at NBA.com, we can know more than we did before and answer these questions.

We can know how many points are created by assist, including threes. We know how many secondary assists a player has. We can determine how many free throws come from would-be assists. Using data provided at Basketball-Reference on each player profile page, we were able to determine passing turnovers. We also used Basketball-Reference to get the pace for each team. The formula is as follows: Assists divided by assist opportunities and then subtracted by teammate field-goal percentage. Using this, we were able to derive how much a player impacted the field-goal percentage of his comrades.

Once again, that last bit requires a bit more explanation.

Dividing assists by assist opportunities told us the field-goal percentage that a passer’s teammates had when he distributed he ball.

Then, using the on/off data supplied at NBA.com/STATS, we determined the team’s shooting percentages when he was on the court (minus the passer’s shots). The difference in those two gave us “field-goal percentage impact,” which is how much a player raises or lowers his teammates’ field-goal percentage when he passes the ball.

Then we put the whole thing in the magic spreadsheet machine and “Passer Rating” popped out. The full formula is here if you want to see it.

The 95-Percent Test and Trends

When compiling a new metric, there are three things I look for: the “95-percent test,” trends and warts.

The 95-percent test means it looks about 95 percent right. Does it tell me basically, but not exactly, what I expect to see? If the results are too unorthodox, there’s something wrong with the formula or methodology. If there’s nothing new, there’s no point to it.

Below is the Passer Rating for every player who met the minimum qualification of 20 games played and averaged a minimum of four assists. You can mouse over the dots to see the individual data of all 135 qualifying players.

As demonstrated by the chart, we passed the test. The slope shows there’s a consistency with assists, but the spread reveals enough disparity to prove the metric is worthwhile.

The next thing we wanted to see is if there were any trends. After playing with the results, something started to become apparent: The so-called "shooting" point guards seemed to benefit more from Passer Rating.

To get a better visualization, I compared our metric with assists*2 (the conventional value assigned to them) side by side:

John Wall, Ricky Rubio, Ty Lawson and Kendall Marshall are grouped fairly tightly in assists, but Wall has a decisive edge in Passer Rating.

Stephen Curry, Kyle Lowry, Mike Conley, Jeff Teague and Kyrie Irving also seemed to receive better treatment.

They all have a fairly high usage rate in common. Lowry is the lowest at 22.9 percent. Most of them are above 25 percent. That goes against the conventional wisdom that point guards who shoot a lot are hurting their teams.

There's a logical reason this would happen: High-usage players tend to draw more defensive attention and double teams. Those who have good court vision are also likely to find their open teammates on those occasions.

As a result, theoretically, the more a player shoots, the greater the chance he’ll have a positive impact on his teammates' field-goal percentage when he passes.

I tested this theory with the supposition that the greater the ratio of field-goal attempts to assist opportunities a player has, the greater his impact on teammate field-goal percentage should be. The chart below demonstrates how the theory holds.

Original Chart

As indicated by the trendline, as the ratio goes up, so does the impact on team field-goal percentage. While the pattern isn't definitive enough to argue that “scoring point guards” are better than “passing point guards,” it’s enough to discredit the argument that the latter is the way that the position is “supposed” to be played.

For example, Russell Westbrook of the Oklahoma City Thunder is notoriously labeled as an inefficient scorer, but when he passes to a shooter, his teammates have an effective field-goal percentage of 64.5. When either he or whomever he passes to shoots, the Thunder boast a collectively effective field-goal percentage of 55.0, and that's very efficient.

By adjusting for the increase in field-goal percentage off a player's passes, we're able to credit the passer for when he creates shots for his teammates.

Finally, adding average points to the Passer Rating gives us the total impact made by the point guard, and the results feel right:

The chart shows what seems to be a pretty accurate point guard ranking, sans defense. This underscores the strength of Passer Rating.

Nuggets

The next thing I always look for are the nuggets—the fun things that make you go “hmmmm.” Here are some juicy tidbits in no particular order:

Chris Paul is actually underrated as a passer, which I didn't think was possible. He is pretty clearly in a league of his own. His Passer Rating reveals that he crates a league-high 7.2 more points than suggested by his assists, which considering he led the league in that category, is phenomenal.

Eric Bledsoe had the smallest impact among point guards, gaining just two points in Passer Rating. That could be influenced by his Phoenix Suns essentially running two floor generals most of the time. It's also worth considering as he pursues a max contract.

had the smallest impact among point guards, gaining just two points in Passer Rating. That could be influenced by his Phoenix Suns essentially running two floor generals most of the time. It's also worth considering as he pursues a max contract. LeBron James, with a Passer Rating of 17.3, fared the best among non-point guards.

Joakim Noah had the greatest impact on his teammates’ shooting, boosting their field-goal percentage by an otherworldly 9.54 percent.

Marshall, with 8.52 percent led the quarterbacks.

Tony Parker’s team shot 1.27 percent better when he wasn’t passing the ball. We’ll have more on that later.

When Marshall passed the ball, his teammates made 56.4 percent of their shots, best in the league.

Andre Iguodala had the highest effective field-goal percentage off passes: a ridiculous 72.8! It helps when you’re passing to the Splash Brothers, Klay Thompson and Stephen Curry.

Thompson and Stephen Curry. The point guard who affected the best effective field-goal percentage was Russell Westbrook, whose teammates knocked down a cool 64.5 percent.

Two players in the league averaged five assists, made more than half their shots and had their teammates hit better than 50 percent off their passes: LeBron James and Kevin Durant. Those guys are pretty good. In other news, the sun rose today.

By adding together field goals and assists and dividing that by the sum of field-goal attempts and assist opportunities, we can get a kind of “total field-goal percentage.” James led the NBA at 55.3 percent.

And, just for fun, here’s the “NBA All-Passing Team:”

NBA All-Passing Team Player Team Passer Rating Position Chris Paul LA Clippers 28.63 PG Rajon Rondo Celtics 25.90 PG Monta Ellis Mavericks 15.24 SG James Harden Rockets 15.16 SG LeBron James Heat 17.34 SF Gordon Hawyard Jazz 14.33 SF Josh McRoberts Bobcats 11.82 PF Kevin Love Timberwolves 10.89 PF Joakim Noah Bulls 14.38 C Marc Gasol Grizzlies 9.86 C Original Formula

Warts

While we're generally pleased with how things look, two anomalies jump out: The first is that Westbrook is not among the point guards with a heavy impact on his teammates' shooting. He does have a positive impact, but just 3.73 percent. That places him behind 73 players, and he’s obviously better than that. The other is Parker had a negative impact, as we mentioned earlier.

With both players, the problem is a large percentage of their assist opportunities are out to the three-point line, which lowers their overall field-goal percentage impact. It's the same as if a player attempts a large number of threes; the field-goal percentage will seem artificially low. In evaluating shooting, this is compensated for with effective field-goal percentage.

It wasn't until writing this article, though, that we figured out how to derive effective field-goal percentage off passes from the available data. Once we did, it boosted both players' numbers considerably.

David J. Phillip/Associated Press

Parker’s effective field-goal percentage off passes is actually 56.4, an improvement of nearly 10 percent over the conventional field-goal percentage. And Westbrook’s leaps from 53.9 to 64.5, more than 10 percent.

It was too late in the game to overhaul the whole stat this time around, but we intend to make that adjustment going forward. I expect that doing so will only reinforce the trends we’re already seeing, as both Westbrook and Parker are premier scoring point guards.

There are still a couple of other problems that we know about, but the data to resolve the problem still isn't available.

The biggest one is that there is an apples-to-oranges comparison involved. Assist opportunities are always going to be off passes, and we’re comparing those with general field-goal attempts, whether they're off the pass or off the bounce.

The former are more likely to go in, but since we don’t have a way of seeing what the numbers are for missed shots, we have to use what is available to us. Ideally, we’d be consistent, but this is the best we can do for now.

Another aspect that influences the numbers was pointed out by Seth Partnow of Nylon Calculus: Not all assist opportunities are counted the same. An assist, generously given, may not have counted as an assist opportunity if the ensuing shot were missed. However, as there’s no reason to believe that would skew in any person’s favor, it’s a minor factor.

Warts are why this metric, like any, should be viewed as a tool in the tool chest. This is not Dr. Who’s screwdriver, it’s another way of looking at passing. We feel it’s a better way to view passing, but it's still not the perfect way. So, if you see a way to improve it, feel free to make suggestions.

We view this as a work in progress.