# Why NBA Superstar Scoring Performances Are Not Created Equal

November 14, 2013All NBA superstars performances are not created equal. So, how do you compare one amazing record to another? How does Kobe Bryant’s 81-point game compare with LeBron James’ streak of 500 double-digit games?

How do you compare one player who reaches some of the loftiest heights ever seen with a player who day in, day out, goes through the grind in an almost unparalleled way? Which matters more, consistency or peak performance?

And for that matter, how do you measure both? How do you compare peak performance and consistency? In order to do that we have to go beyond the traditional sort of analysis since this judges everything solely by averages.**Explaining Standard Deviations**

Imagine that you go to a hotel and there are two conventions being held there. One is just a standard convention. In the other, former NBA centers and derby jockeys are teaming up for some kind of “Giants and Jockeys Feed the Poor” charity.

The *average *height of both events may be very similar, but if you were to walk in on both, you would easily identify which is which.

The point is, averages are a poor way to judge consistency or extremes. Looking at scoring averages doesn’t tell us much about the singular games.

There is an answer found in statistics though. It’s called a standard deviation.

For those who have no background in statistics, without going into a lot of detail, the basic idea of a standard deviation is very simple. It tells you a range from the mean (average) within which a percentage of all results will fall in. Specifically, about 68 percent of events will fall within one standard deviation, 95 percent within two, and 99 percent within three.

How it’s derived is more complicated, but not really needed for this article. In fact, Excel did that work for me, so, score one for Bill Gates.

The nice thing about standard deviation is that it measures consistency. The more compacted the events are, the smaller the standard deviation will be. So, using the example above, the standard deviation of the normal convention is going to be several inches shorter than the Giants and Jockeys convention.

Additionally, by looking at the events outside of the range of two standard deviations, we can see the 7-footers and the 4-footers in that convention greatly outnumber those in the normal convention. These are what we statisticians call “outliers.”

They use standard deviations in measuring IQ. The average IQ is 100, and the standard deviation is 15. 68 percent of people fall within the range of 85-115, and 95 percent between 70 and 130, or within two standard deviations.

Those who are two deviations outside of the range are identified as either mentally disabled or "genius." Roughly around 2.5 percent of the population is on either end of that spectrum. By measuring these outliers in NBA games, we can identify how players do at their best and worst.

**The Ways and Mean**We can apply this same logic to player game logs, and this is where things get really interesting. Which of the truly great scorers were the most consistent players? Which had the most spectacular outliers? And also of significance, which players from time to time, stank the joint up the most?

I compared six players in particular. They are six of the greatest perimeter scorers in the recent history of the game, Bryant, James, Michael Jordan, Kevin Durant, Carmelo Anthony, Kevin Durant and Allen Iverson.

My goal was to compare the players when they were the player we recognize. When they do political polling they try and find get a represetnative sampling, so they take certain steps to do that, by eliminating things that are going to bias the sample size. So for instance, they're not going to poll the Hamptons, because in no way is that indicative of the population at large.

Similarly, these players had certain events which distort the true picture of their consistency. Therefore, in order to do a truly honest comparison, I eliminated some of the statistical noise

- For Bryant and Iverson, I only counted starts.
- For Jordan, I eliminated the heretical Wizard years.
- For Durant and James, I didn’t count the first season, because they were thrown to the wolves.
- For Anthony, I didn’t count the first two seasons; He took another year to get going.
- With all players, I only included games with at least 20 minutes played.

So, with those qualifiers, here is each player’s average.

Jordan stands well above the rest, but after that there's not that huge of a distinction between the other five. Only 1.9 points separate James and Anthony, compared to the 3.3 points between Jordan and James.**Standard Deviations**So, with that, let’s look at the standard deviation of each player.

There are four things that stand out here.

First, Durant is amazingly consistent. He has by far the lowest standard deviation of the six.

Second, James is the second-most consistent player, even ahead of Jordan, who has the record for consecutive double-digit games with 866, per Ira Winderman of the *South Florida Sun Sentinel*. Can he catch Jordan?

Third, Bryant and Iverson have the biggest swings.

Fourth, you have to ask, "Is Anthony really more consistent than Jordan?"

This is where we need to understand how numbers can get tricky. The higher the average, the higher the standard deviation is going to be. A player who averages 50 points and has a standard deviation of five is going to be less consistent than a player who averages 10 and has a standard deviation of five, because the former will vary his scoring by 10 percent and the latter by 50 percent.

When we look at the standard deviation compared to the average, it looks a little different. Here is the standard deviation by percent of the scoring average.

So, this reveals that Jordan actually is more consistent than Anthony, which we sort of intuitively knew anyway. It also shows that Durant still deserves a ton of praise for being an absolute constant. James still is the second most consistent. However, Jordan cuts the gap considerably when we account for the fact he's a higher overall scorer. **Where They Live**By adding and subtracting each player's standard deviation to his average, we get a good view of what he typically does. Here’s what this looks like on a night-to-night basis. This is where these players “live(d).” It’s the range that 68 percent of their games fall into.

The red bar is the low range. The blue bar is the high range.

Jordan has the highest floor and the highest ceiling. We also start to see the difference between average and consistency here in Bryant. He has the second-highest ceiling, but he also has the second lowest floor.

In fact, with Bryant, Iverson and Anthony, all three have a pretty wide range. Durant, on the other hand, has the second highest floor. So here you have to ask, which matters to you more, a higher ceiling or a higher floor?**The Outliers**Another angle is to look at the outliers, for better or for worse. First, let's look at the ugly. The range shown below is roughly the worst 2.5 percent of each individual’s performances.

It is a remarkable thing that Jordan, as a Bull, never played 20 minutes and failed to score in double digits. Durant has been nearly equal to that task since his sophomore year, with just one game that failed to reach 10, and that by a single point. James has one 8-point game.

Bryant, Iverson and Anthony have had truly bad games, and Anthony has put in an absolutely awful, one-point performance. He has the single worst performance, but his bad-range does extend over the 10-point barrier.

However, Bryant and Iverson have their entire range of awfulness in single-digit territory. When they are at their worst, they are the worst of the worst.

That Jordan and James have such a high floor is why they have such long streaks. In fact, it shouldn't be surprising that Kevin Durant is currently on a lengthy streak of his own, 331.

But you can’t define an athlete by his worst performances. How does each player fare when he is at his best? Here are the peak outliers.

At the worst, Bryant may be the bottom of the group, but at his best he’s at the top—though Jordan has an argument.

Jordan’s ceiling starts at 50 points, which is phenomenal, but the Mamba has the best game on the list and has five 60-point games to Jordan’s four.

James and Durant, who though consistent, don’t hit the same heights as Jordan, Bryant or even Iverson.

***

So which is preferable, consistency or ascendancy? Perhaps the thing to consider here isn’t “which is better?” so much as just to recognize there are different aspects of great players to appreciate.

In some ways, the 81-point game is no different from the 500-game, double-digit streak, because both are about measuring what happens in the outliers more than what happens day to day. Bryant just had a couple of really bad games scattered in with some magnificent ones.

Where players live, inside that standard deviation range, is just as telling as what happens on the fringes of their careers. Whether you’re talking about James’ streak, Durant’s consistency, Bryant’s explosions, or Jordan’s everythingness, there’s something to be admired about each player.

Superstars aren't equal because that all depends on what you're measuring with. There might be less of one aspect, but more of the other.

So I’m going to give you a completely honest, yet total cop-out answer to the question of which matters more. The answer is unequivocally, “Yes.” Whether it’s Bryant going off for 81, LeBron being great every single day, or Durant putting in his standard 28-point game, just enjoy what you’re watching.

*All stats from this article were compiled from game logs obtained from Basketball-Reference. *

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