# Catching Kareem

*By Neil Rangwani*

With opening night for the NBA regular season one week away, one storyline that isn’t getting much attention is Kobe Bryant’s pursuit of greatness. Already one of the greatest players of all time, Kobe enters this season with five championships, two Finals MVP Awards, a regular season MVP Award, fifteen All-NBA selections, two scoring championships, and innumerable comparisons to the G.O.A.T. However, one often overlooked career milestone is total points, in which Kobe is fourth, all-time, with 31,700 career points. The all-time leader, of course, is Kareem Abdul-Jabbar, with 38,387 points. With no top-tier teammates this year and in the foreseeable future to share the ball with, Kobe is uniquely positioned to make a run at the points record.

However, this past season certainly did not go according to plan for Kobe, who played in only 6 games as he recovered from injury. Now 35 years old, with 18 NBA seasons under his belt, and still recovering from a series of injuries, popular opinion is that Kobe’s chances of catching Kareem are slim. After reading this article, I decided to analyze Kobe’s chances of catching Kareem.

For reference, here’s a table of some of the top scorers in NBA history:

Although Kobe is pretty far from Kareem, he’s closing in on Michael Jordan, so I added Jordan’s 32,392 points as a benchmark in the analysis. I’ve also included some of the other leading scorers in the NBA: LeBron James, Carmelo Anthony, and Kevin Durant, to see if they have any chance of reaching the upper echelon of NBA scorers.

First, we’ll calculate how many points per game (PPG) each of the active players would need from this point on to reach Kareem and MJ’s numbers. The biggest assumption in this calculation was the number of seasons they’d play. So, I made a table of how many PPG each player would need to catch Kareem, based on number of seasons played.

In this table, red represents a scoring average that’s greater than the player’s current average, yellow represents an average that’s 90% of the player’s current average, and green represents an average that’s less than 90% of their current average. The reasoning behind that is that players tend to score less as they age, which we’ll come to soon.

Taking a closer look at that table, it’s not that far-fetched that LeBron or Durant reach Abdul-Jabbar’s record. If they play 19 or 20 seasons at a high level, they’ll at least come close. However, while plausible, it’s very unlikely that either will play for so long at such a level. It seems even more unlikely that Kobe will reach the record, as he’d need to average 41 PPG to do it playing two more seasons, and it doesn’t seem that his body will hold up longer than that. However, to account for the case where Kobe continues playing past the next two years, I extended the analysis, with the results below:

This graph essentially shows how hard it will be for Kobe to catch Kareem. We see that this is a plot of Min PPG = [(38,387 – 31,700) / 82] / (Seasons – 18). This behaves similarly to the inverse function y = 1/x, so we see that the Minimum PPG decreases quickly at first, and more slowly as the number of seasons increases. To move from the realm of math to basketball, it’s important to keep in mind that the only players to play more than 20 seasons are Kevin Willis and Robert Parish, who each played 21. If Kobe reaches 21 seasons, he’ll need to average 27.18 PPG for 82 games from here on out to catch Kareem, an incredibly unlikely result.

It is almost impossible that Kobe will break Kareem’s record at this point. However, reaching Michael Jordan’s 32,292 points is also a huge achievement, and one that’s much more attainable. Currently only 592 points behind, Kobe can easily reach that target by averaging a little over 7 PPG next season if he plays all 82 games. That milestone also seems to be in reach for LeBron, Melo, and KD, due to the fact that Michael Jordan only played 15 seasons.

This analysis is pretty straightforward, but it ignores the common phenomenon in NBA players I alluded to earlier: decreasing point totals late into a career. To account for that, I looked at the season-by-season point breakdowns for each of the top five scorers in NBA history (excluding Kobe), and calculated their point totals each season as a percentage of their highest-scoring season. I did this on a PPG basis rather than a total basis to factor in injuries and other missed time. This chart essentially shows a peak in scoring 3 or 4 seasons into an NBA career, and a decline in scoring into later seasons.

Then, for each season (from 1 to 20), I took the average of the top four scorers’ PPG each season as a percentage of their respective top-scoring seasons. I called this average the seasonal aging factor, which is represented visually as the bolded black line on the chart. This seasonal aging factor is a proxy for an aging curve for top-tier NBA scorers, and can be interpreted as the percentage of their highest-scoring season (in PPG) that an elite scorer can be expected to reach in any given season.

The seasonal aging factor table is below. I also included the percent of career average that the aging factor represents. An example is that, in the 8^{th} season, we can expect an elite scorer to score 73% of their maximum single-season PPG, which represents 102% of their eventual career average.

We can now apply this aging factor to active players to predict how many points they’ll score each season. However, there are a few assumptions which restrict the players we can consider. First, this assumes that players will age similarly to NBA greats Abdul-Jabbar, Malone, Jordan, and Chamberlain. Thus, we’ll have to consider only the top-tier of NBA scorers, who are able to score in different ways and will be able to play at a high level late into their careers. Next, by the design of the model, we’ll have to consider only players who have already experienced their highest scoring season. Even with these restrictions, I think Kobe, LeBron, Carmelo, and Kevin Durant all fit the bill, so we’ll continue with those players in mind.

Next, I multiplied each player’s highest PPG average for a season by the aging factor for each season (up to season 20) that they haven’t yet played, in order to come up with an expected PPG for each season. Next, I used these expected PPG to predict the number of points each player will accumulate by the time they retire and based on the number of seasons they play.

In this chart, green represents totals that exceed Michael Jordan’s. It seems likely that Kobe, LeBron, and Durant each exceed Jordan’s total, and it seems unlikely that Carmelo Anthony will. However, I don’t think any of these players will come close to Kareem’s record, which stands far above every projection.

In addition to the point estimates, I also projected what I believe are likely ranges for the players to score in. I did this by computing the standard deviation of the age factor of the retired NBA players for each season, and then averaging those to come up with a universal standard deviation (about 13%). I then made low and high estimates of points for each season which assume that the players will hit 1 standard deviation above or below their expected point total for each season. I also compounded the effects, so that the high estimate represents the player overperforming expectations by 1 standard deviation in each preceding season. Here are those ranges:

These ranges reaffirm my belief that Kobe, LeBron, and KD will reach Michael Jordan’s total, and, if you look carefully, the blue box in Durant’s high-end projection shows him crossing Kareem – a very unlikely scenario, but one that’s certainly possible.

Special thanks to basketball-reference.com for the statistics used in this article, and to Nate Silver’s The Signal and the Noise for inspiring an NBA aging curve.