The Most Unbreakable NBA Record (Mathematically!)

Quite often debated is which all-time record is actually the most unbreakable NBA record. Commonly cited candidates include Wilt’s 100 point game, Wilt’s 48.5 minutes per game, or Russell’s 11 rings. While these are compelling statistics in the pantheon of all time NBA performance, they feel more like relics of a bygone era. This is because…they are.

To me, these records don’t belong on all time lists because they are representative mostly of a change in the way the game is played. When I talk about the most unbreakable NBA record, I like to think about more traditional stats like career points, rebounds, or assists. It is from this perspective that we try to answer the question of the most unbreakable NBA record.

As always, the approach we take to answering this question will be based on rigorous mathematics and statistics. The question of the most unbreakable NBA record in particular is one that is often studied with ‘gut feelings’ and impassioned, emotional arguments. However, the approach I am taking is statistical and is based on the techniques described in a previous article about curve fitting tails of distributions.

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Which Stats are Considered?

As described above, we want to determine the most unbreakable NBA record from among the list of ‘more traditional’ statistics. In particular, we are going to look at career and playoff totals for traditional counting stats like points, rebounds, assists, etc. We’ll also look at one advanced statistic: value over replacement player (VORP).

The full list of stat categories that we considered when determining the most unbreakable NBA record is:

• Career Points
• Career Rebounds
• Career Assists
• Career Steals
• Career Blocks
• Career Fouls
• Career Field Goals (Total, 2PT, 3PT)
• Career Free Throws
• Playoff Minutes
• Playoff Points
• VORP

The full methodology for rating the unbreakability of a record is contained in a later section. However, we’ll include a short description here for reference.

In each category, we look at the all-time leader versus the next 50 on the all time list. By comparing the record holder’s stats to the stats of the other 49, we can get a feel for how much of an outlier the record is. Bigger outliers mean more unbreakable records.

For example, if numbers 2-50 on the all time list for a stat were only separated by 1000 but the leader was 1000 above #2, that would be a big outlier. However, if the #1 all time stat was only 1% larger than numbers 2-50, that all-time record is likely to be broken soon. This methodology is formalized here.

Lastly, we also look at where current active players are on the list in order to adjudicate whether or not active players are likely to break records. For example, if our method determined that career points was the most unbreakable record, this wouldn’t be a very satisfying result because Lebron is about to break this record. Therefore, that would make the record not among the most unbreakable.

In this way, we combine robust statistical methods with an adjudicating eye to determine the most unbreakable NBA record. The winners are….

The Most Unbreakable NBA Record

Is John Stockton’s career assist mark. Lets look at how Stockton’s stats compare to the other all time top 10 in assists. An unbreakable record can be identified by looking at the all-time records list and seeing a huge difference between #1 and the rest of the top 10.

Stockton has 31% more career assists than the second best mark all time! That means that Jason Kidd – who accrued the second most all time assists – would have needed to play until he was about 46 years old to have caught Stockton. And, he would have had to play those additional 7 years at his career average level.

Similarly, Chris Paul who is widely considered the best true point guard of the current generation, would have to continue playing until 44 (7 more years) at his career average production to catch Stockton.

Giving the title of most unbreakable NBA record to Stockton’s assist mark boils down to two considerations. First, our mathematical model indicates this record is the most unbreakable. There have been about 5000 NBA players to ever play. This means that we would expect the player with the most assists all time to be in the 99.98th percentile of total assists. Our statistical methods suggest Stockton’s mark is closer to the 99.9996th percentile. The league would need to exist for over 3000 years for that percentile to be within the realm of expectation.

Second, by looking at the list of all time leaders and where the current best players fall on the list, we can judge that nobody is really close. Chris Paul is the most traditional point guard in the modern NBA. However, he would need to increase his career production by 40% to catch Stockton. Considering that he is well past his prime, this feels…unlikely.

Moreover, it is much more common for modern point guards to play more like Steph Curry and Kyrie Irving than Chris Paul. Shooting is king. Very rarely is a point guard a true creator like they used to be in the earlier days of the league.

For these two reasons, we’ve declared John Stockton’s all-time career assists mark as the most unbreakable NBA record.

Who else was close?

Some Other Nearly Unbreakable NBA Records

We wanted to include three other honorable mentions in our discussion of the most unbreakable NBA record. Two are suggested very strongly by our metric, a third is suggested very strongly by both the metric and an inspection of the all time leaderboard.

First, I want to discuss the “two suggested strongly by our metric” together. These two records are VORP and playoff points. Both of these stats are led by Lebron James.

One of the most impressive feats of Lebron James’ career is his insane longevity. His peak was high – probably not as high as Jordan’s – but he has stayed at his peak for a very long time. This is why he is about to break Kareem’s all-time scoring record.

His longevity is also why he leads the way in both VORP and playoff points. VORP is ‘value over replacement player’ and is a measure of how many points better than a league-average player somebody is on a roughly per game basis. Typically, somewhere in the 7-10 range is the league best value. Over his career, Lebron has accrued 140+ VORP which is anywhere between 14-20 seasons of near league-best performance. Incredible.

Second place in VORP all time is Michael Jordan with about 115. Lebron’s career value has been about 25-30% more than Jordan’s. If we estimate the percentile of Lebron’s record here, it is roughly the 99.9993rd percentile. Not quite as good as Stockton’s assists, but it is close.

In a similar vein, Lebron’s playoff points record is impressive. To this date, Lebron has 7631 playoff points to Jordan’s second place number of 5987. Lebron’s number is 27% more than Jordan’s number and should be roughly in the 99.9994th percentile.

The picture below shows the all-time list for playoff points. Remember, an unbreakable record can be identified by the leader being significantly above each of the rest of the top 10.

The other record I wanted to include is Wilt Chamberlain’s total rebounds record. This record isn’t notable as much for being an insane outlier. However, when you look at the all-time lists, it becomes clear this one won’t be broken any time soon.

Wilt put up 23924 rebounds; second place is Bill Russell with 21620. Wilt’s number is only 11% more than Russell’s number and is only roughly in the 99.997th percentile (count the 9s relative to the previous records!). This feels reasonably breakable compared to the others we’ve considered.

However, we wanted to include this record because of the lack of modern players on the list. The only modern player in the top 25 is Dwight Howard at 11th. Big men just don’t get nearly as many rebounds as they used to. Even though Wilt’s record is less of a statistical outlier, because the game has changed his record is likely to stand for decades or centuries.

The Most Breakable NBA Record

We also wanted to look at which stat categories are the most due for a new record being set. For this, we’re going to ignore the fact the Lebron is about to break Kareem’s points record. That is, career points is trivially the most breakable NBA record because it will be broken imminently. Which other records are ripe for the breaking?

According to our methodology, points per game is a record that is overdue to be broken. Currently Michael Jordan has the crown, just barely edging out Wilt’s numbers. But look at the shape of the top 10 list compared to those shown previously in this article.

These lines are nearly flat. There is hardly any separation between number 1 and the rest of the top 10. That means that lots of players have gotten close to breaking the record. It is not infeasible that one of these players could have had a slightly better career and taken the crown.

Looking at percentiles, Michael Jordan’s points per game falls in the 99.88th percentile. In a league with 5000 players, we would expect the best mark to be closer to the 99.98th percentile. This is one way we measured that this record is ‘behind where it should be’.

Another way to determine the most breakable record is to look at where the current elites fall. Both Lebron James and Durant are within spitting distance of the record. Moreover, I think certain young players – in particular Luka Doncic – have a chance of getting where they need to be. At the time of writing this article, Luka is averaging 34 points per game which only serves to increase his career mark of 27 ppg. Just 5-8 more years of league-leading scoring from Luka will put him at or above where Jordan is. And he is still getting better.

More on our Methodology

To determine the most unbreakable NBA record, we reduced the problem to two things. First, estimating the percentile of the current record holder. A higher percentile for a given record indicates a harder record to break. Then, with a careful eye, the records were adjudicated to account for the chances that the game has changed so much that a record may remain unbreakable.

The most difficult portion of our work is estimating the percentile of a record. Statistically, the percentile of a data point is not observable. It has to be estimated via parameterization of the probability distribution. We did our estimating of percentiles by fitting curves to the top 50 list in each stat. Doing so lets one estimate the percentile of the leader.

One assumption had to be made in our analysis. Curve fitting requires choosing a family of distributions. For no particular reason except by inspecting the data, we chose to assume that the distribution in each stat roughly follows an exponential distribution. An example of a cumulative distribution curve fit to the data for the career points stat is shown below.

There is reason to suspect that the exponential distribution is not a good model, though. In particular, I would expect the all-time records list to have much heavier tails than an exponential distribution. For example, polynomial decay or a t-distribution might be a more appropriate model. However, this choice only changes the computed percentiles and not the results when deciding ‘the most unbreakable NBA record’.

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