Chasing 403: How Long Will Steph’s 3-Point Record Stand?

By: Thomas O’Farrell

Reading Time: 7 minutes

In the early 1900’s, baseball was ruled by the small ball era. Players bunted, stole, and sacrificed their way into a few runs every game. This was until 1920, when Babe Ruth hit 29 homeruns, one less than the next three closest combined. One year later, Babe Ruth hit 54 homeruns, shattering his own record by an unfathomable amount. The record seemed untouchable by any other player, but the trend of the league was changing, and teams were quickly adjusting to embrace the longball. When Babe Ruth set his career high of 60, second place was 47 homeruns from his teammate Lou Gehrig. But even though teams were hitting more home runs than ever, Babe Ruth was so far ahead of his competition that it took years for his record to finally fall. It was not until 34 years later that Roger Maris finally unseated him, hitting 61.

Nearly one hundred years after Babe Ruth’s home run revolution, basketball has also begun to embrace the longball. This revolution of three pointers has been led by Steph Curry, who in the 2014-2015 season broke Ray Allen’s record of single season 3 pointers made with 286. In a Ruthian fashion, Curry followed up this performance by demolishing his own record, hitting an implausible 402 three pointers. In his tour de force 2015-2016 campaign, he shot 46% on 11 3’s per game, hitting 286 3 pointers with 24 games to spare. No one in the history of the NBA has come remotely close to 402, and it looks like this record is here to stay for a while. However, in each of the last six seasons, the NBA as a league has broken their record for three pointers made. As the league continues to embrace 3-point shooting, shooters will adjust to shoot more and shoot better. This means it is likely only a matter of time until Steph Curry’s record falls. But how much time?

For the purpose of this study, I am mostly going to be focusing on the top thirty players in three pointers made for each season dating back to when the NBA line was pushed back to its current distance. This includes all season from 97-98 to 17-18, excluding the lockout seasons of 98-99 and 2011-12. I assumed that it would be more useful to look at the trends of the top shooters in each season rather than the league as the whole. Additionally,because we are looking for a player to exceed Steph Curry’s production, I have excluded him from all of these statistics.

For both the top 30 shooters each season, and the league as a whole, 3-point percentage has remained remarkably consistent. The improvements in accuracy have been offset by the increase in volume, such that there is no discernible improvement over the years. The charts below show how 3-point percentages have changed over the years.

Screen Shot 2018-10-28 at 5.25.55 PMScreen Shot 2018-10-28 at 5.54.09 PM.png

Linear regressions of the two sets yield R^2 of less than 0.1, and both contain variable coefficients of 0.0003. This implies an increase in 3-pointpercentage of 0.03% per year, a statistically insignificant amount. If players were shooting more 3’s, and making them more accurately, then we would almost definitely have an exponential increase in 3 pointers made by players.

 

The chart below displays box plots of the top 30 players in 3 pointers made for each season.

Screen Shot 2018-10-28 at 5.25.44 PM

As we can see from the chart, there has been a noticeable increase in the average number of 3 pointers made per season amongst the top shooters. This graph is best modeled through a linear regression, which shows an annual increase of about 2.66 to the average top 30 player’s 3 pointers made.

 

Equipped with this tool, we can begin to form an estimate of how long it will take for Steph Curry’s record to be broken. The first part we want to establish is the chance of someone hitting 403 three pointers in today’s era. To do this, I combined the top 30 leaders in three pointers made in each of the last three seasons, and created a frequency distribution based on their 3 pointers made.

Screen Shot 2018-10-28 at 5.25.36 PM

This can be interpreted as:

Probability of making >X three pointers = 49.557e-0.026x

For example, the probability of a player amongst the top 30 shooters in the NBA making 200 3 pointers would equal:

49.557e-0.026*200=0.2733384=27.33384%

Now the real question we want to try to answer is the chances of making 403 3 pointers:

49.557e-0.026*403=0.001394978=0.1394978%

We can then calculate the probability of all 30 players not reaching 403 3 pointers in a season:

(1-0.001394978)30= 95.98%

Therefore, given the current rate of 3 point shooting, it has a 50% chance of falling within the next 17 years. 60 seasons from now, there would be a less than 10% chance Steph Curry’s record would still be standing.

Screen Shot 2018-10-28 at 5.25.29 PM
Graphical representation of Probability=(1-49.557e-0.026*403)30*seasons

However, this is only accounting for the current level of production. To get a more accurate adjustment, we need to adjust for the growing volume of 3 pointers made.

The current formula for the frequency distribution is 49.557e-0.026x. This has an average of about 176.8. We have assumed a an average increase of 2.66 by year. This means the next years formula will be equivalent to 49.557e-0.026*(x-2.66), which means the next year’s average value will be below 179.46.

We can then apply this to create an adjusted graph. This adjusted graph is shown in blue below, juxtaposed with the prior graph presented in green. Once the league’s increasing 3-point volume is factored in, Steph Curry’s record is projected to fall far faster.
Screen Shot 2018-10-28 at 5.25.21 PM

While Babe Ruth’s record held for 34 years, it was lucky to make it that long. Jimmie Foxx and Hank Greenberg had hit 58 home runs in 1932 and 1938, respectively. So clearly other hitters were capable, it just took a while for someone to break through. On a similar note, Steph Curry’s record is not expected to last nearly as long. Adjusting for the NBA’s top shooters’ 3 point improvements, Steph Curry’s record has a 50% chance of falling within the next 11 years. While Steph Curry’s dominance might seem untouchable today, the amount the NBA’s shooting has already improved and will continue to improve shows how fast the times are changing. This research clearly implies that it is not a question of if Curry’s record will fall, but rather when, and by who?

Posted in NBA

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