Written by: Carlo Duffy

According to NBA fans who believe that the sophomore slump exists, players who excel in their first year are likely to decline in performance from their first year to second (or sophomore) year in the league. Perhaps other teams are able to expose a player’s weakness, and as a result, it is hard for that player to adjust. Maybe the pressure to improve can prove daunting, or a rookie’s stats seem so good that they can’t possibly be replicated the next year.

As an Economics & Statistics major, I was skeptical. How could there possibly be an overwhelming pattern of athletes getting worse from their first to second year of experience? Yes, someone could dip in performance, but others could just as well improve. A two-year window seemed too small of a sample size to conclude that a player had “regressed to the mean” (*i.e*., his first year is a fluke, while his worse second year better represents his skill level). I figured that randomness had to be at work.

This led me to wonder whether any evidence existed in support of the sophomore slump among NBA players.

Before beginning my analysis, I first searched for previous attempts to answer my question. One article caught my attention. A few years ago Tim Marcin (@TimMarcin on Twitter), currently a staff writer at *Newsweek*, wrote a piece for the *International Business Times* on the validity of the sophomore slump in the NBA [1]. To measure change in a player’s performance, Marcin used a player’s difference in win shares from years 1 to 2 in the NBA. Basketball Reference formulated win share to quantify a player’s contribution to his team [2]. Marcin created a scatterplot of differences in win shares for players who got at least one vote for a rookie of the year from 1984 to 2013. His visualization showed no pattern of players being worse in their second year . . . and gave a sound no to my question of interest.

But although Marcin gave convincing evidence, with all due respect, I couldn’t ignore his inclusion of NBA rookies who played very few games their second year. Look at Michael Jordan’s career, for instance. As Marcin mentioned, MJ suffered a steep decline in win shares from his first to second year, but in his second year, he played only 18 games. It’s unfair to say that MJ was a victim of the “sophomore slump.” 18 is not enough games to get a true sense of a player’s performance that year.

Thus, to definitively put the nail in the sophomore slump’s coffin once and for all, I made two slight adjustments to Marcin’s analysis.

- I would only look at players who played at least 30 games in each of his first and second years in the NBA [3]. This would control for players whose win shares were not the result of a very few number of games played. I’d ultimately look at 1,909 players.
- I would include every player who met this requirement, rather than only focus on players who received a vote for rookie of the year. To restrict my analysis to high-performing rookies, though, I can instead look at the highest win shares for each rookie class. This eliminates any chance of ignoring players who were actually good but unable to receive a vote for ROY.

Given the vast amount of publicly available data on Basketball Reference, I explored any potential differences in change in win shares. First, I extended Marcin’s analysis to include all NBA rookies spanning from 1951 to 2017 (the season before this recent one). I then looked for any differences in change in win share by (1) a player’s position, (2) the decade when he entered the NBA, and (3) whether he had a top-ten win share among everyone in his rookie class during his rookie year. The third aspect, in particular, would gauge whether exceptional NBA rookies tended to decline in their second season.

*Data Collection*

Basketball Reference provides the players for the rookie classes for all of my seasons of interest [4]. Using R, I wrote a function that scraped this data directly from the web for every season from 1951 to 2017. Then, using the ballr package, for every rookie class, I took Basketball Reference’s player’s statistics from the rookie and sophomore seasons, obtained data only for the rookies, and retained each player’s position and win share for the two seasons [5]. This produced the dataset for my analysis.

*Results *

Here are the changes in win share for all NBA rookies who qualify over time.

**Figure 1: Change in WS vs. rookie-season WS for all NBA rookies who played at least 30 games in their first 2 seasons from 1951 to 2017.**

Like Marcin’s plot of win-share differential, the scatterplot above shows no distinct pattern. The only difference is that I explicitly made my x-axis a player’s win share during his rookie season. If the sophomore slump were real, then I should be able to draw a horizontal line at a negative value for change in WS, and that should capture where the data clusters. Here, that is not the case. In fact, of the 1,909 NBA rookies in this plot, win shares increased for around 65 percent and decreased only for around 31 percent. These percentages are similar to Marcin’s. For his players of interest, roughly 65 percent improved their win shares, whereas roughly 35 percent worsened theirs. As seen by the line of best fit, though, several players with negative changes in win share were influential enough to result in a negative correlation (r = -0.15).

However, if you look at certain segments of the x-axis, there is an interesting change in the nature of this random scatter. Going from the start of the x-axis to a first-season win share of around 4, the variation in the change in WS increases. The shape resembles that of a funnel. Maybe in this range of first-year win shares, players with better first-year contributions to their teams have more volatile second-year contributions. One potential reason is fatigue due to the increased physical exertion for greater roles on teams. From a win share of 4 onwards, though, this funnel shape disappears as there are less points.

I labelled in this plot several well-known NBA players with noticeably high or low changes in win share. Unsurprisingly, as Marcin emphasized in his piece, great players have fallen on both extremes. On the one hand, players that improved their win shares the most include the likes of LeBron James, Rudy Gobert, and Kareem Abdul-Jabbar. On the other hand, players that decreased their win shares the most include Magic Johnson and Tim Duncan. This randomness helps to dismiss the sophomore slump’s premise.

Before getting into the three further ways that I broke down the data, I also created a simplified version of my first plot to see if I missed anything due to the sheer volume of data.

**Figure 2: 95% CIs for change in WS vs. rookie-season WS for all NBA rookies who played at least 30 games in their first 2 seasons from 1951 to 2017.**

To create this simplified scatterplot, I rounded every player’s rookie win share to the nearest integer. Then, for every bin of rounded rookie win shares, I plotted the mean change in win share, and added a 95 percent confidence interval around the mean. The plot does not really change my previous analysis. But interestingly, players with a rounded rookie win share that falls from -1 to 4 tend to improve during their sophomore seasons, since these confidence intervals are clearly above an average change in win share of 0. I can’t say the same for the other rounded rookie win shares because the other confidence intervals do contain 0. Note that points for rounded win shares of 15 and above do not have confidence intervals because each of those bins only has one value; thus, those standard deviations are incalculable. The main takeaway is that since no confidence interval is entirely below an average change in win share of zero, there is no evidence in support of the sophomore slump.

Now let’s look at the three ways that I further analyzed the data. To simplify the visualizations, I replicated the graph of the intervals, not the original scatterplot with non-rounded rookie win shares.

**Figure 3: 95% CIs for change in WS vs. rookie-season WS for all NBA rookies who played at least 30 games in their first 2 seasons from 1951 to 2017.**

For the plot above, which separates the NBA players by position [6], the only confidence intervals that fall completely below the horizontal zero line are those for PGs with a rounded rookie WS of 11, and PFs with a rounded rookie WS of 12. Otherwise, though, no luck here in finding evidence of the sophomore slump. This is essentially what I expected.

**Figure 4: 95% CIs for change in WS vs. rookie-season WS for all NBA rookies who played at least 30 games in their first 2 seasons from 1951-2017.**

Interestingly, looking at NBA players by decade, the only confidence intervals that fall completely below the horizontal zero line are those for 1950s players with a rounded rookie WS of 9, 1970s players with a rounded rookie WS of 9, and 1990s players with rounded rookie WS’s of 6 and 8. Generally, though, there is also no overwhelming evidence of a sophomore slump for any of the groups of NBA players by decade.

Finally, as the last hope for any evidence of the sophomore slump, I looked specifically at NBA rookies with the ten highest win shares for every rookie class.

**Figure 5: 95% CIs for change in WS for NBA rookies with top-ten WS who played at least 30 games in their first 2 seasons from 1951 to 2017.**

Well, if any hope was left, this plot erased it. Every confidence interval here contains a non-negative change in WS. This holds even for the highest-performing rookies.

Overall, basketball fans can put to rest the idea that high-performing NBA rookies tend to decline in their second year. Just because a rookie fails to live up to his first-year performance doesn’t mean that his career is doomed. One’s second year stats are not necessarily a better indicator of skill level than one’s first year stats. Ultimately, the data shows that throughout NBA history, and regardless of one’s position, a player who becomes worse in his second year can still be a star, even a legend.

**Notes/References**

[1] http://www.ibtimes.com/nba-news-data-behind-sophomore-slump-if-it-exists-all-1818298

[2] https://www.basketball-reference.com/about/ws.html

[3] I chose 30 due to the Central Limit Theorem: http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_Probability/BS704_Probability12.html

[4] Here’s an example: https://www.basketball-reference.com/leagues/NBA_2018_rookies.html

[5] Here’s an example of what the ballr package would show for every year: https://www.basketball-reference.com/leagues/NBA_2018_advanced.html

[6] Basketball Reference lists a very small number of players that features a combination of positions (F-C, G-F, etc.). Since so many more players were given one of the five starting positions (PG, SG, SF, PF, C), though, I ignored players listed with combination positions.