Was Yao Ming’s career unusually short for a Hall of Fame inductee?


A few weeks ago, former Houston Rocket, Yao Ming, was inducted into the Naismith Memorial Basketball Hall of Fame. Yao’s classmates in Springfield included a pair of his more prolific contemporaries, Shaquille O’Neal and Allen Iverson. By comparison, Yao’s NBA career was relatively short-lived. He played only 486 regular season games — the equivalent of less than six complete seasons — and only 28 more in the playoffs.

Still, in that short time, Yao racked up eight All-Star selections — including one in 2011 when he missed 77 games (thank you, Chinese fan voting!) — and, more tellingly, five All-NBA team honors (two as part of the 2nd-Team and three on the 3rd-Team).

So, Yao’s recent induction had me wondering — was his Hall of Fame career unusually short or did it have a historical precedent?

Comparable Hall of Fame careers

More from Nylon Calculus

To identify similarities between the careers of the 129 NBA players inducted in the Hall of Fame, I used an approach similar to what Basketball-Reference does to make similarity scores. For each Hall of Fame player, I sorted the seasons of his career by regular season Win Shares from highest to lowest. Next, I compared the ranked seasons between a pair of players. For my comparisons, I used the sum of squared errors to quantify similarities and differences over entire careers. That is, I found the difference between two players’ best seasons and raised the difference to the second power. Next, I repeated those steps — subtract and square — for the second-best season, then the third-best, etc. Finally, I summed the squared errors across all the seasons of the players’ careers. For each player, in order to find the most comparable career throughout Hall of Fame history, I just looked for the corresponding player with the smallest sum of squared error.

This approach enables us to identify careers of equivalent length, peak, and shape, but it also has some limitations. Here are some important career characteristics that are IGNORED by this method: position played, style of play/skill-set, post-season success, including championships won, non-NBA achievements (e.g., in the ABA, international leagues, NCAA, etc.), and
regular season productivity not reflected by Win Shares.

These limitations notwithstanding, below, you’ll find the closest Hall of Fame comparisons for the careers of Shaq, A.I., and Yao using my simple similarity scores.

Hall of Fame careers most similar to those of Shaq, AI, and Yao

career-comparisons-yao-shaq-iverson-recolored /

For reference in the plot above, I’ve outlined three tiers of regular season productivity based on Win Shares, as follows. MVP-caliber: 16.9+ WS; achieved by 24 MVPs and 23 non-MVPs throughout NBA history. 1st-Team-worthy: 11.4+ WS; achieved by 216 1st-Team NBA selections and 215 players who were not selected for the 1st-Team. All-Star-level: 6.8+ WS; achieved by 1191 All-Stars and 1135 non-All-Stars

In essence, these Win Share levels represent the breakpoints at which the specified career achievement was more likely than not to be bestowed upon the player.

So, as you can see, Yao does indeed have a historical Hall of Fame precedent; one George Harry Yardley III. If you’re not familiar with Ol’ Yardbird, he played in the 1950s for the Fort Wayne Pistons (fantastic logo!) and the Syracuse Nationals. Like Yao, he played seven more-or-less healthy seasons. Yardley posted five All-star-level seasons to Yao’s six and both had one 1st-Team-worthy season. Given the relatively modest salaries of the 1950s NBA, it’s easy to understand why short careers were more common back then, even for great players. For his part, Yardley’s career was especially brief, owing to his debut as a 25 year-old rookie after a college career at Stanford and a few years of service in the U.S. Navy.

While we’re here, Shaq’s closet comp was his TNT co-star, Charles Barkley; whereas the best match for Bubba Chuck was Mr. Clutch, Sam Jones.

Clustering Hall of Fame career types

It’s fun to pair up these most recent Hall of Fame inductees with some of their predecessors, but the similarity scores don’t reveal the big picture. Ideally, it would be nice to see how the full set of Hall of Fame careers cluster into groups, so we could understand where Yao’s career ranks relative to the full Springfield cohort.

To find the most meaningful groupings, I performed hierarchical clustering using the sorted Win Share statistics of the 129 Hall of Fame players (with hclust in R). Here is the resulting dendrogram, which I split into 13 clusters, each shown with a different color below.

dendrogram-with-colors-reorganized /

It’s probably a bit hard to read the players names, but it looks cool right?

Anyways, you can follow the colors from the dendrogram (above) to the table (below) to see some of the most notable players in each of the 13 clusters along with the characteristics of each group (number of players in the group, range of total career regular season Win Shares, range of career length i.e. total career regular season games divided by 82, and the average number of seasons at each Win Share breakpoint defined above).

hof-clusters-in-table-form-w-color-and-order /

As expected from the similarity scores, Yao’s cluster-buddy is George Yardley. However, what the cluster analysis shows us that we couldn’t see from the similarity scores is how Yao and his other nearest neighbors in the light orange group fit into the big Hall of Fame picture. These 17 guys each had a career somewhere between five and ten years long. On average, they achieved only four all-star-level seasons and less than one 1st-Team-worthy season (based on the Win Share breakpoints defined above). Relative to the other Hall of Fame groups, those accomplishments represent pretty modest production.

While the table is informative, It’s also helpful to resolve the 129 careers by the two most relevant components — career length and average Win Shares per season — and display the clusters on a scatter plot.

Hall of Fame career clusters, resolved by career length and average Win Shares per season

hall-of-fame-clusters-scattered /

The bottom lefthand corner of the scatter plot represents Hall of Fame players who had short careers that were comprised of modestly productive seasons. In the plot, careers get longer as your eye moves from left to right and average productivity increases as you scan from bottom to top — so that the upper righthand corner represents players with both long and highly productive careers. The lowliest group (green) are former NBA players who were honored for their subsequent success as coaches and/or front office employees: Pat Riley, John Thompson, Red Holzman, etc.

The next rung up the ladder — the light blue group — includes some of the NBA’s most tragic heroes. There’s Bill Walton, who led Portland to a championship in his third NBA season and won the league MVP Award the following year (despite playing in only 58 games!) before a series of foot injuries robbed him of his full capabilities. There’s Drazen Petrovic, who achieved international success and reached the status of 3rd-Team All-NBA in his sixth season in the league before dying in a car accident on the autobahn the following summer. And there’s Maurice Stokes, who won the Rookie of the Year Award and broke the league’s single-season rebounding record before a hard fall during the final game of his third season left him paralyzed. To some extent, all the members of this group were honored for their unrealized potential as much as for their accomplishments.

Yao is over there in the light orange cluster — located on the plot just a bit higher and further to the right than the ‘Tragic Heroes’ cluster. As mentioned above, each individual in this group had relatively modest NBA success and there’s generally a mitigating circumstance that can help explain why he was inducted into the Hall of Fame. In addition to George Yardley, some other 1950s-era Hall of Fame players in this group also had relatively short careers by modern standards: Arnie Risen (10 yrs starting at age 24), Andy Phillip (10 yrs starting at age 25), Bobby Wanzer (9 yrs starting at age 27), and Bob Davies (7 yrs starting at age 29 yrs).

Likewise, by the time Arvydas Sabonis entered the NBA at age 31, the 7-footer already had a career’s worth of experience in Europe. In this group, there are also some players who had their greatest success in other domestic leagues, including the ABA: Zelmo Beaty, Billy Cunningham, Connie Hawkins, Spencer Haywood, and David Thompson. Similarly, “Pistol” Pete Maravich and Tom Gola were inducted, at least in part, on the basis of their collegiate careers. The group was rounded out by Coach Jerry Sloan and two players who won multiple championships with the Celtics without posting gaudy regular season stats: Frank Ramsey and Jo Jo White.

So, what was Yao’s mitigating circumstance? Well, he had at least three. First of all, he had a successful career in the Chinese Basketball Association before joining the NBA — winning the championship with the Shanghai Sharks during his final year. Second, like Walton, his promising career was cut short by foot injuries. And third and most importantly, Yao was an international icon. As his official Naismith bio makes clear, his cultural stature played an important role in his induction:

"“Yao was a cultural and physical phenomenon with the personality to balance the demands of playing in a foreign land on the biggest stage while bridging the social, economic, and political landscapes of two very different worlds.”"

Yao was the first Asian superstar of the NBA. He introduced the NBA to about a billion new Chinese fans and paved the way for other Asian players to follow him into the League.

There’s a precedent for the inclusion of cultural heroes in the Hall of Fame. For example, Earl Lloyd (2.8 WS per season, light blue cluster), the first African-American to play in an NBA game, was inducted into the Hall of Fame. Likewise, Nathaniel Clifton (2.3 WS per season, light blue cluster), the second-ever African-American NBA player, and Don Barksdale (2.8 WS per season, green cluster), the first African-American to play on the U.S. Olympic basketball team, were both worthy honorees as well.

So, YES, Yao had a pretty short career by Hall of Fame standards, but, NO, he wasn’t alone. Like other players in his cluster, there were larger circumstances — beyond his on-court NBA stats — that justify his inclusion in the Hall of Fame.

So that’s it from me on Yao. But, as long as we have the matchmaker machine cranking, we might as well see how some future Hall of Fame nominees will fit into these Hall of Fame career clusters, too.

Future Hall of Famers

Kevin Garnett announced his retirement last week, joining the likes of his long-time rivals, Tim Duncan and Kobe Bryant. KG’s former running mate, Paul Pierce, just announced his plans to hang up his sneakers next summer, too. All four players are no-brainer Hall of Fame selections.

Despite his continuing struggles with blood clots, Chris Bosh is hoping to return to the NBA someday; but even if he never makes it back, he may already have done enough to earn a Hall of Fame nod, too. Finally, after his own recent retirement, Amar’e Stoudemire’s prospects for a trip to Springfield are somewhat less certain, but we’ll see who his best HOF match is too.

Here are the career pairings from the Hall of Fame cohort for those six modern players (colors correspond to the clusters identified above):

Hall of Fame careers most similar to those of KG, Duncan, Kobe, Pierce, Stoudemire, Bosh

career-comparisons-kg-duncan-kobe-pierce-amare-bosh-recolored /

KG and Kobe will each join the aquamarine group (‘Great for a decade-and-a-half’) along with their career doppelgangers Shaq and Moses Malone, respectively.

The ridiculous consistency of the ageless one, Tim Duncan, will earn him a spot in the pink group (‘The Models of Consistency’) along with his match, John Stockton, Stockton’s constant companion, Karl Malone, and Kareem Abdul-Jabbar.

Next: Hopefully possible 2016-17 win projections

Paul Pierce finds himself in the red cluster (‘Very good for a decade’) along with his career counterpart, Gary Payton. Both the Glove and the Truth had a career peak similar to Iverson — who is located in the adjacent Mustard cluster (‘Run of the Mill Hall of Famers’) — but they each stuck around for a few more years than A.I. Chris Bosh is also in the red cluster along with his career-twin, Wes Unseld. Bosh (106), Unseld (110), and Iverson (99) collected a similar number of career Win Shares over a similar number of years, but Bosh and Unseld had a flatter distribution across the seasons than did Iverson.

Amar’e achieved regular-season success comparable to Tiny Archibald and the rest of the guys in the dark blue cluster (‘Great for a few years’). However, 13 of the 15 players in that cluster also won at least one championship ring, which, of course, is something Stoudemire cannot claim. This resume will likely leave STAT on the cusp of induction — with his status unclear for now.