the silk pajamas effect
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I think that the 2 main factors behind the age distribution in professional sports are:
1. Athleticism declines with age and athleticism is a major contributor to being good at sports. You can see this in the pattern of which players do stick around into their 30s - they are often players who have a role that is less dependent on athleticism (e.g. in the NFL kickers, punters, quarterbacks, and long snappers, in the NBA very tall big men) or star players who were much better than baseline in their prime so they continued to be useful even when they weren't as good as they used to be. (Injuries are a component of this - one way that a person's athleticism can decline is if they get an injury that they never fully recover from; also older people tend to recover more slowly from injuries and playing through a nagging injury is another way of having reduced athleticism.)
2. Option value for young players: Young players can get a chance on a professional franchise when there's uncertainty about how good they are or will become, based on the possibility that they will turn out to be good enough to be useful. Players who are out of the NBA or NFL in 2 years are usually players who were never quite good enough to play at that level, but who got a brief chance to be on a roster (or multiple rosters) based on the hope that they were before it became clear that they weren't good enough.
Even the “poorest” veteran is pushing nine figures.
Source? Athletes are often bad with money for the same reason they're good at the game, so I wouldn't count on this.
was just going off of career earnings that I posted in the table above for active players over 35, yes it's less after taxes and expenses.
Haven’t vetted the underlying data, but I think it’s commonly accepted wisdom that despite earning a lot of money, young professionals athletes also spend a lot (and subsidize their families) such that a bunch of them go broke
Definitely the earnings pile up, but the net worth doesn’t necessarily
“ According to a 2009 Sports Illustrated article, 35% of National Football League (NFL) players are either bankrupt or are under financial stress within two years of retirement and an estimated 60% of National Basketball Association (NBA) players, 78% NFL players and Russell Wiggs,[2] and a large percentage of Major League Baseball (MLB) players (4x that of the average U.S. citizen)[3] go bankrupt within five years after leaving their sport” - from https://en.wikipedia.org/wiki/Personal_finances_of_professional_American_athletes
I think the NBA has tried to counter this by having former pros come in and talk to rookies about financial management - https://www.complex.com/sports/a/adam-caparell/for-nba-rookies-financial-literacy-is-more-than-scared-straight-stories
1(To be clear, I still appreciate the analogy, especially about thinking about how to re-tool as a veteran player)
Silk pajamas sound like the inverse of "In for a penny in for a pound" - when you're already in the overalls doing 5am road work already, 4:30am seems a lot more plausible than it does in silk pajamas.
I can't help but compare your NBA statistics to Formula One - where there are only 20 positions available (unless you're a substitute) - although 15% of drivers are 35 or older (3... exactly three drivers are 35 or older). The average age of a driver in this year's season is 27, last year it was 26. There are two prominent outliers, Fernando Alonso is 43 and was in Formula One before some other current drivers were even born. Lewis Hamilton is 40.
The third oldest driver Nico Hulkenberg is is 37. The next oldest driver is spring chicken Carlos Sainz Jnr at the practically neophyte age of 30.
I am left to assume that the physical injuries of NBA curtail careers much more than they do in F1 where even though drivers may encounter crashes above 24 Gs... they are protected by disintegrating carbon fiber. If a Basketballer tears a ligament, there's no carbon fiber that can save them. If I may be facetious - How many injuries are you experiencing in trading?
Now what's particularly interesting is that Alonso and Hulkenberg both have had "sabbaticals" - Alonso didn't contest the 2002, 2019 and 2020 seasons. In fact at the end of 2018 he had a very highly publicized retirement. Hulkenberg didn't compete in the 2019 season either, he was not meant to compete in the 2020 season but was brought in as a substitute for 3 races, didn't compete at all in 2021, was a substitute for 2 races in 2022, before finally returning full-time in 2023. Compare to recent outlier - Kimi Raikkonen who was 42 years old when he retired from Formula One in 2021, he too had taken a sabbatical over the 2010 and 2011 seasons. These sabbaticals often involved the drivers still engaged in some sort of racing - just not F1 and not always open wheelers: Alonso's most recent sabbatical saw him win the WEC and Lemans 24 hours; and have a attempt at the Dakar Rally. Raikkonen competed in WRC during his sabbatical because, he's from Finland, duh. And in his "retirement" has switched to NASCAR. Hamilton is very unique in that he's managed a 18 year unbroken streak of seasons. Perhaps all these drivers aren't so much in silk pajamas as feeling they might as well spend the whole pound if they they're in for a penny.
These ancient F1 drivers sound like a good contrast to the NBA stats presented: if it was simply wealth/success, shouldn't there be a 'pyjama effect' there too? F1 drivers get paid pretty well too.
Most players don’t survive very long. Over a third don’t make it past two years. The average person lasts five years. The odds of making it to the ten year mark is less than 25%. This curve is starkly contrasted to most modern jobs, with the median teacher career for example lasting over 25 years.
...Once the wealth and fame pile up, the grind feels optional. You can coast on talent for a while, but eventually the league catches up. Athleticism fades, the diet slips, weight creeps in, and injuries become inevitable. The denial of your reduced athleticism prevents you from reinventing your game in the offseason. The superstar ego keeps you from accepting a reduced role or doing dirty work on the bench that secures you a roster spot.
From a statistical perspective, I don't think your NBA survival curve shows this. This looks like a rather constant hazard, consistent with an exponential sort of distribution (steady plunge at every part), whereas a 'pyjama effect', where the wealth from previous seasons makes you ever more likely to quit, would generally look different (flat, then plunging).
So I think it's the other stuff:
Many stars that dominated when I was in college are out of the league at 33 years old. Loss of athleticism and injuries are factors
Accidents, fluctuations in athleticism, and sheer chance in very small n of coaches/scoring/games/etc, all seem like they drive the overall exponential much more than any 'pyjama effect'.
NBA history is full of generational talent that flopped because they never pushed past the first peak.
Or just bad luck, or regression to the mean.
If you’re still suiting up past 35, it’s not about the paycheck. Even the “poorest” veteran is pushing nine figures. Yet they still roll out of silk sheets at 5 am, lift, practice, hop on flights for 82 games, undergo intense recovery protocols, and attend film sessions. For the love of the game.
You would expect a fatter tail at the end, rather than the exponential going to ~0, if that were a major factor, as the heterogeneity reveals itself.
1Accidents, fluctuations in athleticism, and sheer chance in very small n of coaches/scoring/games/etc, all seem like they drive the overall exponential much more than any 'pyjama effect'.
Personally I think careers getting derailed by non-contact accidents, creeping athletic decline, and coach/system variance aren't exogenous to the silk pajama thesis, because those areas are exactly where complacency if it exists manifests.
1, non-contact injuries can be minimized with year round strength and mobility work, recovery tech, dedicated staff, prehab, weight/diet control, etc... Lebron famously spends 2m a year on his body and takes his regimen very seriously and has never suffered a serious injury.
2. athletic decline can be addressed by evolving mechanics of your game to rely more on craft. Vince Carter pivoted from an athletic dunker to a 40% shooter and played until he was 43.
3. Same goes with coach/system, if you don't adjust your game it increases the probability you will get cut.
In my head it's something like this:
Base hazard (pure bad luck) is X%.
hazard given “kept the hunger” is X – δ.
hazard given “cashed out & coasted” is X + δ.
I agree with you that a simple one line survival curve is too coarse to reveal what δ is if it even exists at all. To show it statistically, you would likely need to stratify the data more.
There is a lot of early washouts that cause the first few years to be steep and contract timing isn't uniform which keeps the aggregate survival line exponential is my guess.
Maybe if you show survival careers of only top 5-10 draft picks it could better show us what we wanted?
F1 drivers get paid pretty well too.
Sometimes more than NBA players but what's perhaps more interesting is the source of those earnings: For basketballers at least most of their earnings come from extracurricular activities and retirement often doesn't curtail their ability to make huge earnings. 1969/71/73 World Drivers Champion Jackie Stewart was still doing endorsements for Heineken at least 8 years ago from a TVC where they Forest Gump'd in their beers, despite his retiring way back in 1973. Pro-Golfer Greg Norman has earned many times what he did when he was playing at his peak.
I mentioned outlier Kimi Raikkonen, in 2009 Forbes tied him for #2 of the world's highest earning athletes in the world. Higher than Lebron James and David Beckham (I have recently seen David Bechkam's likeness being used to sell mattresses of all things).
What is important to note is one of the athletes Raikkonen was tied with was a retired Michael Jordan. Not only is an Athlete's earning potential not tied to continuing to compete, but much of their earnings even when at the peak of their careers comes from extracurricular activities like endorsements.
A long career might be lucrative, but sometimes you can outearn in retirement.
Returning to current players: In Forbes' most recent global rankings, the only basketballers who out-earn F1's top earners are Stephen Curry, Lebron James, Kevin Durant, Giannis Antetokounmpo.
Forbes claims Stephen Curry is the second highest paid athlete in the world, and estimate he's pulling in $156 million, $56 of which is "on-field" (on-court?) as they call it. Lewis Hamilton, who is one of the outliers I mentioned, and currently not performing at his peak is, is currently ranked all the way down in tied for 22 with boxer Canelo Alvarez, but both Alvarez Hamilton are earning even more on-field (in the ring and on-track?) than Curry. Hamilton earns $60 million from a lucrative contract with Ferrari. Right below him is Max Verstappen in 24 who earns $78 million on the track from his contract with Red Bull Racing.
There is no cost-cap on pilots salaries in F1 even though, there is a cost-cap on the teams and technical staff. In theory at least[1] - I mean that doesn't stop superstar Technical Director Adrian Newey from earning a reported $40 million a year. Former F1 pilots like David Coulthard and Niki Lauda have, like Greg Norman, had very lucrative and entrepreneurial post-racing careers. Former World Champion, Lauda bucked the trend in that he returned to f1 racing in the mid-1980's to help get the capital to fund his own successful Airline which later merged with Austrian Airlines.
How accurate any of these reported figures are, I don't know
- ^
"There was much talk about cost caps, with the spin doctors of some of the big teams trying to keep the story in the news. Still, it might not be a great idea as I did hear of a ruse that one team has which allows them to get tax breaks from their government for five years of reduced taxation for super skilled foreign workers, which means that the team can offer (and declare) a lower salary than its rivals while the employee gets more money because there is no tax to pay… Sneaky, huh? "- source
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