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.
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’.
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?
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
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.
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:
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’.
Or just bad luck, or regression to the mean.
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.
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?
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