You bring up a good point that profitable trading doesn't imply a globally better calibrated worldview, just a locally better calibrated one.

In your example:

If someone thinks that if it's raining, the home team will win 100% of the time, then they will bet too much size.

Betting "sensibly relative to their bankroll" is 100% of your bankroll if you truly think the chance of something occurring is 100%.

Revealed belief vs. Preferred belief.

100% + size accordingly ⇒ eventual ruin via ergodicity

100% + size small ⇒ they don’t actually believe 100%; their behavior encodes meta-uncertainty, and optimal sizing assuming long run profitability converges to the true conditional edge after costs.

the path matters just as much as the destination

thanks for letting me know. I've reposted the images.

video games < poker < trading < life in terms of money as a signal, which reflects increasing complexity of each

also, it's not unheard of to to beat live games for 30-100+ bb/100

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?

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.

thank you. cleaned it up.