I see your point --
However, I would say someone betting $10/ game with $1000 bankroll that made say $500 would have a 50%ROI... However, they can withstand the variance much better than someone that is fully invested for $200 betting $10/game. (250% ROI).
The key is to maximize ROI, while making sure you are protected against the inherent variance of gambling.
For example: If someone were to give me $1000 and say -- I want a 200% ROI in one year. It wouldn't matter what I did with it, as long as in one year I gave them back $3000.
This is how I view my system - Over the baseball season I had a 150% ROI. When it started I invested $200, and when it ended I recieved back $500. So my ROI over the season was 150%.
Don't mean to argue -- just trying to explain my POV.
I don't think it's a matter of point of view, I think it's fact that you can't use your bankroll amount to judge profits.
This is the best way I can think of putting it:
If I sat down at a $1/$2 LIMIT holdem table with a $10K roll (which every poker site in the world allows you to do), should I judge my profits based on a percentage of my roll I earn back, or based on how much %value I return on average for every $1/chip/bet/whatever I put into the pot? Clearly the answer is the latter because my roll can be whatever it is I want it to be. Pretend your sports bets are calls or poker bets, and pretend the team your betting against on each of your wagers is your poker opponent's hand. Same deal.
Anything not put into the pot is not at risk, and thus is not considered invested. Only thing at risk is your bets. You calculate profits based on your risked money.
In fact, all your book roll really is is you creating a separate bank account for the purpose of the ease of your book to access your money. If I took paper money out of my savings account and bet cash in Vegas every day, vs. me transferring whatever arbitrary amount I want into Pinny and making the same exact bets that way, you're saying profits should be calculated differently in each scenario. (As a % of my total net worth, vs as a % of how much I decided to give Pinny)
On an aside:
The hedge fund analogy is erroneous because you are still investing in their strategy of NOT putting your money into the market. If he thinks the best way to make money right now is to not put it into the market, then that is part of the investment. If I gave my investment adviser $1000 to invest, and he decided that it's wise to only put 10%/$100 of it into the market right now, it's not the same as saying I gave my adviser only $100 to play with and that all his returns should be based on the number of $100. Had I invested $100 with him, he would have only put $10 into the market.
End point is your roll is never at risk, only what you bet is. Your profits are only based on money you return vs. money you risked to get that return. Not whatever arbitrary amount that's left in your roll is.