ROI to ITM Calculation

Hello,

Trying to understand more about sit n' go's. Preemptively, yes, I used the search function and looked through a bunch, but couldn't find anything about this because ROI and ITM returned insane #'s of results.

In the FAQ's post pinned at the top of this forum, there is a table of sustainable ROI's for various stakes of sit n go, and a listed maximum ITM%. The ROI's ranged from 25% for the 5+1's and down to 6% for 200+15's. However, it was stated that the ITM% capped at 4/9ths, regardless of whether you were playing for pennies or thousands of dollars, due to the luck factor involved in poker.

My question is this: if your ITM% is constant accross limits, why does ROI go down?

For a 5+1 player with a 45% ITM%:
profit/tourney = .45(25+15+10/3) - 6 = $1.5 dollar/tourney.

ROI = 7.5$/$6 = 25%.

For a 50+5 player with a 45% ITM%:
profit/tourney = .45(250+150+100/3) - 55=$20 dollar/tourney.

ROI = $75/$55 = 36%.

The ROI actually goes up given a constant ITM, due to the reduced rake. Given a constant rake, the ROI's would be identical.

What am I doing wrong? Understanding that ROI = $payout/$paid for tourneys, and your $payout should be directly proportional to your ITM%, why does ROI go down with increases in stakes instead of up? I must be missing something.

Thanks for replies