I did a few web searches and as far as I can see the ROI as calculated in my spreadsheet is the way it is widely expressed in the betting world. I cannot comment on how this is calculated in the financial world and as such I will have to take both your words for it. The method of dividing by total capital as opposed to invested amount seems to me to offer little value because imo it then loses its objectivity. My ROI used with standard deviation etc is a superb way to backtest etc etc, I can see little use for a ROI which was composed by dividing by capital as like I mentioned earlier it is effectively a spin on P&l weighted by initial bank size. So your method rewards for the investor getting the stake size correct, whereas my method objectively measures whether the underlying method has an edge.
I have to get back to my bet research and don't want to spend more time writing on this, because I think none of us will ever agree. Will be interesting how the other thread goes.