Yield ROI and Return ROC in sports betting

If I say that I earned 100 euros last week, it is difficult to know if I was really good (and/or lucky).
Fundamental information is missing: how much did I bet to get there: if I bet 40 euros out of my portfolio for this, that's a good profit. On the other hand, if I had to bet 300 euros to win this hundred euros, the result is not amazing...

ROI and ROC are two math tools to measure betting efficiency, and are both concepts that professional sports bettor just as much as casual better should know and use.
The Yield or ROI, for Return On Investment, is the ratio of total profits to total money bet; that is, how much we win (or lose) for each euro waged. ROI is a local mathematical measurement tool, to calculate if a particular investment, or wager, or sport bet, was efficient.
The return ROC, for Return On Capital, is an overall mathematical measurement tool. It is defined as the ratio of the total capital or banrupt at the begining of the period to its value at the end.
These two math tools are detailled below, how to calculate use them.

ROI

The math tool that allows us to measure the efficiency of a transaction (wager, sports bet, or financial more generally) is a ratio between the investment made and the gain perceived in return. The acronym for this yield is ROI : Return On Investment:

ROI = Net profit/Investment

With the two previous examples, calculations yield

100 euros gain a gain back from 40 euros bet, which give the yield ROI = 100/40 = 2,5 = 250%
100 euros gain a gain back from 300 euros bet, which give the yield ROI = 100/300 ≃ 0.33 = 33%

The ROI characterizes the efficiency of the investment and its profit, independently of their respective values, but of their ratios.
For multiple bets and winnings, we adapt the calculation formula by

ROI = Net profit/Cumulative stakes

So, if I bet 10 euros and earned 12 (i.e. 2 euros net), and I also bet 5 euros for which I earned 8 (3 euros net), the yield is ROI = 2+3/10+8 ≃ 0.27 = 27% ROI only measure efficiency of investments, not an overall strategy. If I have a total 100 euros bankroll, and I wager 1 euro and earn 3 euros net profit. Even if the ROI is excellent (300%), my overall strategy is somehow poor and not efficient because I leave unusued almost my bankroll.
The math measurement tool for the overall strategy is given by the ROC return which follows.

ROC

ROI makes it possible to measure the return, or efficiency, of investments or bets.

To evaluate ones overall strategy a global indicator is required: the ROC, or Return On Capital.
We do not count here the stakes, that is to say actual investment, but the entire capital or bankroll, and the formula is then quite similar:

ROC = Net profit/Bankroll

For example, if I have a 200 euros bankroll, and I wager and earn as before: bet 10 euros for a gain of 12 euros and bet 5 euros for a gain of 8 euros, then the ROC is ROC = 2+3/200 = 0.025 = 2.5%

The ROI characterizes the efficiency of my investments or bets, while the ROC characterizes my overall portfolio or bankroll management.
A strong ROI shows good quality as a bettor. A strong ROC shows a good manager.
If I have a bankroll of 200 euros as before, but I only use 10 euros to bet, then even if my bets are effective (high ROI), I am not using my potential optimally and my ROC is low.

Both math indicators, ROI and ROC, are fundamental in a strategy that will be overall winning.

Difference ROI/ROC: the martingale example

To fully understand the difference between ROI and ROC, and their respective interest, we can take the example of a martingale, and for example, with the help of automatic bet calculator for martingale.
With 100 euros in bankroll, when I win my martingale, I have the return on my capital

ROC = 10/100 = 10%

no matter how many bets were necessary..

On the other hand, if I win my martingale on my first bet (or first round), my

ROI = 10/5 = 200%

while if I win it on the 2nd bet,

ROI = 10/12,5 = 80%

etc... and my ROI decreases as I place successive bets in the martingale.

Thus, the appropriate math tool to measure the return on bets is the ROI which has a very limited interest in the long term.
To study and implement a winning long-term strategy, the ROC is the essential measuring tool .

What are considered Good Sports Betting ROI and ROC ?

High ROI is not the really important indicator, beacause of its local property: if you have sometimes high ROI and later high loss, that is not a good overall strategy. What is actually really important is to be winning in the long term run, and that ROC which speaks.
Some percents for the ROC can be considered a good return, see Making a living from sports betting. Professionnals may aim for higher but some percents can accumulate a nice bankroll over time. If a consistent ROC can be settled over time, then each euros earned will also return new profit, and so on. Bankroll increase is thus exponential, see the bankroll simulator.