What are ROI and yield?
ROI (return on investment) and yield are two metrics used to measure the profitability of a player's betting activity. Though closely related, they measure different things and are useful in different contexts.
Yield
Yield is the net profit expressed as a percentage of the total amount wagered. It measures the average profit per unit of money wagered, regardless of the initial bankroll:
y: yield
P: total net profit (total returns minus total amount wagered)
W: total amount wagered
y = P / W
For example, if a player has wagered a total of ¤10,000 across all his bets and his net profit is ¤350:
y = ¤350 / ¤10,000 = .035 = 3.5%
This means that, on average, the player has earned ¤0.035 for every ¤1 wagered. Yield is the empirical counterpart of expected value: while expected value is a theoretical quantity based on probabilities, yield is the observed quantity based on actual results. Over a large number of bets, the yield should converge toward the expected value.
A positive yield indicates profitability. A negative yield indicates losses. The magnitude of the yield indicates the degree of the player's advantage or disadvantage relative to the bookmakers.
Typical yields for profitable players range from 1% to 10%, depending on the markets they operate in, the volume of bets, and the sophistication of their analysis. Even a yield of 2% or 3% is considered a strong result, as it indicates a consistent edge over the bookmaker.
ROI
ROI measures the net profit as a percentage of the initial capital invested (the starting bankroll):
R: ROI
P: total net profit
B₀: initial bankroll
R = P / B₀
For example, if a player starts with a bankroll of ¤1000 and after a period of betting his net profit is ¤350:
R = ¤350 / ¤1000 = .35 = 35%
ROI is more useful for evaluating the overall growth of the player's capital over a given period. However, ROI depends on how much of the bankroll was wagered — a player who bets aggressively (wagering a large fraction of his bankroll on each bet) will have a higher ROI than a conservative player with the same yield, because the total amount wagered relative to the initial bankroll is larger.
Relationship between yield and ROI
The two metrics are connected through the turnover ratio, which is the total amount wagered divided by the initial bankroll:
T: turnover ratio = W / B₀
R = y · T
In the examples above:
T = ¤10,000 / ¤1000 = 10
R = .035 · 10 = .35 = 35%
This relationship shows that ROI can be increased either by improving the yield (finding bets with higher expected value) or by increasing the turnover ratio (placing more bets). However, increasing turnover by placing bets with low or negative expected value will decrease the yield and can turn the ROI negative.
Sample size and significance
Both yield and ROI are meaningful only when calculated over a sufficiently large sample of bets. A yield of 20% over 10 bets is statistically insignificant — it could easily result from chance. A yield of 3% over 5000 bets is much more likely to reflect a genuine edge.
The number of bets required to distinguish a genuine positive expected value from random variance depends on the magnitude of the expected value and the standard deviation of the individual bets. The smaller the expected value relative to the standard deviation, the more bets are needed.
As a rough guideline, a player should not draw strong conclusions about his strategy from fewer than several hundred bets, and ideally should evaluate performance over thousands of bets. Until then, the observed yield is a noisy estimate of the true expected value, and it is possible for a profitable strategy to show a negative yield (or vice versa) over short periods.
Tracking performance
Systematic tracking of every bet placed is essential for computing yield and ROI accurately. For each bet, the following data should be recorded:
— The event and option selected
— The decimal odd at which the bet was placed
— The amount wagered
— The result (win or loss)
— The return (amount received if the bet won)
From this data, the player can compute the total amount wagered, the total returns, the net profit, the yield, and the ROI at any point in time. This record also allows the player to analyze his performance by market type, by sport, by odd range, or by any other dimension, to identify where his edge is strongest and where it might be absent.