ROI, yield and units: how to calculate them from your own bet log

ROI, or yield, is total profit divided by total amount staked. Units profit is total profit divided by the value of one unit. An invented log of ten bets at 20 each, with five wins, four losses and one push, shows +29.41, which is +1.47 units and 14.7% ROI on 200 staked. Ten bets carry far more noise than that figure suggests.

The bet tracker page offers a sheet that computes all three for your own entries.

The three numbers

• Profit. The sum of the profits on settled bets. A win pays stake × (decimal price − 1), a loss costs the stake, a push or void is zero.
• Units. Profit ÷ value of one unit.
• ROI or yield. Profit ÷ total staked, as a percentage.

The denominator is a choice

ROI depends on what counts as staked. With the push included, the total staked is 200 and ROI is 29.41 ÷ 200 = 14.7%. With the push left out, it is 180 and the ROI is 16.3%. Both are used. Voided bets are normally excluded because nothing was ever at risk. Pick one convention, write it at the start of the log and keep it. Comparing your figure with someone else's is only meaningful if theirs is stated.

ROI and units are different things

Units measure how much you won in the size of your usual bet. ROI measures how much you won per amount put at risk. A bettor who stakes 1 unit on every bet has the same units profit and ROI scale, since total staked is the count of bets. A bettor who varies stakes does not, and one big losing stake can leave positive units and a negative ROI or the reverse. When stakes vary, report both and say what a unit is, as in the units to risk or to win article.

How much noise is in a small log

At near even-money prices, the profit on a single bet has a standard deviation of about 1 per unit staked, and longer prices have more. For n bets the standard error of the ROI is therefore about 1 ÷ √n, expressed as a share of the amount staked.

• 10 bets: about 32 points of ROI
• 100 bets: about 10 points
• 1,000 bets: about 3 points

A 14.7% ROI on ten bets sits inside one standard error of zero, and within one of -17%. The win-loss column and ROI both behave like this. The break-even logic for the same reason is in the break-even article, which shows the rate a price needs.

Read the log beside the closing prices

Because the results are so noisy, a log that also keeps the closing price carries a second, faster-moving measure: the average closing line value, covered in the averaging article. Neither is a promise of future results. They answer different questions, one about money won and one about the price taken.

Work out yours. The bet tracker page has a sheet that totals profit, units and ROI as you add rows.