Averaging CLV across bets: simple mean, stake-weighted and how many bets

To average closing line value across bets, add each bet's CLV in probability points and divide by the number of bets for a simple mean, or weight each by its stake for a stake-weighted mean. Five bets at +2.4, +1.0, -0.5, +3.0 and -1.2 points average +0.94 simple and +1.63 weighted. The average only means something once the sample is large.

The closing line value calculator computes the CLV of each bet; this page covers how to combine them.

Three averages from the same log

The simple mean treats a 10 stake and a 50 stake as equal. The stake-weighted mean says what the money as a whole got, and here the largest stake had the strongest number, which lifts it. The median and the share of bets that beat the close are less sensitive to a single extreme figure.

When to use which

• Simple mean. Answers "how good are my prices per bet?" Use it when your stakes are about the same size.
• Stake-weighted. Answers "how good were the prices my money got?" Use it when stakes vary, and read it with the stake sizes in view. It is also the more easily misled one: one large stake can move it by itself.
• Share beating the close. A count of how many bets had positive CLV. It ignores size and shows consistency.

Using points rather than cents

Average in probability points, not cents, so that bets at different prices share one scale. The reason is in the cents and points article.

How many bets before the average means anything

The standard error of a mean is the standard deviation of the individual figures divided by the square root of the count. The five figures above have a standard deviation of 1.80 points, so the standard error of their mean is 1.80 ÷ √5 = 0.81. The simple mean of +0.94 is about one standard error from zero, which is not distinguishable from nothing.

• If individual CLV figures spread about 2.5 points (an assumed spread; measure your own), 25 bets give a standard error of 0.5 points.
• 100 bets give 0.25 points.
• 400 bets give 0.125 points.

An average more than about two standard errors from zero is the usual rough threshold for "unlikely to be nothing". With a 2.5-point spread and a true average of +0.5 points, that needs about 100 bets. A true average of +0.25 needs about 400. This is the reason a short run of positive CLV is weak evidence, as the measurement article says.

What the average does not include

• The choice of closing price. If you use different reference books for different bets, the mean mixes definitions.
• Bets with no close. Props that never get a closing price, or bets placed after the close, are left out, which can tilt the sample toward markets that are easy to measure.
• Margin. Raw implied probabilities include the margin of the close. The no-vig article shows how the answer changes.

Log it. The closing line value calculator gives each bet's figure, ready to enter in a sheet like the one on the bet tracker page.