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Maths · the arithmetic behind a price

Maths

CLV in cents or in probability points: converting between the two

Closing line value in cents is the difference between the price you took and the closing price. In probability points, it is the closing implied probability minus your price's implied probability. A 10-cent move is 2.16 points from -110 to -120, but 1.08 points from -200 to -210, so cents are not comparable across prices and points are.

The closing line value calculator gives both measures for any pair of prices.

Cents

In American odds, "cents" counts the difference in the price number. A bet taken at -110 that closes at -120 beat the close by 10 cents: you got the shorter-priced side at a longer number. A bet taken at +150 that closes at +140 beat the close by 10 cents. Across even money the scale has no 100, so +105 to -105 is 10 cents in the way bettors count it, though the arithmetic gap in the numbers is 210. Cents are quick to say and quick to compare on the same market type.

Probability points

Convert each price to implied probability, then subtract. For a negative price, probability = price ÷ (price + 100) with the sign removed. For a positive price, 100 ÷ (price + 100). CLV in points = closing probability − probability at your price. A positive number means the market moved toward your side after you bet.

The same 10 cents is worth different amounts

  • -110 to -120: 52.38% to 54.55%, +2.16 points
  • -200 to -210: 66.67% to 67.74%, +1.08 points
  • +150 to +140: 40.00% to 41.67%, +1.67 points
  • +300 to +290: 25.00% to 25.64%, +0.64 points
  • +105 to -105: 48.78% to 51.22%, +2.44 points

A move of 10 cents near even money represents about twice the probability change of the same move at -200 or +300. Averaging cents across bets at a mix of prices therefore mixes different units. Points use a single scale.

Bet at -110, close at -125 -110 implies 52.38% and -125 implies 55.56%. CLV is 55.56 − 52.38 = +3.17 points, or 15 cents. The same 15 cents from -200 to -215 would be 66.67% to 68.25%, only 1.59 points.

Sign and direction

The sign is where most mistakes happen. If the closing price is shorter (a higher implied probability) than the price you took, you got the better of the move and CLV is positive. For a negative price, shorter means a larger number: -125 is shorter than -110. For a positive price, shorter means a smaller number: +140 is shorter than +150. If you remember to convert to probability first, the sign takes care of itself.

When the line also moves

If the spread or total moved as well as the price, the two numbers are different bets. A bet at -3 and -110 that closes at -3.5 and -110 has a line gain that cents do not capture. The honest way is to compare the same line, using the price the market offered for your number at the close. If the closing market did not offer your exact line, estimate carefully and note that it is an estimate. The half-point article explains why a half point is worth different amounts at different numbers.

What CLV in either unit is

It is a comparison between two prices, as the CLV definition sets out, and the measurement method is in the measurement article. It is not profit, and it does not tell you whether any one bet was a good one.

One bet proves nothing A positive CLV on a single bet is a fact about that price on that day. The number only becomes informative averaged over many bets, and even then it is a measure of a price and not a result. Use the same unit throughout your log.

Convert a pair. Enter your price and the closing price into the closing line value calculator for the cents and the probability points.

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