ENSign in

Maths · the arithmetic behind a price

Maths

Closing line value against a no-vig close: a worked example

Raw CLV subtracts your price's implied probability from the closing price's. No-vig CLV first removes the margin from the closing market. Bet -105, close -125 on your side and +105 on the other: raw CLV is +4.34 points and no-vig CLV is +2.03 points. Both are legitimate, and a log has to say which it reports.

The closing line value calculator shows the raw figure and the no-vig figure side by side.

Why the close has a margin in it

A two-way market never prices both sides at their fair probabilities. The implied probabilities add to more than 100%, and the excess is the margin. The closing line is the most accurate estimate of the real chances the market produces, but its raw prices still carry that excess. Subtracting a raw close from a raw bet price mixes two margins together.

The raw calculation

You bet -105. The market closes -125 on your side, +105 on the other -105 implies 51.22%. The close of -125 implies 55.56%. The other side at +105 implies 48.78%. Raw CLV = 55.56 − 51.22 = +4.34 points.

Removing the margin from the close

The two closing probabilities add to 55.56 + 48.78 = 104.34%. Divide each by 104.34% (the method in the de-vigging article): your side is 55.56 ÷ 104.34 = 53.25%, the other 46.75%. No-vig CLV = 53.25 − 51.22 = +2.03 points.

The two figures differ by 2.3 points, which is more than half the raw number. The raw figure includes a margin that no one pays you for. The no-vig figure compares your price with the market's opinion of the true chance, which is the thing closing line value is meant to approximate.

The other way to look at it

The raw measure answers a practical question: how much better is your price than the price you could have taken at the close? If you could only bet the close at -125, the shorter price is what you avoided paying, and the raw gap is real money in that sense. The no-vig measure answers a different one: how far ahead of the market's estimate of the chance did your price put you? Neither is wrong. They suit different purposes, and only mixing them is a mistake.

Keeping a log consistent

  • Pick one method before you start and write it in the log.
  • Always use the same reference for the close: the same operator throughout, or a fixed set of them, and the same time before the event starts.
  • Record both sides' closing prices so the no-vig figure can be worked later.
  • Do not compare your numbers with another record unless its method is stated. Raw figures run higher, and the gap depends on the margin of the market.

Three-way and thin markets

For a three-way market, divide each closing probability by the total of all three, as in the three-way de-vigging article. For thin markets where the close is a few small bets, even the no-vig close can be a poor estimate, and the CLV figure inherits that. The simple proportional method also assumes the margin is spread evenly, which may not match how a particular price is built. It is a standard simplification and not the only one.

It is still only a price comparison Neither version of CLV is profit and neither is proof that a bet was good. The no-vig figure is closer to an estimate of the market's view, and the market can be wrong on any single event. The definition and its limits are in the CLV article.

See both. Enter your price and both closing prices into the closing line value calculator for the raw and the no-vig figure.

Today's free pick (not the main pick)

Today's free pick, for your email

Team, bet, price and the hash it was sealed under, on this page the moment you send. Lose or win, it stays public.

Unlock today's pick in Telegram →Telegram channel: sealed picks and the record, 21+ →

or by email

Public record of the main pick, losses included: 115 won, 44 lost. See every pick

One free pick a day by email until you unsubscribe, in one click. 21+.

More Maths