What Is Closing Line Value (CLV)? The Metric That Measures Skill

By · author of the MIT-licensed teachersbettextbook library ·

Winning does not prove you were right. Getting a better number than the closing price nearly does.

Meet your classmates

Same five. Today we grade the ticket, not the race.

The race is a terrible report card

Joe backs Chalk. Chalk wins. So Joe was right?

No. A coin flip wins half the time, and a bad price still cashes plenty of afternoons. One race says almost nothing about the ticket you bought.

A whole season of them says surprisingly little more. That is a long time to wait to find out whether you know what you are doing.

So grade the ticket instead of the race. There is a number that does that, and it lands the second the race starts.

Brian’s last number is his best one

The price is not fixed. Brian nudges it all afternoon as money lands and news arrives. Every opinion in the room ends up pushing on it.

By the bell it has soaked up everything anybody knew. That last price is the sharpest guess the market will ever make about the race, and it is called the closing line.

One catch. It still has the vig in it, so take that out first. What is left is the fair chance at the close. Grade yourself against the raw price and you are flattering yourself for free.

Two tickets, one race

Evan watches the number all afternoon and takes Chalk at +110 while it is still up there. Joe wanders in at the bell and takes Chalk at −110, because that is what is on the board when he arrives.

Same hamster. Same race. Same result, whatever it turns out to be. The only thing that differs is the price on the ticket.

The charts underneath the two of them are a separate thing: 400 bets Evan made across a season, counted two ways.

Brian’s price on Chalk, all afternoon fair 50.6% Evan buys early: +110 CLV +2.9 pts. Grade A. Joe buys at the bell: −110 CLV −1.8 pts. Grade D. Average Joe Bookie Brian +EV Evan Evan’s money, $1 a bet Evan’s average CLV, in points $0 +$60 0 +6 Chalk wins +$23 +2.9 Chalk wins. Both tickets pay. Evan an A, Joe a D. Pip wins −$8 +2.8 Pip wins. Both tickets lose. Evan an A, Joe a D. Chalk wins +$40 +3.0 Chalk wins. Both tickets pay. Evan an A, Joe a D. Pip wins +$12 +2.9 Pip wins. Both tickets lose. Evan an A, Joe a D. Chalk wins +$13 +2.6 Chalk wins. Both tickets pay. Evan an A, Joe a D. Pip wins −$37 +3.0 Pip wins. Both tickets lose. Evan an A, Joe a D. Graded A all season, and still finished down. That happens. Brian moves his number all afternoon. Then it stops. Evan bought at +110. Joe bought at the bell, at −110. The race pays one of them. The close grades both.
The afternoon along the top is fixed, because the lesson quotes it: Brian closes Chalk at −110 and Pip at −105, which de-vigs to a fair 50.6% on Chalk. Only the winner changes from run to run, and the two grades never do. The charts are a different thing: a real simulation of 400 bets Evan made across a season, one season out of six picked at random, with the opening number modelled as a rough guess and the close as a much better one. Same bets, measured two ways. His money needs about 2,400 bets before it is three standard errors clear of zero. His average CLV gets there in about 16. That gap is the whole reason this site grades prices instead of results.

The race decides who gets paid. The closing line decides who was right.

Evan paid a price implying 47.6%. The fair close says 50.6%. He is 2.9 points to the good, and on the Report Card that is an A.

Joe paid a price implying 52.4%, which is 1.8 points the wrong side of fair. That is a D. He did not misread the race. He took the number exactly as it closed, and those 1.8 points are Brian’s cut.

Zero is where B starts. Anything that beat the fair close grades at least a B, and A+ is kept for betting nothing at all, which is the right answer on most days.

Both of them learn whether they won at the same moment. Only one of them already knew how he had done.

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Advanced material. Nothing above depends on it.

How to measure it honestly

Grade against the de-vigged closing line, not the raw closing price. Leave the vig in the benchmark and you’ll flatter every bet you ever made. Your price’s implied probability below the fair closing probability = positive CLV. The Report Card grades every bet A to F on that one number and shows every step.

Grading one bet, end to end

Worked example: grading a bet

You take side A at +145  ⇒  qimplied=40.8%\text{You take side A at } +145 \;\Rightarrow\; q_{\text{implied}} = 40.8\%
De-vigged fair probability at close: pfairclose=43.0%\text{De-vigged fair probability at close: } p^{\text{close}}_{\text{fair}} = 43.0\%
CLV=43.0%−40.8%=+2.2 pts  ⇒  positive\text{CLV} = 43.0\% - 40.8\% = +2.2\text{ pts} \;\Rightarrow\; \text{positive}
You bought a 43% outcome at a 40.8% price. The close said you underpaid. A beat, however the game landed.

The grading rubric, and why it converges fast

The letter grade is a step function of one number. CLV is the de-vigged fair probability at close minus the implied probability you paid, in probability points (0.010=1 point0.010 = 1\text{ point}):

CLV=pfairclose−qimplied\text{CLV} = p^{\text{close}}_{\text{fair}} - q_{\text{implied}}

The grade scale

grade={Aif CLV≥+0.010(a full point past the close)Bif CLV≥0Cif CLV≥−0.010Dif CLV≥−0.025Fotherwise\text{grade} = \begin{cases} \text{A} & \text{if } \text{CLV} \ge +0.010 \quad(\text{a full point past the close}) \\ \text{B} & \text{if } \text{CLV} \ge 0 \\ \text{C} & \text{if } \text{CLV} \ge -0.010 \\ \text{D} & \text{if } \text{CLV} \ge -0.025 \\ \text{F} & \text{otherwise} \end{cases}
One band per bet, and zero is where B starts: nothing that beat the closing benchmark can grade below a B. A+ is reserved for betting nothing at all, so a logged price tops out at an A. These cutoffs live in GRADE_SCALE and ship with every graded card, so the ladder printed on your report card is read from the same constant this page describes.

GPA is the plain mean: letters to grade points, then average. No weighting by stake, odds, or sport. Every bet counts once, so one big wager can’t drag the average. Watch this number, not your win-loss record.

GPA: the plain mean

A=4,B=3,C=2,D=1,F=0\text{A} = 4,\quad \text{B} = 3,\quad \text{C} = 2,\quad \text{D} = 1,\quad \text{F} = 0
GPA=1n∑igi\text{GPA} = \dfrac{1}{n}\sum_{i} g_i
Grades A, C, B, F  ⇒  4+2+3+04=2.25\text{Grades A, C, B, F} \;\Rightarrow\; \dfrac{4 + 2 + 3 + 0}{4} = 2.25
School-transcript arithmetic: sum grade points over your nn graded bets, divide by nn.

Why so fast? Each bet is a continuous measurement, not a noisy coin flip. Win-loss carries Bernoulli noise of p(1−p)≈0.5\sqrt{p(1-p)} \approx 0.5 per bet near even odds, so the mean of nn results shrinks only as 0.5/n0.5/\sqrt{n}. CLV scatter is a couple of probability points, so at the same nn the standard error is roughly 25 times smaller.

Standard errors: continuous beats binary

SE(win rate)=p(1−p)n≈0.5n\text{SE(win rate)} = \sqrt{\dfrac{p(1-p)}{n}} \approx \dfrac{0.5}{\sqrt{n}}
SE(CLV‾)=σCLVn\text{SE}(\overline{\text{CLV}}) = \dfrac{\sigma_{\text{CLV}}}{\sqrt{n}}
sample-size ratio=p(1−p)σCLV2≈0.250.022=625\text{sample-size ratio} = \dfrac{p(1-p)}{\sigma_{\text{CLV}}^{2}} \approx \dfrac{0.25}{0.02^{2}} = 625
At 2 points of per-bet CLV scatter, win rate needs roughly 625 times as many bets for the same precision. That ratio is the whole argument for grading on CLV.

D and F matter as much as A. A negative mean CLV shows up after dozens of bets, long before any bankroll chart could tell you. The grade is a measurement of the price you took. It predicts no single bet’s result.

Where the evidence comes from

“The close is the sharpest number the market produces” is a testable claim. Finance journals have graded lines as forecasts since the 1980s, and posted lines pass rationality tests.[3] The reading:

  1. Gandar, J. M., Dare, W. H., Brown, C. R. & Zuber, R. A. (1998). “Informed Traders and Price Variations in the Betting Market for Professional Basketball Games.” The Journal of Finance 53(1), 385–401. Open-to-close moves significantly improve the line’s forecast accuracy. That is why the close, not the open, is the benchmark.
  2. Levitt, S. D. (2004). “Why are Gambling Markets Organised so Differently from Financial Markets?” The Economic Journal 114(495), 223–246. Bookmakers price more skillfully than the bettors they face, so beating their considered number takes skill rather than luck.
  3. Gandar, J. M., Zuber, R. A., O’Brien, T. & Russo, B. (1988). “Testing Rationality in the Point Spread Betting Market.” The Journal of Finance 43(4), 995–1008. The classic NFL point-spread efficiency test. Rationality of posted lines can’t be rejected, so the market price is a serious forecast.

Every formula here lives on the Formula Sheet.

Check your understanding

Frequently asked questions

What is closing line value?

The gap between the price you got and the de-vigged closing line. Beat the close and you found value.

Why is CLV better than win rate?

Win rate takes hundreds of bets to mean anything. CLV is measurable on every bet and converges much faster.

How do you calculate closing line value?

Compare your price's implied probability to the de-vigged fair close. Lower than the fair close = positive CLV.

Do sportsbooks limit players for beating the closing line?

Commonly, yes. CLV signals a long-term winner regardless of short-term results.