Expected value

Expected value, or EV, is what a bet is worth on average if the win chance behind it is right. Unitley reports it three ways: the edge, the EV in dollars for your stake, and the EV per dollar staked.

EdgeCopy Anchor Link

The edge is your win chance minus the chance the price implies, in probability points. The implied chance includes the book's margin, so this is the edge over the price you actually bet into.

At 55% on a −110 price, the price implies 52.38%. The edge is 0.55 − 0.5238… = 0.02619047619047621, about 2.6 points.

EV in dollarsCopy Anchor Link

EV in dollars is the win chance times the profit, minus the lose chance times the stake:

EV = probability × stake × (decimal − 1) − (1 − probability) × stake

At 55% on −110 with a $100 stake: 0.55 × $90.91 − 0.45 × $100 = $5.00.

Pushes are not modeled. On a market that can push, take the push chance out of your win chance first.

EV per dollarCopy Anchor Link

EV per dollar is the same figure for a stake of 1: the win chance times the decimal price, minus 1. At 55% on −110 it is 0.55 × 1.909 − 1 = 0.05, or +5%. A value of 0.05 means 5 cents of expected profit for every dollar staked.

Worked exampleCopy Anchor Link

calc_ev takes probability (your win chance, 0 to 1), americanOdds, and an optional stake in dollars that defaults to 100.

curl -X POST https://console.unitley.com/api/v1/tools/calc_ev \
  -H "Authorization: Bearer YOUR_UNITLEY_TOKEN" \
  -H "Content-Type: application/json" \
  -d '{"probability":0.55,"americanOdds":-110}'

{
  "data": {
    "probability": 0.55,
    "americanOdds": -110,
    "decimalOdds": 1.9090909090909092,
    "impliedProbability": 0.5238095238095238,
    "edge": 0.02619047619047621,
    "stake": 100,
    "expectedValue": 5.000000000000021,
    "expectedValuePercent": 0.050000000000000044
  }
}

• impliedProbability is 0.5238095238095238, the break-even rate at −110.
• edge is 0.02619047619047621.
• expectedValue is 5.000000000000021, or $5.00 on $100.
• expectedValuePercent is 0.050000000000000044, or +5% per dollar.

The values are not rounded. Round them for display.

A positive-EV bet still loses oftenCopy Anchor Link

A 55% bet loses 45% of the time. EV is an average over many bets at a chance that may itself be wrong, and any one bet can lose. Positive EV is not a promise of profit, over one bet or over a season.

The EV is only as good as the chance you give it. If the true chance of a −110 bet is 52.4%, not 55%, its EV is about zero. This is why Unitley sizes every stake at a fraction of Kelly with a cap. See Kelly and stake caps.

Where the chance comes fromCopy Anchor Link

Unitley gives EV in two places, and they start from different chances.

expectedValue in get_game_odds is per 1 staked: 0.021 is +2.1%. It is rounded to six decimal places. A positive value means FanDuel's price pays more than the market's fair chance calls for. It says nothing about your own view of the game. No-vig odds explains how the consensus is built. get_player_props gives each prop the same value.

save_recommendation uses your chance, the way calc_ev does. You send americanOdds and modelProbability, and Unitley works out the implied probability, the edge, the EV per dollar and the suggested stake on the server. A stake or edge sent with the card is ignored.

RelatedCopy Anchor Link

• Expected value and edge, the guide on the Unitley site.
• The expected value calculator, to try a bet in the browser.