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How EV is Calculated

What it is

EV% tells you, on average, what fraction of your stake you expect to win or lose per bet. A +5% EV bet returns $1.05 for every $1 you stake, on average. Computing it requires three numbers: the fair probability of winning, the price you are getting (as a payout multiplier), and a tiny bit of arithmetic.

When to use it

Every time you size a bet.
Every time you compare two edges.
Every time someone claims an edge without showing the math.

How to read it

The formula

payout_multiplier = decimal_odds = (american_odds / 100) + 1   if american > 0
                  = (100 / abs(american_odds)) + 1            if american < 0

EV%  = (fair_prob * payout_multiplier) - 1
EV$  = stake * EV%

Step by step

Step	What it does
1. Sharp anchor	Get the v4 blended probability from sharp consensus.
2. Book price	Convert the offered American odds to a payout multiplier.
3. Implied prob	Convert offered odds to implied probability for sanity (do not use for EV math directly).
4. Compute EV%	fair_prob × payout_multiplier minus 1.
5. Sanity	If EV% is greater than ~10% on a deep market, double-check the inputs. Real edges are usually 1-6%.

Worked example

Bet: NBA Lakers ML at +120 (DraftKings)

Sharp consensus (v4 blended): Lakers fair probability 48.5% (fair odds ≈ +106).

american_odds = +120
payout_multiplier = 1 + 120/100 = 2.20
fair_prob = 0.485
EV% = 0.485 * 2.20 - 1 = 1.067 - 1 = +0.067 = +6.7%

On a $100 stake:
EV$ = 100 * 0.067 = $6.70 expected profit per bet
Win:  $100 * 1.20 = +$120 profit (probability 48.5%)
Lose: -$100              (probability 51.5%)
Check: 0.485 * 120 + 0.515 * -100 = 58.2 - 51.5 = $6.70 OK

Implied vs fair sanity:

Implied at +120: 100 / 220 = 45.5%
Fair at sharp anchor: 48.5%
Edge: 48.5 - 45.5 = +3.0 percentage points
EV% (alt computation): 0.030 / 0.455 ≈ +6.6%   (matches above, rounding)

Common mistakes

Using book implied prob as fair prob. That is circular: it just gives you 0% EV. Always use the sharp anchor.
Confusing percentage points with percent EV. A 3-point gap in probability is roughly a 6-7% EV at -110/+110, not 3%.
Forgetting the negative odds case. American -110 is not a 1.10 multiplier. Use the formulas above.
Trusting massive EV numbers. Edges over 8-10% on liquid markets are almost always input errors or stale lines.
Sizing without recomputing. Lines move. Recompute EV right before placing, not when you saw it 20 minutes ago.