Expected Value (EV)

Expected value is the long-run average return per dollar wagered, given a true probability of winning and the payout offered by a book. A bet is profitable in expectation when the price the book is charging implies a probability lower than the true probability of the outcome.

Why it matters

Most casual betting analysis stops at "the underdog is live." That isn't enough. A 56% true probability against +100 odds is a +12% EV bet. The same 56% probability against -200 odds is a negative EV bet — the payout is too small to compensate for the risk. EV resolves the question: not "do I think this side wins?" but "does the price compensate the risk?"

BaseCase's Edge Finder displays an EV column on every detected edge. Rows with EV at or above 3% are tinted green. Rows between 1% and 3% are amber. Rows below 1% render in neutral gray. Free users see the lowest-EV edges as a preview; the highest-EV edges are gated behind Sharp.

The math

For a bet with American odds, convert to decimal payout-per-dollar-risked b:

b = (american / 100)        if american > 0
b = (100 / |american|)      if american < 0

Then expected value per dollar risked is:

EV = p * b - (1 - p)

where p is the true probability of winning. BaseCase reports this as ev_pct (the field name in edge_log).

Worked example. Suppose BaseCase's fair value model assigns a 56% probability to a moneyline. DraftKings is offering -130, which converts to b = 100/130 ≈ 0.769. The book's implied probability at -130 is 130 / (130 + 100) ≈ 56.5% — but that includes the vig. After de-vigging, the book's implied probability might be 53%. The edge is the gap between BaseCase's 56% and the de-vigged 53%, or 3 percentage points. The EV is:

EV = 0.56 * 0.769 - 0.44 = 0.431 - 0.44 = -0.009

Negative. Even though there's a 3% edge, the price isn't generous enough to overcome the cost of being wrong on the other 44%. This is the core lesson: edge and EV are not the same number.

How BaseCase distinguishes edge from EV

The Edge Finder shows two related but distinct columns:

• Edge — the percentage-point gap between BaseCase's de-vigged fair probability and the book's de-vigged implied probability. This is independent of the payout.
• EV — the expected return per dollar risked, factoring in the offered payout.

A 4% edge on a heavy favorite produces a smaller EV than a 4% edge on an underdog, because the underdog's payout is larger. The same fair-value gap translates to different long-run returns depending on price. Both columns appear because both signals matter: edge_pct is the cleanest measure of how mispriced a market is, while ev_pct is the cleanest measure of how attractive the bet is to take.

Caveats

EV is a long-run quantity. A +5% EV bet can lose. A +5% EV bet can lose ten times in a row. EV calculations assume the fair probability is correct; if BaseCase's fair value is biased, EV is biased. Sample sizes matter: in any given session, your realized return will deviate from EV by an amount governed by variance, which is why position sizing — covered in quarter-Kelly bet sizing — is the second half of the discipline.

Edge tells you how mispriced the market is. EV tells you how much money mispricing earns you. Kelly tells you how much to bet on it.

Further reading

• Quarter-Kelly bet sizing — once you have a +EV bet, how much of bankroll to risk
• Why fair value beats consensus — how the p in the EV formula is estimated