Expected Value (EV)
The probability-weighted average outcome per repetition — each result's payoff times its probability, summed. A positive EV means the strategy profits over the long run.
Formula
EV = p × gain − (1 − p) × loss (p = probability of being right, 1 − p = probability of being wrong)
Flip a coin once and you cannot say whether it lands heads or tails, but flip it a few hundred times and you can predict the average result with real confidence. Expected value is exactly that average — what you win or lose per bet, on average, if you could repeat the same wager over and over. In prediction and betting, that average matters far more than any single win or loss.
You compute it by multiplying each outcome's payoff by its probability and adding those up. If p is your chance of being right, EV is p times the gain minus the chance of being wrong times the loss. The key insight is that you do not need to win more than half the time: if your wins are large and your losses small, a low hit rate can still carry a positive EV over the long haul.
This is where a good bet and a good outcome part ways. Winning once does not prove the bet was smart, and losing once does not prove it was foolish — a single result is mostly luck. Whether the judgment was sound only shows up in which way the average tilts once the same situation plays out many times.
So calling a strategy positive EV is a claim, not a fact, until you actually run it many times. Estimating the probability p by gut feel is easy to get wrong, and in a noisy arena like markets it is easier still. In the end, only a large sample of real results can tell you whether the edge was ever really there.
Example
A call that wins 40% of the time, paying +100 when right and −50 when wrong, has EV = 0.4 × 100 − 0.6 × 50 = +10 per bet — you lose 6 of every 10 yet net about +1,000 over 100 repetitions.
How LDBD uses it
On LDBD the starting point for the probability p is base_rate_up, the prior chance that a given asset rises over a given timeframe. Skill Rating's expected term (your chance of being correct) is precisely this expectation, and predictions are scored as skill_delta = K × (actual − expected). The headline metric, rate, is the average directional log return across many predictions, so a positive rate is a positive expected directional return. Bayesian smoothing (K=100) sets a prior of no edge (EV of zero), which pulls rate toward zero when your sample is small. Any single call can miss, but once enough predictions resolve and the 95% confidence interval clears zero (Verified), the data confirms the positive EV was not just luck.
FAQ
How can you make money without winning more than half the time?
You can, as long as your wins are large enough relative to your losses. EV weighs the size of each payoff, not just the odds, so a strategy that wins rarely but big can beat one that wins often but small.
Why do I still lose money when the EV is positive?
EV is a long-run average. Over a handful of tries, variance can hand you a losing streak, and the true expectation only surfaces as the sample grows. That is exactly why LDBD pairs its ranking with confidence intervals and tiers that reflect how many predictions have actually resolved.