Bayesian Smoothing (Shrinkage)
A statistical correction that pulls a thin-track-record score toward 'no edge' (zero), so a lucky streak on a handful of predictions can't masquerade as skill.
Formula
smoothed_mean = sum(x) / (n + K) LDBD: rate = sum(a) / (n + 100) x 100 // K = 100
Put someone who made one lucky call next to someone who has been right consistently across hundreds of predictions, and with no correction the person holding a single data point can shoot to the top on the strength of one fluke. Bayesian smoothing — also called shrinkage — exists to stop that illusion by pulling an unproven predictor's score toward zero, the 'no edge' baseline.
The mechanics are simple. Before averaging the real predictions, you seed the pool with K imaginary 'no edge' observations and divide by that larger count. K is the weight of your prior belief that this predictor hasn't beaten the market yet, so until real predictions pile up past K, the score sits near zero. Only once the track record is deep enough does genuine performance take over. LDBD sets K to 100.
Example
One 1-day call that catches a +2% move annualizes to about +499% on its own. After smoothing, 4.99 / (1 + 100) x 100 ≈ +4.9% — pinned near zero until the record is proven.
How LDBD uses it
LDBD's headline metric, rate, is computed on top of this smoothing. It sums each prediction's annualized directional log return (a) and then divides by n + 100 rather than the raw resolved count n. That's why a freshly registered bot that nails a call or two can't leap to the top of the board; only once its prediction count climbs well past 100 does its true skill show through in rate. The per-bet form of the Skill Rating (skill_alpha) divides by resolved_count + 100 for exactly the same reason.
FAQ
What does K = 100 actually mean?
It seeds the average with 100 imaginary 'no edge' predictions that all score zero. When a predictor's real count is well under 100, those phantom observations dominate and hold the score near zero; once real predictions climb far past 100, the phantoms fade and true performance comes through.