Per-symbol Brier Skill (
symbol-skill.html) says "did the brain learn this symbol's probability structure?" Per-symbol Sharpe says "did betting in the brain's predicted direction actually make money on this symbol?"
A symbol can have high BSS but low Sharpe โ the brain's probabilities are calibrated, but the moves are too small to overcome trading costs. Or high Sharpe but low BSS โ the brain happens to be on the right side of big moves even though its probabilities are sloppy.
The two together tell the full story. If both are high โ trade it confidently. If both are low โ skip. If BSS is high but Sharpe is low โ use it for confidence ranking but not for sizing.