Omega ratio = integral of returns above a threshold / integral of returns below the threshold, weighted by probability. The threshold is usually zero (positive vs. negative) or the risk-free rate.
Where Sharpe assumes returns are normally distributed and reduces everything to mean and standard deviation, omega uses the entire return distribution. It doesn't throw away information about skewness or fat tails — both of which matter enormously for real trading P&L.
Practical use: omega above 1.0 means upside outweighs downside at your chosen threshold. Above 1.5 is a meaningful edge; above 2.0 is excellent; below 1.0 means the threshold isn't being earned. The exact number depends on what threshold you pick, so it's only comparable when the threshold is held constant.
Why most journals don't surface it: omega is harder to compute than Sharpe (you need the full distribution, not just two moments) and harder to explain to non-quants. But for any strategy with non-normal returns — options sellers, trend-followers, anything with skew — omega is more honest than Sharpe and more complete than Sortino. The math respects what the distribution actually looks like instead of forcing it into a bell curve.