Bayesian thinking: updating a win rate as trades accumulate

[Shadow Trader]

After 20 trades with 13 wins, is the win rate 65%? A Bayesian view says: probably not exactly, and here's how uncertain it is.

Start with a prior belief, such as "the win rate is somewhere between 40% and 60%, most likely near 50%". As trades accumulate, update the belief. With a simple Beta distribution, the update is easy: add the wins and losses to the prior's parameters. Starting from a flat prior, after 40 wins in 70 trades the posterior mean is about 57%, and the range of plausible values runs from roughly 45% to 68%.

That wide range is the lesson. Even 70 trades leave huge uncertainty about the true win rate. A strategy with a 57% observed rate could easily have a true rate of 48%, which would be a losing system after costs.

The approach also encourages sensible behaviour: more data narrows the range, and decisions can be tied to the probability that the true edge exceeds some threshold, such as the break-even win rate.

Spreadsheets handle the Beta distribution through built-in functions, so the calculation takes minutes.

A tip for spreadsheet users: the BETA.INV function returns the percentile of a Beta distribution, so the 2.5% and 97.5% points give a credible interval directly. With wins and losses in two cells, the whole update takes a single formula, and it can be recalculated after every session.

It also supports a practical decision rule. Instead of asking "is the win rate above 50%?", ask "what's the probability that the true win rate exceeds the break-even level after costs?" If that probability is only 60%, the evidence is thin, whatever the point estimate says.

What is the plausible range for the current strategy's true win rate, given the number of trades logged?