Bayes in Trading (1/3)
Rare events may not be your friend in trading...
You often see trading or ML models online claiming 90% accuracy. On common events, that can be meaningful. On rare events, it is often useless.
Many models try to predict chart patterns, breakouts, or specific market regimes that occur only a small fraction of the time. Even with very high conditional accuracy, these models can still lose money. Why?
Because accuracy is not the right question to ask. And Bayes explains exactly why.
1. A quick reminder on conditional probability
A conditional probability answers a simple question:
Given that A happened, how likely is B?
In trading and machine learning, this often appears as:
P(Signal | Event)
When the event truly occurs, how often does the model detect it?
This is what most people mean when they talk about model accuracy.
The problem is that this is not the probability traders actually care about.
What matters in practice is the inverse question:
P(Event | Signal)
When the model triggers a signal, how likely is it that the event is real?
These two probabilities are not the same.
And when events are rare, the difference can be massive.
This inversion of perspective is exactly what Bayes forces you to confront.
2. Rare events break intuition
Most trading signals are built to detect unusual situations.
Breakouts, chart patterns, volatility expansions, regime shifts. By definition, they do not happen often. This already changes how probabilities should be interpreted.
When an event is rare, the main risk is not missing it. The main risk is seeing it everywhere. A model can be very good at detecting the event when it happens,
and still generate mostly useless signals in practice.
This is not a modeling issue.
It is a base rate issue.
3. The wrong performance metric
Most models are evaluated using metrics that answer the wrong question.
They focus on:
Accuracy
Recall
Detection rate when the event is present
All of these describe P(Signal | Event).
But trading performance depends on:
How often you trade
How often those trades correspond to real opportunities
How much noise you are exposed to
In other words, trading cares about P(Event | Signal).
Bayes is simply the formal way of forcing this inversion.
4. Why this matters in practice
When base rates are low, false positives dominate.
That leads to:
Overtrading
Higher transaction costs
Unstable equity curves
The model is not necessarily wrong. The interpretation is.
A concrete example
Assume the following:
A trading model detects a specific market pattern.
When the pattern truly occurs, the model is correct 90% of the time.
The pattern itself occurs in only 2% of market observations.
When the pattern is not present, the model still triggers a signal 12% of the time.
Question: When the model triggers a signal, what is the probability that the pattern is actually real?
Answer: 13,27%.
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With such a low signal reliability, an extremely high risk-reward ratio would be required just to break even.
In the next newsletter, we will go through the exact calculations and show how these numbers combine, using Bayes, step by step.
👉 If you want to go deeper into each step of the strategy building process, with real-life projects, ready-to-use templates, and 1:1 mentoring, that’s exactly what the Alpha Quant Program is for.
Reminds me of the Abraham Wald bullet hole story, the military wanted to armor where returning planes had holes, but Wald pointed out those were the survivable hits. Same thing here: backtests love to highlight the catches, but the real question is what happens across *all* the signals. Stats 101 stuff that's easy to forget when you're deep in the data.