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What Does Not Work, and the Data

The Base-Rate Problem

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The Base-Rate Problem

A technical analysis indicator shows a buy signal. It has been correct 60% of the time historically. A trader feels confident and places a trade, expecting a 60% edge. But this reasoning commits one of the most insidious logical errors in finance: ignoring the base rate. The base rate is the probability that something happens by random chance, without any signal or skill. If the stock is in a bull market and has a 65% historical chance of rising any given week without looking at an indicator, then a 60% accurate indicator is actually worse than random. This is the base-rate problem, and it explains why technical traders often feel their signals are working (they confirm successes, forget failures) when they are actually underperforming random chance.

Quick definition: The base rate is the underlying probability of an event (e.g., a stock rising) before considering any signal or prediction. Ignoring the base rate leads traders to overvalue signals that are only marginally better than random and to miss that many signals are actually worse than random.

Key takeaways​

  • Base rates—the probability of an outcome without any signal—often exceed the accuracy of trading signals
  • A trading signal that is correct 55% of the time might sound useful, but if the base rate is 58%, the signal is actually harmful
  • In bull markets, the base rate for a stock rising is naturally high; a mediocre signal adds no value
  • Traders confuse the accuracy of a signal with its predictive power; accuracy is meaningless if the signal is worse than doing nothing
  • Properly accounting for base rates eliminates most technical analysis claims of edge

Understanding base rates with a concrete example​

Imagine a screening tool that identifies stocks likely to rally 10% or more in the next month. The tool's historical accuracy is 55%—of 100 stocks it flagged, 55 rallied 10% and 45 did not. A trader hears this statistic and considers the tool an edge.

But consider the base rate. During the same historical period (say, 2015–2023), what percentage of all stocks rallied 10% or more in any given month, without using the screening tool? The answer varies by market regime:

  • In a strong bull market (2017, 2021): 40% of stocks rally 10% in a month (high base rate)
  • In a neutral market (2015, 2019): 25% of stocks rally 10% in a month (medium base rate)
  • In a bear market (2022): 10% of stocks rally 10% in a month (low base rate)

Now evaluate the tool:

  • In a bull market: Tool is 55% accurate; base rate is 40%. The tool adds 15 percentage points. This is an actual edge.
  • In a neutral market: Tool is 55% accurate; base rate is 25%. The tool adds 30 percentage points. Strong edge.
  • In a bear market: Tool is 55% accurate; base rate is 10%. The tool adds 45 percentage points. Exceptional edge.

But here is the catch: The tool's accuracy (55%) is fixed across all market regimes. Only the base rate changes. If a trader uses the tool in a neutral market without realizing that the tool was designed in a bull market, they are likely using a tool that barely beats random, because the test period (bull market) had a higher base rate.

Moving averages and the base-rate paradox​

A stock trading above its 200-day moving average is supposedly bullish. Historically, when stocks are above the 200-day average, they rise 60% of the time over the next month. A trader who ignores moving averages buys all stocks and sees a 50% chance of a month-over-month rise (random or based on long-term historical drift). The moving average signal appears to add 10 percentage points.

But this ignores the composition bias. Stocks that trade above their 200-day moving average are, by definition, in uptrends—they have risen recently. The base rate for a stock in an uptrend to continue rising is naturally high, say 58%. The moving average signal does not create this edge; it simply filters for the uptrend that was already there.

A proper test of the moving average would compare:

  • Strategy A: Buy all stocks; hold for 1 month. Expect 50% to rise.
  • Strategy B: Buy stocks above their 200-day moving average; hold for 1 month. Expect 60% to rise.

The difference (60% - 50% = 10 points) is not the value of the moving average; it is the difference between buying uptrend stocks and buying all stocks. This difference would be the same if you used a different filter (stocks up more than 5% in the last month, or stocks with positive earnings momentum). The filter, not the specific technical rule, is the source of the edge.

In fact, if you tested:

  • Strategy C: Buy stocks down more than 20% in the last month. Expect 48% to rise (slightly less than 50%).

This is mean reversion, and it shows an edge of -2 points. But the 200-day moving average, applied to this mean-reversion condition, might show 55% upside, appearing to add +7 points when it is really just noise around the base rate.

RSI overbought/oversold and the Bayesian mistake​

An RSI above 70 is called overbought, and traders believe it predicts a pullback. Historically, when RSI is above 70, price falls 55% of the time over the next 5 days. This looks like an edge: 55% is above the 50% random chance.

But here is the Bayesian catch. Stocks with RSI above 70 are, by definition, stocks that have risen sharply in the last few days. The base rate for a stock that has just risen sharply is actually for it to continue rising, not to pull back. A stock in a strong uptrend might have RSI above 70 for a week, continuing to rise the whole time.

The proper base rate question: "What percentage of stocks that have risen 5% in the last week continue to rise in the next week?" The answer is probably 58–62% (they are in uptrends). If RSI overbought occurs in 80% of these cases and predicts a pullback 55% of the time, then the RSI is worse than the base rate of continuation. The RSI is identifying uptrends (which it should, given how it is calculated) and incorrectly labeling them as reversals.

Extreme moves and mean reversion: A base-rate trap​

Mean reversion—the belief that extreme moves reverse—seems intuitive and has some statistical support. A stock falls 20% in a day; traders expect it to bounce. The base rate for a 20% down day is for the stock to recover 5% over the next week. Is this an edge?

Only if the base rate for all stocks (without a 20% down day) is lower. And indeed, it is. A random stock might be expected to rise 0.5% in a week (slight upward drift). A stock that fell 20% has a base rate of +5%, or about 10 times higher.

This is not a technical edge; it is a base-rate phenomenon. The extreme move itself (the price change, not any indicator) contains information. Any rule that trades on extreme moves will capture this base rate, but the rule itself adds nothing.

The confusion arises because traders attribute mean reversion to a technical pattern (a V-shaped reversal, a hammer candle) when they should attribute it to the base rate of extreme moves.

Real-world case: The SPY indicator in 2022​

In late 2021 and early 2022, the SPY (S&P 500 ETF) fell sharply, declining 10% in a month—a relatively rare event. Technical traders flagged this as a "capitulation" signal, predicting a reversal and bounce. The accuracy was noted: After the 10% monthly decline, SPY had bounced an average of 5–7% within a month.

But what is the base rate for a 10% market decline to bounce 5–7% within a month? Historically, it is about 65%. This is not a technical insight; it is the nature of mean reversion in markets. A trader who simply bought the dip without looking at technical signals would have the same expected return.

The confusion was magnified because some traders compared the "capitulation" strategy to not buying the dip, rather than to buying without the signal. The real comparison:

  • With capitulation signal: Buy after 10% decline, hold 1 month. Expect +5% to +7%.
  • Buy the dip without signal: Buy after 10% decline, hold 1 month. Expect +5% to +7%.
  • Do nothing: Stay in cash, expect +0.5% (3-month Treasury rate at the time).

The technical signal did not add edge; it identified a high-base-rate situation (buy dips in downtrends, which naturally reverse).

Testing for base-rate correctness​

A rigorous test of any trading signal must account for base rates. Here is the framework:

  1. Define the signal: "RSI above 70 means sell."
  2. Measure the signal's accuracy: "RSI above 70 has been followed by a decline 55% of the time."
  3. Measure the base rate: "Stocks in uptrends (which usually have high RSI) continue rising 58% of the time."
  4. Compare: Signal accuracy (55%) is lower than base rate (58%), so the signal is worse than random.

A proper edge exists only if the signal accuracy is meaningfully higher than the base rate, and the difference is larger than transaction costs.

Common mistakes​

  • Focusing on accuracy, not edge. A 55% accurate signal sounds good; a 55% accurate signal when the base rate is 57% is a disaster. Always compare to the base rate.
  • Using the wrong base rate. A trader might use the 50% "random" chance and ignore that their signal targets a specific subset of stocks (uptrends, for example) with a different base rate.
  • Conflating historical accuracy with predictive power. A signal might have been 60% accurate in a bull market (high base rate) but only 51% accurate in a neutral market (base rate 50%), making it nearly useless in the neutral regime.
  • Ignoring regime-dependent base rates. In a strong uptrend, the base rate for continuation is high (65%+). A mean-reversion signal in this regime is fighting the base rate and is likely to lose.
  • Not accounting for selection bias in base-rate measurement. If you measure the base rate only on days when your signal fires, you are creating circular logic. Measure the base rate on all days.

FAQ​

How do I calculate the base rate?​

For a signal like "buy if RSI < 30," the base rate is the percentage of days (or weeks, or months, depending on your holding period) when price rises, without filtering for RSI < 30. Look at all days in your historical sample and calculate the percentage that experienced a price rise. Then compare to the percentage on days when RSI < 30.

What is an acceptable edge above the base rate?​

An edge of 2–3 percentage points (e.g., base rate 50%, signal accuracy 53%) is borderline and likely erased by transaction costs. An edge of 5+ percentage points is meaningful, though even this is often found to be unstable over time. In academic research, 1–2% annual alpha after costs is considered robust for an individual signal.

Can I combine signals to improve the edge above the base rate?​

Sometimes, if the signals are uncorrelated. But most technical signals are correlated with each other and with momentum, so combining them does not help. A signal that is worse than the base rate will not improve if you add another signal that is also worse than the base rate.

Should I adjust base rates for my specific trading style or market?​

Yes. If you trade small-cap stocks, the base rate for a small-cap rising might be different from the broader market. If you trade during the first hour of the trading day, the base rate for a move might be different. Calculate the base rate for your specific conditions.

Is the base-rate problem the same as overfitting?​

Related, but different. Overfitting is using historical data to design a rule that fits the past but not the future. The base-rate problem is ignoring the prior probability of an event, even with a perfectly accurate signal. A signal can be fit perfectly to history and still be worse than the base rate if the test period was unusual.

How do I test if my signal is worse than random?​

Run a simple test: randomize your signal (generate random buy/sell dates instead of signals from your rule) and measure the returns. If your real signal is not meaningfully better than random signals, you do not have an edge. This is called a permutation test.

If base rates are this important, why do traders ignore them?​

The base rate is invisible. You see a chart with a signal; you do not see a statistical baseline. It is easier to remember "RSI overbought followed a fall" (confirmation of the signal) than to calculate "overbought stocks in uptrends continue rising 58% of the time anyway." Human psychology and the nature of patterns make base-rate thinking unnatural.

Summary​

The base-rate problem is why most technical signals appear to work but actually do not. A signal that is correct 55% of the time means nothing if the base rate—the probability of the outcome without any signal—is 57%. Traders see a 200-day moving average breakout followed by a rally and believe the indicator caused the move; in reality, the base rate for breakouts in uptrends to continue rising is naturally high. Rigorous testing requires comparing a signal's accuracy to the base rate for the same outcome, then subtracting transaction costs. When this comparison is done honestly, most technical signals vanish. The ones that survive are often mean-reversion signals in extreme conditions, which really just exploit the base rate that extreme moves tend to reverse—a phenomenon that requires no technical expertise to trade.

Next​

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