What Equity Curve R² Tells You: Doubting Too-Smooth EAs

Bottom line: R² measures smoothness, not safety

How close an equity curve is to a straight line can be expressed as a number using the coefficient of determination, R². The closer R² is to 1, the closer the curve is to a rising straight line.

That said, we don't treat a high R² as proof of a good EA on its own. If anything, a curve that is too close to a straight line is a reason to look harder. This article explains how R² works, the checks to run when you're suspicious, and what R² can't tell you.

How R² works

What is being calculated

Put time (or trade sequence) on the horizontal axis and cumulative profit and loss on the vertical axis, then fit a straight line by least squares. R² is the share of the curve's ups and downs that this line explains.

• R² close to 1: the curve sits almost on a straight line
• Low R²: the curve has deep dips along the way, or long flat stretches

What to do before calculating

An EA whose lot size grows with compounding produces a curve that bends upward like an exponential. Fitting a straight line to it directly gives an unfairly low R². Use fixed-lot results, or take the logarithm of the balance before calculating.

Another important point is whether you measure the balance curve or the equity curve. The balance curve only records closed trades. An EA that holds on to floating losses can look smooth if you only look at the balance.

How to doubt a "too smooth" EA

Compare balance DD with equity DD

The clearest example of this gap among our EAs is GOLD KING v6. In its backtest, balance DD was 7.45%, while equity DD was 91.3%. Even though the balance curve looks smooth, the floating loss before closing grew to a level that nearly used up the account. The 83.1% win rate and the maximum of 44 consecutive wins also contribute to that smooth look.

We publish this EA as an aggressive type, for people who use it on that understanding. We mention it here honestly as a typical case where "the curve looks clean, so it must be safe" is the wrong reading.

Checklist

The same goes when other metrics look "too good"

This isn't limited to R². When any metric looks too good, question the assumptions behind the calculation first. For example, GOLD TRIPWIRE's backtest shows a Sharpe ratio of 94.75, but we don't treat this as a measure of how strong the EA is. For EAs with short holding times, the value can come out extreme depending on how the calculation is segmented. Read it together with other metrics such as PF and maximum consecutive losses. You can compare each EA's figures in the measured ranking of all EAs.

Limits of R² and cautions

• It says nothing about slope: Even an almost flat curve can show a high R² if the variation is small. You need to look at the size of the profit separately from R².
• A low R² isn't necessarily bad: Trend-following EAs tend to produce a staircase-shaped curve that alternates between flat stretches and sharp rises. The DONCHIAN ENGINE backtest has a 34.5% win rate and a maximum of 11 consecutive losses, so it never forms a smooth straight line. Even so, that is the expected shape for this type of EA.
• Small samples are unreliable: With few trades or a short period, R² can come out high just because the points happened to line up neatly.
• Past shape doesn't guarantee the future: R² is only a number describing the shape of a past curve.

At this point we do not publish R² for each EA as an official metric. Given the limits above, we think presenting it as a standalone number would be misleading.

A note on forward testing as well. The figures are as of October 24. GOLD KING's forward test on an Exness demo account showed a profit rate of 17.13%, DD of 4.6%, PF of 3.75, and 136 trades. This is not a live-account result. The period is also far too short to say anything about the linearity of the curve.

Summary

• R² is a metric that quantifies how smooth a curve is. It does not measure safety or the size of profit
• For compounded results, convert to fixed lot or logarithm before calculating
• Measuring only the balance curve hides floating losses. Always check the gap against equity DD
• For a curve that is too close to a straight line, suspect grid trading, doubling up, overfitting, and data quality
• For trend-following EAs, a lower R² can be exactly what the design predicts
• More on reading metrics is collected in EA & MT5 Know-How