How Far Is Far? From Price Distance to Standardized RSISuppose someone tells you:
The current price is 30% above its 200-day moving average.
The statement sounds informative because it gives both a reference point and a distance. But it still leaves out the part that matters most: is 30% a normal displacement for this market, or an extreme one?
Raw distance tells us where price is relative to an average, but not how large that displacement is relative to the normal movement of the series. To make the number comparable, distance needs a reference scale.
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This idea begins with the familiar Bollinger Band framework, then uses RSI Chart Overlay to make the same measurement problem visible on price. From there, we can see why a bounded RSI scale needs a different coordinate system before different lookback lengths can be compared.
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1. Giving distance a unit
One of the most familiar ways to give distance a scale is Bollinger Bands.
Let's start with a 20-bar moving average and bands two standard deviations above and below it. Instead of saying only that price is a certain number of dollars or percent away from the average, we can express the displacement in standard-deviation units:
z = (Price - Average) / Standard Deviation
Now the distance is dimensionless.
A reading of +1 means that price is one standard deviation above its average. A reading of +2 means two standard deviations above it.
On a conventional 20-bar chart, this feels natural because the center, the scale and the outer reference levels all behave in a familiar way.
That is why the z-score is such an attractive answer to the original question. It appears to turn raw distance into a common unit of extension.
I used this public Rolling Z-score script.
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2. What happens at a very short lookback?
After going from 20 days to 5 days, the picture changes immediately. The standardized series remains crowded inside the ±2 reference lines, even though price is moving aggressively over the short window.
The supposedly common unit of extension is clearly behaving differently from the 20-bar example.
That is the important observation:
We changed the lookback, but the supposed common unit of extension stopped behaving in a visually comparable way.
A z-score still gives distance a unit, yet the result is not independent of the geometry created by the window used to calculate it.
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3. The common workaround
A practical response is simply to avoid very short lookbacks. Many indicators impose a minimum input, and many traders naturally gravitate toward lengths where the familiar band structure looks more stable.
That can be perfectly reasonable as a usage rule, but it is still a workaround.
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4. RSI makes the same problem more obvious
Price-based rolling z-scores already become awkward at short lookbacks. RSI sharpens the issue because its raw coordinate has hard bounds: it cannot move above 100 or below 0.
This is where RSI Chart Overlay becomes useful as an explanatory tool. In the AdaptiveRSI representation, RSI describes normalized price position relative to the Wilder moving average of the same length. The key relationship is simple: RSI 50 corresponds to price at Wilder EMA(n).
This lets us treat RSI not only as an oscillator pane, but as a coordinate system that can be translated back into price.
RSI Chart Overlay projects chosen RSI coordinates back onto the price chart. RSI 50 becomes the middle line. A selected RSI level above 50 becomes a price band above it, and a selected value below 50 becomes a corresponding band below it. We do not need the full RSI derivation here; we only need this mapping so that the geometry of the RSI scale can be seen directly on price.
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5. Equal standardized steps do not occupy equal price space
Now take RSI(14), but instead of starting with familiar raw levels such as 70 and 30, start with equal positions on a standardized scale.
z = 0 → RSI 50.00
z = +1 → RSI 63.52
z = +2 → RSI 75.20
The negative side is symmetric around 50.
We can already see that the distance from 0 to +1 is larger than the distance from +1 to +2.
RSI Chart Overlay is not creating that compression. It is exposing it. The Overlay projects raw RSI coordinates onto price, and those raw RSI coordinates are already getting closer together as standardized position moves farther from the center.
The supporting formula is:
Price offset = (RSI - 50) / 50 × CC volatility × (n - 1)
Full overlay formulas: Projecting RSI Levels Directly onto Price
The formula matters only because it confirms what the chart already shows:
when the gaps between raw RSI coordinates shrink, their projected gaps on price shrink with them.
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6. The same compression is visible on the 0–100 scale
The price chart is showing the same geometry that exists inside RSI itself. For RSI(14), the equal standardized steps map to:
z = 0 → RSI 50.00
z = +1 → RSI 63.52
z = +2 → RSI 75.20
z = +3 → RSI 84.08
The standardized increments are identical, but the raw RSI increments are not. The move from 50.00 to 63.52 uses 13.52 RSI points. The next move, from 63.52 to 75.20, uses 11.68 points. The move from 75.20 to 84.08 uses only 8.88.
This is the tail-compression problem in its simplest form. The closer RSI gets to 100, the less raw coordinate space remains for the next equal standardized move. The same happens toward 0. A bounded scale therefore gives progressively less visual resolution to increasingly extreme standardized positions.
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7. RSI(2) makes the problem obvious
RSI(2) is the useful stress test because a very short RSI spends much more time near the boundaries. Use the same market and the same period in two aligned panes.
The difference is not that one pane contains more market information than the other. They represent the same underlying RSI observations. The difference is that the raw pane compresses increasingly extreme values into the last few RSI points before 0 or 100, while the standardized Logit RSI pane gives those tail observations additional room.
That distinction matters at very short lengths. A common workaround for awkward short-lookback behavior is simply to avoid very short n. Standardized Logit RSI is designed to remove the bounded-scale problem instead, so RSI(2) can remain on a usable standardized axis rather than being excluded by construction.
Logit RSI script:
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8. Why raw RSI 70 is not universal
The bounded scale is only one part of the problem. Lookback length changes the meaning of a raw RSI value as well.
The same standardized position maps to very different raw RSI values at different lengths, and the same raw RSI value maps to very different standardized positions. RSI 70 is therefore a coordinate on the 0–100 scale, not a universal measure of extremity.
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9. Two transformations, two jobs
The complete transformation from raw RSI to Logit RSI has two separate jobs:
Logit transform addresses the hard 0/100 bounds.
The theoretical scale then addresses lookback dependence.
That is all we need from the mathematics at this stage. Logit opens the bounded coordinate system. The length scaling puts different RSI lengths onto a common standardized axis.
RSI 0–100
→ Logit
→ unbounded coordinate
→ length scaling
→ standardized z
Different RSI lengths still represent different horizons and will not produce identical paths or signals. Standardization makes their positions comparable; it does not make the underlying series the same.
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10. Define zones in standardized space first
Once RSI is expressed on a common standardized axis, reference regions can be defined in z-space first and then translated back to the raw RSI scale for the selected lookback length.
The current AdaptiveRSI framework uses:
|z| ≤ 0.66 → Body / consolidation
0.66 < |z| ≤ 1.00 → Support / resistance region
1.00 < |z| ≤ sqrt(3) → Trend region
sqrt(3) < |z| ≤ 2.14 → Overbought / oversold stretch
|z| > 2.14 → Tails
Full math: RSI Beyond 70/30: Position, Structure, and Adaptive Zones
This also makes it possible to compare different RSI lengths on the same standardized basis.
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11. From fixed levels to a common measure of position
The practical consequence is that raw RSI levels should not be treated as universal units of extension. A reading such as RSI 70 tells us where the oscillator is on its 0–100 scale, but its standardized position depends strongly on lookback length.
The price projection makes the geometry visible. Equal steps in standardized space become progressively narrower when translated back to raw RSI and then projected onto price. Logit removes that bounded-scale compression, while the 2 / sqrt(n - 1) scaling provides a common length-aware coordinate system.
The main takeaway is that RSI can be treated as a standardized measure of position around its Wilder EMA equilibrium. The underlying information does not change. The coordinate system used to measure it does.
Related tools:
RSI Chart Overlay
Logit RSI
RSI Adaptive Zones
RSI Tutorials:
Projecting RSI Levels Directly onto Price
RSI Beyond 70/30: Position, Structure, and Adaptive Zones
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