This version keeps the same raw input as the Realized Price Oscillator — ln(Price / Realized Price) — but then rescales it against its own decayed historical min/max. The result is not a fixed valuation multiple. It is an adaptive score showing how historically extreme the current reading is within the cycle.
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The raw input is still the same:
Raw = ln(Price / Realized Price)
That raw log value tells you the exact valuation multiple versus Bitcoin's realized price. This indicator then starts on 2012-01-01, tracks the highest and lowest raw values seen so far, applies a small decay factor of 0.9999 each day, and rescales the current reading into a fixed range from -1 to +1.
Normalized = ((2 * (Raw - MinSeen)) / (MaxSeen - MinSeen)) - 1
The key distinction is what the number means. A raw log oscillator reading tells you the exact distance from realized price. A normalized reading tells you how historically extreme that distance is relative to previous cycles after the old extremes have slowly faded.
Use this together with the raw Realized Oscillator. The raw version answers: "how far above or below realized price are we?" This normalized version answers: "how extreme is that reading versus Bitcoin's own history?"