Rebuilding the relative strength index as open-scale buy-sell pressure

Two smoothed columns, then a bounded map

The relative strength index begins by splitting close-to-close changes into two non-negative series, one for up-day changes or zero and one for down-day changes or zero. Each series is then smoothed with exponential smoothing: a recursive average that blends a new observation with the prior average. In this construction the effective length of that average is twice the oscillator lookback minus one.

The relative-strength ratio is the intermediate quotient of the up-day average over the down-day average, before any 0–100 mapping. A 14-day lookback therefore applies a 27-day exponential average to both series before that ratio is formed and mapped onto the oscillator.

Lookback sets how long pressure is retained

Because those exponential averages lengthen with the lookback, the intermediate ratio retains older observations for longer and the oscillator becomes less responsive as the lookback increases. Across lookbacks from 6 to 42 stepped by 2, the built-in smoothing weight is the reciprocal of the lookback, and the equivalent exponential length runs from 11 to 83 using the identity 2/(L+1).

Range compression on the 0–100 scale

On the 0–100 scale the mapping is nonlinear. A tenfold rise in the relative-strength ratio from 1 to 10 lifts the oscillator only from 50 to about 91, and a tenfold fall from 1 to 0.1 lowers it from 50 to about 9.

The same mapping can turn a move in the up-to-down pressure ratio from 3:1 to 12:1, a 300 percent increase, into a move on the oscillator from 75.0 to 92.31, about a 23 percent increase. Equal-magnitude pressure ratios of 4:1 and 1:4 both sit 30 points from the midline of 50, printing 80 and 20, so the numeric labels are not symmetric with the underlying force. That nonlinear squeezing of large moves in the ratio into small moves near the 0 and 100 bounds is range compression.

Open-scale buy-sell pressure

Open-scale buy-sell pressure is a signed transform of the same ratio. It reports the ratio itself when the ratio is at least 1, and the negative reciprocal when the ratio is below 1. The result is a signed reading of how many times one side exceeds the other, with no fixed ceiling or floor, and with symmetric pressure readings such as +10 versus -10.

The same signed series can be recovered from the oscillator. Below 50 it equals (0.01 times the oscillator minus 1) divided by (0.01 times the oscillator). At or above 50 it equals (0.01 times the oscillator) divided by (1 minus 0.01 times the oscillator).

Original update versus a standard exponential mix

For a 14-day lookback the original RSI update applies 1/14 of the new observation and 13/14 of the prior average. A standard EMA update applies 2/15 of the new observation, about 0.13 versus 0.07. On the same reconstructed series the standard mix moved sooner, and the signed pressure series continued to accelerate after the 0–100 reading had flattened above 90.