A 24-Point Drop Is Not a 24% Saving

Ada re-runs the frost-protection saving and keeps percentage points and proportional reduction apart

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Ada ADA · CALCULATION AUDIT

A 24-Point Drop Is Not a 24% Saving

A citrus grower’s frost-protection system cut false wind-machine activations from 40% to 16% of frost events, and with 30 machines burning 30 needless hours a season at $85 per hour the baseline waste is $76,500. The tempting read is to subtract the rates — 40 minus 16 — and bank a 24% saving. This audit re-runs the figure and asks whether the value tracks the 24-point gap or the 60% proportional reduction, a difference of $27,540.

Companion to the chapter Smart Agriculture and Livestock — every number here comes from that chapter.

The frost example says false wind-machine activations fell “from 40% to 16% of frost events,” then asks for the fuel saving. The trap is to subtract — 40 minus 16 is 24 points, so surely you save 24% of the cost. Let me keep the percentage-point drop and the proportional saving apart, because only one of them scales the money.

The baseline waste

30 wind machines running 30 unnecessary hours a season at $85 per hour:

30 × 30 × $85 = $76,500 per season

The reduction — two different numbers

From 40% to 16% is a drop of 24 percentage points:

40 − 16 = 24 points

But as a fraction of the original false-alarm rate it is a 60% proportional reduction:

(40 − 16) / 40 = 0.60  →  60%

The saving follows the proportion, not the point gap:

$76,500 × 0.60 = $45,900

What the trap would have paid

Subtracting the points instead would pay out:

$76,500 × 0.24 = $18,360

— barely 40% of the real figure, and short by:

$45,900 − $18,360 = $27,540

Design meaning: when a rate improves from one percentage to another, the value it unlocks tracks the relative reduction between them, not the difference in points — conflating the two is how an IoT business case quietly mis-states its own payback.

Every number above is taken from the chapter’s own frost-protection example and re-derived step by step.