Back to Calculator

How The Math Works

Simple explanation of the Convenience Theorem formula

The Core Formula

PCR = Premium ÷ (Convenience Value × √(Alt Price ÷ Industry Avg) × Psych Calibration)

Lower PCR = Underpriced convenience | Higher PCR = Overpriced convenience

Premium

Convenient Price - Alternative Price

How much extra you're paying for convenience

Convenience Value

Distance + Time + Effort + Risk + Brand Preference

Total dollar value of convenience benefits including brand/quality preferences

Industry Magnification

√(Alternative Price ÷ Industry Average)

Adjusts for industry - convenience matters more for expensive items

Psychological Premium Caps

Hard dollar limits by price range

Caps final pricing based on consumer research - people have absolute limits regardless of convenience value

Breaking Down Convenience Value

Distance Savings

Miles × $0.65 per mile

Gas, wear & tear costs saved

Time Savings

(Minutes ÷ 60) × Hourly Rate

What your time is worth

Effort Avoided

Your estimate in $

Parking, walking, waiting, searching

Risk Reduced

Your estimate in $

Weather, safety, uncertainty

Brand Preference

min(Price × 30%, √Price × 2.5)

Sophisticated scaling: realistic brand premiums that scale with product price

Why Industry Magnification Matters

The square root formula adjusts convenience importance based on what you're buying:

  • Cheap items ($2 candy bar): Convenience matters less → Lower magnification
  • Expensive items ($500 electronics): Convenience matters more → Higher magnification
  • The psychology: When buying something important/expensive, you value convenience more

Why Premium Caps Matter

Convenience value calculations remain objective, but final pricing respects hard psychological limits:

  • Under $1.50: Max $0.50 premium - consumers reject higher amounts regardless of convenience
  • $1.50-$3: Max $0.75 premium - daily purchase frequency creates strict limits
  • $3-$5: Max $1.25 premium - weekly purchase patterns allow moderate premiums
  • $10+: Up to 50% premium - expensive items follow normal economic theory

This makes the PCR a better decision-making tool by reflecting how people actually behave with money at different price points.

Smart Brand Preference Scaling

Brand preference now scales intelligently with product price using sophisticated math:

The Formula

min(Price × 30%, √Price × 2.5)

Takes the smaller of percentage cap or square root cap

Real Examples

  • $2 candy: ±$0.60 (30% wins)
  • $5 coffee: ±$1.35 (30% wins)
  • $100 electronics: ±$25.00 (√ wins)

Why this works: Prevents unrealistic brand premiums (like $8 on $2 candy) while allowing meaningful adjustments on expensive items. Based on real brand loyalty research showing 25-30% typical maximum premiums.

Quick Example

Airport Coffee: $6.00 vs Street Café: $4.50

Coffee industry average: $6.85

  • Premium = $6.00 - $4.50 = $1.50
  • Distance = 0.3 miles × $0.65 = $0.20
  • Time = 15 min × $30/hr = $7.50
  • Effort = $3.00 (security, walking)
  • Risk = $2.00 (missing flight)
  • Max Brand Preference = min($4.50×0.3, √$4.50×2.5) = min($1.35, $5.30) = $1.35
  • Brand Preference = $0.00 (neutral: 0% × $1.35)
  • Base Convenience Value = $12.70
  • Industry Magnification = √($4.50 ÷ $6.85) = 0.81
  • Psychological Calibration = 0.77 (moderate price point)
  • Final Convenience Value = $12.70 × 0.81 × 0.77 = $7.93
  • Final PCR = $1.50 ÷ $7.93 = 0.189

Result: Excellent deal! You're paying $1.50 for $7.93 worth of calculated convenience value.

What PCR Scores Mean

PCR < 0.30

Excellent Value - Great convenience deal

PCR 0.30-0.70

Fair Value - Reasonable convenience premium

PCR > 0.70

Poor Value - Paying too much for convenience