_Before asking if a number is exactly right, ask if it's roughly right. Most errors are 10x, not 10%._ --- ## The sanity check A team presents a business case: £2m investment, £800k annual return, 40% ROI. Before digging into assumptions, ask: is £800k plausible? The product serves 50 customers paying £20k each — £1m total revenue. After costs, £800k profit would require 80% margins. For a services business, that's impossible. For software with existing infrastructure, it might be reasonable. For a new product requiring dedicated support, it's optimistic. The calculation might be internally consistent. But if £800k can't physically emerge from 50 × £20k, the spreadsheet is fiction. --- ## Fermi estimation Enrico Fermi famously estimated the yield of the first nuclear test by dropping scraps of paper and measuring how far the blast moved them. He was within a factor of 2 — close enough to be useful, from almost no data. The technique: break a problem into components you can estimate, multiply rough guesses, and accept that being within 2-3x is often good enough. **Example: How many plumbers work in London?** - London population: ~9 million - Households: ~3.5 million (rough average of 2.5 people per household) - Plumber visits per household per year: maybe 0.5 (every other year on average) - Visits per plumber per day: maybe 3-4 - Working days per year: ~250 So: 3.5m × 0.5 = 1.75m visits annually. 1.75m ÷ 250 days = 7,000 visits per day. 7,000 ÷ 3.5 visits per plumber = 2,000 plumbers. Is that exactly right? No. Is it roughly right — closer to 2,000 than to 200 or 20,000? Almost certainly. The value isn't precision. It's having a baseline to compare against claims. If someone says "there are 50,000 plumbers in London," you can say: that seems high by 10x, show me the maths. --- ## Spotting errors Most serious errors aren't small — they're orders of magnitude wrong. **Decimal place errors.** £200k becomes £2m or £20k. These are obvious if you have order-of-magnitude intuition, invisible if you're just checking whether the spreadsheet formulas work. **Unit confusion.** Monthly figures treated as annual. Per-customer figures treated as totals. Thousands confused with millions. The number is "correct" in the wrong unit. **Missing scale factors.** A cost per unit multiplied by the wrong volume. A rate applied to the wrong base. The calculation is right; the inputs are mismatched. **Implausible outputs.** A margin that exceeds 100%. A growth rate that would make the company larger than its market. A headcount productivity that would require each person to work 200 hours per week. The defence isn't checking every cell. It's asking: does the answer make sense given what I know about the world? --- ## Building intuition Order-of-magnitude intuition comes from accumulating reference points. **Revenue per employee.** Software companies: £200-500k. Professional services: £100-200k. Retail: £50-150k. Manufacturing: varies wildly by automation level. If someone quotes £1m revenue per employee for a consulting firm, something is off. **Gross margins.** Software: 70-85%. Professional services: 30-50%. Distribution: 15-25%. Retail: 25-40%. A "software" company with 40% gross margin isn't really software — it's services dressed up. **Customer acquisition payback.** Healthy SaaS: 12-18 months. Aggressive growth mode: 18-24 months. Unsustainable: 30+ months. A business claiming 6-month payback on enterprise customers is probably miscalculating. **Growth versus market.** If the total market is £500m and the company projects £200m revenue in five years, they're claiming 40% market share. Possible, but requires extraordinary execution or a flawed market sizing. These baselines don't tell you if a number is right. They tell you if it's in the right neighbourhood — or wildly outside it. --- ## The practice **Estimate before you calculate.** Before opening the spreadsheet, guess what the answer should be. If the calculated answer differs by 10x, either your intuition is wrong or the calculation is. **Triangulate with different methods.** Estimate the market size top-down (population × penetration × price) and bottom-up (known customers × expansion potential). If they're wildly different, investigate. **Know your reference points.** For your industry, know the typical ratios: margins, productivity, growth rates, retention. When a number departs from typical by more than 2x, ask why. **Ask "is this physically possible?"** £10m revenue from 100 customers requires £100k average. Is that plausible for the product? £50m from a 10-person team requires £5m per person. Is that achievable? --- Precision is overrated. A number that's right to two decimal places but wrong by a factor of ten is worthless. Get the order of magnitude right first. Refinement can come later. --- **See also:** [[Ideas/Base Rates|Base Rates]] — Start with what usually happens before refining the specifics.