Before anything gets priced, someone has to count it: linear feet of pipe, square feet of drywall, cubic yards of concrete. That count is the takeoff, and every number in the final bid traces back to it. A takeoff that's off by 15% produces a bid that's off by roughly the same amount, no matter how careful the pricing is afterward.
Manual takeoff means a ruler, a printed plan set, and a lot of trust in whoever's counting. Digital takeoff tools remove the ruler but still require someone to catch every callout across a 300-page set — the software measures what you tell it to measure.
Example
An estimator takes off a floor plan by hand, printed at a copy shop, ruler and highlighter. A revision lands the next day changing three room dimensions. The whole takeoff for that area gets redone from scratch, because there's no way to isolate just the changed portion.
Where this goes wrong on real jobs
A manual takeoff is only as accurate as whoever's holding the ruler that day.
“…You spread them across a table, grab a scale ruler, a highlighter, and a calculator. Four hours later you've got a takeoff that might be right. Or might be off by 15% because someone bumped the ruler on page 23.”