Market Sizing: Numerical Narratives

Chris Dixon posted about market sizing using narratives as opposed to numbers, and Fred Wilson agreed - even demonstrating market sizing with a cartoon illustration. 

It is easy to see why Chris' and Fred's "narratives over numbers" market sizing might be appealing. After all, as Brad Feld writes, "Almost every market sizing presentation is incorrect - by a lot. Enough to make it irrelevant." Chris writes, "you should never rely on quantitative analysis to estimate market size. Venture-style startups are bets on broad, secular trends."

This seems to make sense: tell a story because your numbers are going to be wrong anyway. But let's analyze the traditional market definitions to see why traditional quantitative methods are incorrect. Non-quantitative analysis (a story) is not enough. Market sizing has to be quantitative because it is a tool to make an investment (i.e. a quantitative) decision.