It’s not really a surprise that companies get less innovative the bigger they get. Bureaucracy creeps in. Talent gets watered down. You can’t move as quickly. Too many cooks in the kitchen; nine women can’t grow a baby in a month; an engineer team should be fed with two pizzas and all of those industry cliches.

But it is sort of surprising how many entrepreneurs forget what they did right as small companies, by the time they get big. Or, in some cases, they forget what big companies did wrong and promptly make the same mistakes.

There’s a lot of bits and pieces of news still coming out about Facebook’s $1 billion purchase of Instagram. But there are two dots that I haven’t seen connected yet: The reason Mark Zuckerberg was successful in buying Instagram in 2012 is directly related to the reason why Yahoo failed to buy Facebook back in 2006.

There’s a telling similarity: The magical $1 billion price tag.

Back in 2006, then Yahoo CEO Terry Semel knew the company was quickly losing relevance in a new Web age, and they had to do something. One of his biz dev guys offered Facebook $1 billion. Based on Facebook’s business, that seemed about as outrageous as offering Instagram $1 billion two weeks ago.

But Semel had seen this movie before, when he passed on the opportunity to buy Google. He didn’t know what to bid, because he had no clue what it was worth. The deal slipped through his grasp.

So he came right out and offered Facebook $1 billion in a time when no one was quite sure that Web 2.0 would amount to much anything. To put the seemingly outrageous sum in perspective, MySpace was still the undisputed giant in social media back then, and News Corp bought MySpace for just under $600 million.

$1 billion was hardly based on any reasonable metric. It was just an amount that is very hard to turn down.

Astoundingly, Zuckerberg didn’t think $1 billion was enough, but his board — which at the time consisted of just Peter Thiel and Jim Breyer — spent some six hours convincing him to consider it.

So far, so good.

A few days later, Yahoo announced disappointing earnings and its stock fell by 20%. This is where Semel royally screwed up. He discounted his offer for Facebook by 20% because his currency had changed. And Zuckerberg immediately said no. For one thing, Yahoo’s problems had nothing to do with the value of his company. For another, there is just something magical about $1 billion. Even $999 million doesn’t feel the same.

Fast forward to 2012, and it’s clear that Zuckerberg wasn’t going to make the same mistake with Instagram that Yahoo made with Facebook. Facebook wanted — needed — Instagram if it was to guarantee its dominance in photo sharing, the core of its service, particularly on mobile. Given the importance of the deal, there was only one possible offer. Perhaps not the $2 billion fantasy price that Systrom reportedly wanted. But not 80% of a billion dollars. Not $999 million dollars. A billion dollars.

Sold.