For a big corporation it is not important to succeed in most acquisition. The real risk, is that some startup eats your current business model and you didn't buy it when you could still afford it. If most acquisitions "fail" that is ok, you still sit on a ton of money.
In other words, probability is more or less irrelevant, because if you fail it means a small loss which does not risk the company's future, on the other hand, if you don't acquire, and the small business succeeds big time, then that is a big loss, and may eventually kill you.
I agree with your point, but just one quibble: from what I'm reading, you've made the argument that the probability of yahoo as a whole failing is the probability to watch during a merger.
I don't see from your argument that probability is a bad tool in analyzing this situation.
Yahoo is not acquiring Tumblr in the traditional sense.
Tumblr is the new Yahoo.
What has been Yahoo up until now will begin to play a secondary and support role to Tumblr. So Flickr becomes the preferred photo sharing service for Tumblr.
Unlike the traditional acquisition where the acquired company disappears, this is the case where the acquiring company will disappear.
Yahoo's ability to stay alive as a large profitable business for another 10 years is dependent upon this transformation.
It's only through this lens that any kind of financial analysis makes sense. Any traditional, or sensible financial analysis will come the logical conclusion that this is an utterly foolish move.
But if you're Google in 2002, Pay Per Click Ads is the company bet -- and today's $300B Google is the result.
Meyer is making the equivalent of Google's PPC bet -- however, the goals are not massive profits as Google's were, but Meyer's goal is to return Yahoo to a role of prominence and profitability as a consumer property.
(that being said, my bet is that this turns ends badly for Yahoo and especially the shareholders).
There is a third option, of course: that they have a stupid plan.