Why would it be a stupid move to invest in a company whose success would make you more money?
If I were Sequoia, choosing between two companies with the same credentials and equally good business models, I would choose the one backed by YC because its success could potentially make me more money in the long run.
Because if the startup wasn't one they'd have funded otherwise, it would be the world's most extreme case of throwing good money after bad. They'd be investing millions to improve their return on an investment of tens of thousands.
Welcome to the difference between theory and practice. In theory you are right. In practice you are not.
I don't know the terms of the deal, but suppose that Y-combinator had a 10% stake in a startup, and Sequoia gets 1/4 of that. Let's suppose you're looking at a round of financing that would dilute that ownership by half. Then Sequoia's investment amounts to an extra 1.25% stake in the company post deal. So if they could get a 50% stake in another company that has a 2% better returns, they would get a 1% better returns from the better company and a 1.25% better returns from their stake, and therefore should go for the Y-combinator company. Right?
Wrong. Sequoia knows that if they pass on something that is almost good enough for them, it is still likely to be picked up by someone else. (Particularly if they let people know that it was borderline.) So they have to think through the difference of having them versus the next VC investing in that opportunity. There is a difference, but it is not actually that big. Therefore even a 1% difference in the two companies should not change their decision.
And when they are making these decisions, there is no way they are trying to measure things to 1% accuracy. So the right thing for them to do is ignore their stake in the Y-combinator investment entirely.
It's not like Sequoia is capital restricted and has to choose between multiple good investments. They have way more money than good opportunities. If they see two companies that are equal they are probably investing in both or neither.
If I were Sequoia, choosing between two companies with the same credentials and equally good business models, I would choose the one backed by YC because its success could potentially make me more money in the long run.