If there is no proof up front then best case it will be equal, worst case it will be (much) worse. Contrary to popular belief investors are conservative, they will gamble on the companies involved but they are less likely to gamble on changing the formula.
There are a number of questions that need answering before you can get someone to take a bigger risk.
20 start-ups at 20K = 400K invested, 20 shots at a payout of a million or more.
5 start-ups at 80K = 400K invested, 5 shots at a payout of a million or more.
The chances of any one of those 5 being successful are not nearly 4 times as high as any one of the 20, and you'd have to cross that hurdle for it to make sense for a VC to drop their working model in favour of your unproven one.
In my opinion, when it comes to seed capital, the amount is the lesser factor in determining success, so I would figure that the chances of success are exactly equal for each of the five as they are for each of the twenty. So it is the other method that has a 4x higher chance of success!
Why not just do $1k x 400 investments, if the number doesn't matter? Obviously it does matter.
The current YC investment size was an estimate based on their own experience raising angel money for Viaweb. It's not some magical number arrived at through hard analysis. It's essentially a guess.
There's no way to know if it's the right number or not. YC can't know who isn't applying. I suspect they're losing out on a large number of the most promising candidates.
Because $1k is too small an amount to be useful. But I think you are not really serious here, you are just trying to argue your point from extremes.
$20k is a useful amount, it will get some work done. $80k is not that much more useful but it is 4 times as much.
$10k is probably still too low.
You optimize the number, and around $20K there is an optimum for the target audience that YC tries to reach, and it makes sure that you don't get a bunch of gold-diggers that see the investment itself as a success.
$20k is enough to get a boatload of applications. YC is limited by the # of people they can invest in, NOT by the # of applicants. They are constantly turning away great startups due to having limited slots. Upping the amount they invest per startup would only help them if they took commensurately more equity ($80k = 24%+). With limited slots, they are simple trading great startups with lean-living co-founders for great startups with a higher price tag.
Who isn't applying? The YC process is -- survive 3 months on ~$20k. Survive 3-4 more months as you raise more money or get to profitability. Presumably you have savings or friends/family you can borrow from. How about a HELOC?
Honestly, if you can't find some way for 2 people to survive on $20k for 6ish months, you're probably either a pretty lousy life-hacker or you've had some bad luck. Either way, you're a bad bet compared to the alternatives.
But, again, if your startup is badass compared to YC applicants, fundraising shouldn't be a problem.
My impression is that they arrived at that based on what it would take young people to live frugally in the area until they built their product and got funding.
They have a very large pool of applicants to choose from even with the small amounts the invest. I think if they decided that they needed to increase the size of the talent pool to get enough quality groups, they would look into ways (such as increasing the investment amount). As it is, they don't seem to need to, so why would they?
There are a number of questions that need answering before you can get someone to take a bigger risk.
20 start-ups at 20K = 400K invested, 20 shots at a payout of a million or more.
5 start-ups at 80K = 400K invested, 5 shots at a payout of a million or more.
The chances of any one of those 5 being successful are not nearly 4 times as high as any one of the 20, and you'd have to cross that hurdle for it to make sense for a VC to drop their working model in favour of your unproven one.
In my opinion, when it comes to seed capital, the amount is the lesser factor in determining success, so I would figure that the chances of success are exactly equal for each of the five as they are for each of the twenty. So it is the other method that has a 4x higher chance of success!