What are the success rates of startups with N founders, where N is a positive integer, for each value of N?
This question assumes a simplistic and absolute relationship between the number of founders and the success rate, which is difficult to isolate in the contextual variable-rich environment of startups.
To get the best perspective, I encourage you to read the "Startup Genome Report 01: A new framework for understanding why startups succeed" published on May 28th, 2011 by Max Marmer, Bjoern Lasse Herrmann and Ron Berman with support of Chuck Eesley, Steve Blank and Fadi Bishara and in collaboration with Stanford University, shared under Creative Commons License:
It's a rather long report, but very enjoyable (for some) to read. It has a summary section, with "primary" findings (which I'm skipping) and "additional" findings, which I'll cite here because it's related to your question:
Sample size of the following statistics: 663 web startups
Founders that learn are more successful: Startups that have helpful mentors, track metrics effectively, and learn from startup thought leaders raise 7x more money and have 3.5x better user growth.
Startups that pivot once or twice times raise 2.5x more money, have 3.6x better user growth, and are 52% less likely to scale prematurely than startups that pivot more than 2 times or not at all.
Many investors invest 2-3x more capital than necessary in startups that haven’t reached problem solution ﬁt yet. They also over-invest in solo founders and founding teams without technical co-founders despite indicators that show that these teams have a much lower probability of success.
Investors who provide hands-on help have little or no effect on the company's operational performance. But the right mentors signiﬁcantly inﬂuence a company’s performance and ability to raise money. (However, this does not mean that investors don’t have a signiﬁcant effect on valuations and M&A)
Solo founders take 3.6x longer to reach scale stage compared to a founding team of 2 and they are 2.3x less likely to pivot.
Business-heavy founding teams are 6.2x more likely to successfully scale with sales driven startups than with product centric startups.
Technical-heavy founding teams are 3.3x more likely to successfully scale with product-centric startups with no network effects than with product-centric startups that have network effects.
Balanced teams with one technical founder and one business founder raise 30% more money, have 2.9x more user growth and are 19% less likely to scale prematurely than technical or business-heavy founding teams.
Most successful founders are driven by impact rather than experience or money.
Founders overestimate the value of IP before product market ﬁt by 255%.
Startups need 2-3 times longer to validate their market than most founders expect. This underestimation creates the pressure to scale prematurely.
Startups that haven’t raised money over-estimate their market size by 100x and often misinterpret their market as new.
Premature scaling is the most common reason for startups to perform worse. They tend to lose the battle early on by getting ahead of themselves.
B2C vs. B2B is not a meaningful segmentation of Internet startups anymore because the Internet has changed the rules of business. We found 4 different major groups of startups that all have very different behavior regarding customer acquisition, time, product, market and team.
I also completely agree with Ryan Lackey that there are diminishing returns on the number of founders above three -- primarily due to the network effect of the communication overhead, which is very expensive at such a fragile stage.
A small 2-3 founder team, balanced across different skill disciplines, well-positioned for learning from its mentor and investor connections, and not over-confident about its market positioning and IP, has the maximal chance of success. Deviations from this formula, depending on the variable, have drastic effects on the outcome.