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Prior Probability of Startup Success [Bayesian Inference
Posted on April 10, 2013 @ 10:26:00 AM by Paul Meagher

One of the pieces of data you should have in your mind as a Bayesian Angel Investor is the prior probability that a startup will be successful. According to Funders and Founders the success rate for first time startups is 12%, going up to 20% if the founder failed in their first effort, and up to 30% if they are a veteran (3 or more kicks at the can).

One way to look at this data is that the success percentages for a startup go up from 12% if you conditionalize your estimate on knowledge about how many times the startup has attempted to start a company. So this could be viewed as one evidence factor to consider when evaluating whether a company will be successful or not (e.g., number of startup attempts).

Another aspect of this data to note is that while 12% may seem like a small percentage, it is not so small (say 1%) that new knowledge is going to keep the conditional probabilities so low that you cannot make a confident decision. Early screening for breast cancer (e.g., at age 40) is difficult, in part, because the base rate of breast cancer at age 40 is so low (1%) that even if you do have a fairly good test (80% true positive rate), and that test is positive, it will only increase the probability of a cancer diagnosis to approx. 8%. With a 12% success rate for first time startups, we can potentially increase our estimate of a companies success rate by quite a bit by taking into account other information about the company. Two good diagnostic tests applied in sequence could get us up to a 80% probability estimate of startup success and increase the likelihood that you will make a good angel investment decision.

Research shows that even doctors are not very good at taking base rates (i.e., priors) into account and put too much emphasis upon the test accuracy to arrive at conditional probability estimates for a diagnosis. Their estimates can be improved considerably if instead of being given information in a probability format (0.12 probability of first-time startup success), the information is presented in a frequency format (120 out of 1000 first-time startups are successful). Sticking with numbers as frequency counts allows us to mentally compute more accurate conditional probabilities.

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