Using Bayes Theorem for NI Startup Probabilities (#startups #clojure #statistics)

This is probably as close to serious as I’ll ever get on the subject, so hold on to your hipster pork pie hats…. The title headings are based on a fairly common path for Northern Ireland startups, other territories will have their own methods I’m sure. Regardless, I need a picture….


The Odds Are Against You.

The harsh reality is that the odds are stacked against you for succeeding. I’ll be ultra liberal with my probabilities and say 4% (I should really be saying 2% but it’s a Bank Holiday Weekend and I’m in a good mood and not my grumpy self). This number could be quantified by mining all the previous startups and seeing who lasted longer than 3 years for example. So four in every hundred isn’t a bad starting point. Let’s call this our prior probability.

What we’re trying to establish is that if an event happens during the startup journey what will that do to the existing probability. The nice thing with Bayes, as you’ll see, is that for every milestone event (or any event) we can re-run the numbers. Ready?

Wow! We Got Proof Of Concept 40k!

Current Prior Probability: 4%

Great news! The good folks at TechstartNI have shone the light on your idea and given the clawback funds for you to build via a respected development house or developer. Will that have an effect on our post probability? It may do but PoC is not a confirmation of your startup really, just access to build.  What we can do though is use Bayes Theorem to recalculate the probability now we have a new event to include.

Bayes In Clojure

So Bayes works on three inputs, the prior probability (in our case the 4% figure we started with), a positive impact on the hypothesis that you’ll last longer than three years and a negative impact on the hypothesis that you won’t last longer than three years.

Assuming that x is our prior, y is the positive event and z is the negative event. We can use the formula: (x * y) / ((x * y) + (z * (1 – x)))

If I were code that up in Clojure it would look like this:

(ns very-simple-bayes.core)

(defn calculate-bayes [prior-prob newevent-positive-hypothesis newevent-negative-hypothesis]
  (double (/ (* prior-prob newevent-positive-hypothesis) 
             (+ (* prior-prob newevent-positive-hypothesis) 
                (* newevent-negative-hypothesis (- 1 prior-prob))))))

(defn calculate-bayes-as-percent [prior-prob newevent-positive-hypothesis newevent-negative-hypothesis]
  (* 100 (calculate-bayes prior-prob newevent-positive-hypothesis newevent-negative-hypothesis)))

The first function does the actual Bayes calculation and the second function merely converts that in to a percentage for me.

Right, back to our TechstartNI PoC. Let’s see how that affects our chances of survival.

Just because PoC funds give you some ground to build a product it has little impact on the survival of the company as a whole. Being liberal again let’s say the positive impact on the hypothesis is 90% and the negative will be 10%. Can only be a good thing to have a product to sell.

very-simple-bayes.core> (calculate-bayes-as-percent 0.04 0.9 0.1)

While PoC has a huge effect on you getting product out of the door (do I dare utter the letters M, V and P at this point) it has little effect in your long term survival. So your 4% chance of three year survival has gone to 27.2%. A positive start but all you have is a product.

Put the Champagne on ice just don’t open it…..

Propelling Forward

Current Prior Probability: 27.2%

The next logical step is to look at something like the Propel Programme to get you in the sales and marketing mindset but also making you “investor ready” which is what I see the real aim of Propel to be. So with the new event we can recalculate our survival probability. The 20k doesn’t make a huge dint in your survival score, it helps you get through though, I will take that into account.

As I’ve not experienced Propel first hand it’s unfair to me to say how things will pan out, you’ll have to ask someone who’s done it. It doesn’t, though, stop me guessing some numbers out of the air to test against, and you should really do the same.

Propel will have a positive impact on your startup, no doubt, there’s a lot to learn and you’ll be in the same room as others going through the same process. The “up to” £20k is good to know but there’s no 100% certainty, apart from death and taxes, that you’ll get the full amount.

Propel’s positive probability on hypothesis: 40%

Propel’s false positive probability on the hypothesis: 80%

Running the numbers through Bayes again, let’s see what the new hypothesis probability is looking like.

very-simple-bayes.core> (calculate-bayes-as-percent 0.272 0.4 0.8)

That brought us back down to earth a bit. 15.74% chance of a positive hypothesis. No reflection on Propel at all, that’s just how the numbers came out. Now I could be all biased as say that if you do Propel you’re gonna be a unicorn-hipster-star but the reality is far from that.

The false positive is interesting, doing these things can sometimes fool the founder into thinking they’re doing far better than they think they are. If 100 startups went through Propel and 40 are still trading today then our positive event probability is right. And that’s the nice thing about applying Bayes in this way, we can make some fairly reasoned assumptions that we can use to calculate our scores with.

I’m Doing Springboard too Jase!

Okay! And the nice thing is these things can happen in parallel, but looks treat it as a sequential matter to preserve sanity in the probability.

Current Prior Probability: 15.74%

I think the same event +/- probabilities would apply here. Springboard is good for mentorship and contacts. My hand on heart gut thinks the numbers are going to be the same as Propel’s for what we are looking at here.

Springboard positive hypothesis: 40%

Springboard as a false positive on hypothesis: 80%

Let’s run the numbers again (now you can see why I wrote a Clojure program first).

very-simple-bayes.core> (calculate-bayes-as-percent 0.1574 0.4 0.8)

Interestingly, according the numbers, doing the two programmes has a negative impact on your startup if you have no revenue and no customers, well the numbers say so.

Getting That First Seed.

Current Prior Probability: 8.54%

Okay, so you’ve your Proof of Concept in hand, grafted through Propel and then gone through Springboard until your get that nice picture on the website. “Investor Ready” is an odd term, markets can change, fashions come and go and investors go looking for different things as time goes by. So all the while you’ve been slaving investors could be looking for something else.

So the opportunity arrives to pitch to one of the NI based VC’s/Angels for some “proper” money. Once again a fairly normal route to go down. It could be a mixture of different funding places (Crescent, Kernel or Techstart). If accepted the goalposts change as it’s people on the board and results focus (ie are you hitting target month on month).

The average figure for a seed round in NI is between £150-£300k but I’ll head for the upper figure. Regardless money in the bank (even though it’s not yours) is a good thing if you are prepared to give up some equity. Saying that investments can go bad, so we need to ying and yang this out a bit. So I’ve put in that there’s a 20% chance of the investment being a false positive. Once again if you had the term sheets of 20 companies you’d be able to do some maths yourself to get a better idea.

Seed round has positive outcome on hypothesis: 70%

Seed round has is a false positive on hypothesis: 20%

Investment is good PR and the hype cycle loves a good startup investment story. it opens up the doors to talking guff in far more many places than you did before. How does that affect our probability though?

very-simple-bayes.core> (calculate-bayes-as-percent 0.0854 0.7 0.2)

Positive indeed. From 4.0% to 24.6% is good. From 1 in 25 to 1 in 4 chance of lasting three years, though the majority hinged on investment in the latter stages of you getting investment. There’s a chance by this point you’d be two thirds the way in of the three year plan.

Blessed Are The 2%

At the start I used 4% as a very optimistic probability of a startup lasting more than three years. I wonder what would happen if I went for a realistic start point of 2%?

Proof Of Concept Stage

very-simple-bayes.core> (calculate-bayes-as-percent 0.02 0.9 0.1)

Propel Stage

very-simple-bayes.core> (calculate-bayes-as-percent 0.1551 0.4 0.8)

Springboard Stage

very-simple-bayes.core> (calculate-bayes-as-percent 0.0840 0.4 0.8)

Investor Stage

very-simple-bayes.core> (calculate-bayes-as-percent 0.0438 0.7 0.2)

So a 1 in 7 chance of you lasting 3 years….. you can also finally put your “passion” line to bed as well.


You can see why some folk decide to hold startup events. The risk is far lower and the chances of sponsorship are increased and repetitive. Saying that we know that those who want to work 17 hours a day by the seat of their knickers will continue to do so. Depending on your point of view it is indeed easier to sell the shovels instead.

And As For That Champagne….

marilynMarilyn drank it.











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