# The concept of expected value in the context of valuations

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I’m reading an article on a hypothetical drug that’s coming to market in the next 6-7 years. The value of the drug is around \$1 billion but it has a 35% chance of passing Phase I and II trials. As a result, the drug has a valuation of 350 million (i.e. \$1B x 35%).

How does this make any sense? How can you use probabilities to value a drug here based on its probability of success?

I’ve read this in other areas too e.g. the probability of a product failure is 23% so if the product costs \$100, the warranty should cost \$23 (i.e. \$100 x 23%).

I’ve tried to believe that this can be quantified e.g. for every 100 products we sell, 23 of them will fail (as percentages are out of 100) so we should charge a warranty of \$23 since we will spend \$2300 on fixing 100 products if those costs are not made back.

However, in the case of the drug pipeline, I don’t understand how this works. As far as I can deduce, for every 100 times you push the drug through, only 35 attempts will be successful. So, the drug will make you \$350M for every time (on average) it passes a test. I don’t understand what the \$350M means in this case.

Any help to wrap my head around this concept would be appreciated!

In: 55

It’s just as simple as you described. You’re basically making a gamble here. 35% of the time you make a Billion dollars so as long as your invest is less than 350 Million its a favorable bet to make. When you get down to the real world everything is about statistics. Absolutes dont really exist in nature.

>The value of the drug is around \$1 billion but it has a 35% chance of passing Phase I and II trials. As a result, the drug has a valuation of 350 million

They came up with “we would make \$350M” here.

>For every 100 times you push the drug through, only 35 attempts will be successful. So, the drug will make you \$350M for every time (on average) it passes a test.

You came up with “they would make \$350M” here.

You came to the same conclusion that they did.

Because the outcome of doing the thing once is uncertain, we quantify it by basically asking what would happen if we somehow did the identical thing a bunch of times. It’s the average outcome you’d expect.

It’s not a real quantity, and it might not be one of the possible outcomes, but it gives you an idea of whether you would expect it to be a good bet.

From the perspective of an investor and/or pharmaceutical company this valuation makes sense right? As an investor / company you want to invest your time and money in the most profitable projects. Since there are a lot of potential medicines you will need to establish criteria how to choose the right ones to invest in. This is one of the possibilities on how to do this. Key aspects in the decision making are indeed the total value or sales potential (the amount of people needing the medicine * the price that can be asked). The second key aspect is the chance the drug will be allowed to enter the market. In most countries the FAA or similar bodies are very strict and the drug must showcase a good positive effect, limited side effects and many other points. In general, 9/10 hypothetical drugs will not enter the market so you can imagine this is a crucial aspect in the decision making.

And you are right, the outcome of the value for your hypothetical drug is indeed either 0 (when not passing trials) or 1 billion (when passing) but since this will happen in 35% of the time it makes sense to value it like this, as it serves as a benchmark compared to other hypothetical drugs with other potential values and passing chances.

>As far as I can deduce, for every 100 times you push the drug through, only 35 attempts will be successful. So, the drug will make you \$350M for every time (on average) it passes a test. I don’t understand what the \$350M means in this case.

Close – it’s more that “if we made 100 drugs with the same value and chance of passing tests, 35 of them would pass and make us a billion dollars”. Which won’t actually happen, each drug they invent will have its own value and probability of passing. And each drug either will or won’t pass – you’re not actually going to get \$350,000,000 worth of value out of the drug, you’ll get a billion or nothing. But in aggregate, over the years if you invent hundreds of different drugs and have good estimates for the probability of passing the necessary trials, you can estimate how much you’ll make based on the expected value calculations of each drug.

If you had a coin you could flip and it paid \$10 if it came up heads and \$0 if it didn’t, you’d calculate the expected value of a flip to be \$5. One coin flip will either give you \$10 or \$0, there’s no way to wind up with \$5 from playing once. But if you played 10 times, then you’d have ten 50/50 chances, and you could easily end up with \$50 at the end. You might end up with \$40 or \$60 instead, because a 50/50 chance doesn’t mean you’re guaranteed an even split of outcomes, but the more times you flip it, the closer your winning would get to the expected value.

How they actually come up with the estimate for how likely it is to pass I have no idea, and getting an accurate estimate makes a big difference in how well your actual results will compare to your calculated expected value in the long run.