By Marcus Wilson 10/05/2016

Probability crops up in many places in physics, not least quantum mechanics and statistical mechanics where we are only sure of things in an average or ‘statistical’ sense. Dealing with probabilities can be a headache for many students. They are also a headache for many in everyday life.

There are numerous occasions where we need to estimate the likelihood of something occurring and we can get it very wrong indeed. What is the probability of encountering a monster traffic jam on the way to Auckland Airport – just how early should I leave for that flight?  What are the chances that my visitor will actually turn up on time – or at all?  Bookmakers make their living on estimating probabilities so it’s always amusing when they get it wrong (I have deep issues with gambling).

### According to the odds

First, congratulations to Leicester City on winning the English Football Premiership.

At the beginning of the season, so I am led to believe by Radio NZ, one of the major bookmakers in the UK had them as 5000-1 outsiders. That’s five THOUSAND to one. Moreover, they thought it more likely, according to the odds that they were offering, that in the coming year:

1. Conclusive evidence would be found of the existence of the Loch Ness Monster

2. Barak Obama would declare the moon landings as faked

3. Elvis Presley would be discovered alive

Really? Come on. Yes, Leicester’s success was unlikely, but THAT unlikely? They had a flurry of success right at the end of the 2014-2015 season, avoided relegation (comfortably in the end) and changed their manager. There were hints that things could go well for them the following year. Offering such extremely long odds seems to fly in the face of the evidence that was there. Rank outsiders do occasionally win sporting events, or elections. It doesn’t happen only once every five thousand times.

### Assessing business opportunities

I remember when I worked in industry in the UK we had an online tool for assessing business opportunities. If we put in a bid or project proposal to a customer, or were even having preliminary discussions with a potential customer, we entered the details into a database including such things as the likely size of the contract and what the probability was of winning it. That would be used to help with our financial planning.

However the reality, as our accountants kept telling us, was that the average person who had discussions with potential customers (for example, myself) was very bad at estimating the probability of success. We tended to severely overestimate the probability. That was evident just from an analysis of what we said were the chances and what actually transpired.

For example, they could pick out the entries where we said there was a 50% chance of securing funding and look at what fraction were actually funded. It wasn’t anywhere near 50%. Given that the organisation was full of mathematicians and physicists, this was quite amusing.  It shows how difficult it is to get a real handle on probabilities.

I’m not sure what the accountants did with our estimates, but they probably halved them or more. Which is what I’ve done with my estimated chance of having my Marsden Proposal get to the second round. I find out later this week.