Two weeks ago me and a few friends went out for Schnitzel and Kolsch. As the topics of discussion bounced between the upcoming Germany vs England game and the recent Brussels attack I was reminded of the fate of the game between Germany and Holland following the Paris attacks. The coincidence that a big friendly match in Germany was again taking place so shortly after such attacks sent us down the path of wondering if this game would also be cancelled.
Then the topic changed, but I decided nonetheless to investigate what the collective view of the group was. Did we think that one single event in the past could predict the next one?
So, I pulled my napkin from under my Kolsch and asked everyone in the group to scribble down what they thought the probability of the game between Germany and England being cancelled was.
29.7% chance of game being cancelled
I received 10 responses on the napkin, and it was clear that the degree in which people incorporated past events into future events varied quite a bit, to say the least.
Four people (including myself) – The Pessimists – thought that history was more likely to repeat itself than not. These people put the probability of the game being cancelled above 50%.
Six people in the group – The Optimists – thought that the chance of the game being cancelled was less than 50%. In fact, three of them thought there was no – zero percent – chance of history repeating it self and the game bing cancelled.
And collectively, the group thought the chance that the game would be cancelled was 29.7%.
A prediction market is born
After forgetting about the napkin and our topics of discussion topics changed again. And while we were discussing something else, I all of a sudden remembered my excellent ability to loose my money at iPredict, New Zealnd’s Predicion Market, and figured that I could open one up a similar market right there at the pub.
With the objective of trying to get as many of the people sitting around the table participating in the market but not expose myself nor anyone else to substantial financial losses I figured I had to properly design how this market should work.
First, to get people onboard without exposing them to substantial financial risk I decided to set the participation fee at £1.00. This amount was then the maximum potential loss of any single participant. Such an immaterial amount would indeed ensure that the market would not send anyone into receivership (that includes me, the market maker itself).
Second, I wanted to ensure that once time had passed and the outcome of the bets was clear that I would neither stand to gain nor loose from this venture of mine. And in order to do that I offered my colleges the odds calculated fairly on the average stated probability on the napkin above, 29.7%.
Following these rules, I came up with the two following offers and presented them to my friends (In both cases the buy-in was €1.00):
- if you think the game gets cancelled and the game does get cancelled you receive €3.30;
- if you think the game will not get cancelled and the game goes on you receive €1.40.*
At this point, since I had designed the bet exactly in line with the population views of the odds, I was fairly certain that the people on the table would indeed bet exactly in line with their previously stated probability. In which case three people would take the “game will be cancelled” bet and seven people would take the low paying “game will go on” bet.
And here comes the however
However, time had passed since the original survey had been carried out and new people had joined the table. This meant that the information I had gathered on my first napkin was no longer a survey of the entire population and the new joiners on the table could indeed have different view of the probability than the survey population.
Indeed, all three new joiners to the table looked at the odds on offer and every single one of them purchased the “game will be cancelled” bet. And this left me in exactly the position I did not want to be in. If the game got cancelled, I would end up loosing €7.20, and if the game went on I would gain €3.04. This was a significant change from my previous range which was purely made up of of rounding errors (-€0.04 to €0.10).
When I saw this, I realised that the original population surveyed was probably a bit too optimistic. In particular The Optimists. And of The Optimists in particular The three Super-Optimists that had placed a zero percent chance that the game being cancelled. These people had caused me to put the “game being cancelled” odds to high and the other odds too low.
When taking into account the new table joiners and the fact that few people had perhaps been a bit to optimistic in their forecasts, I think that the true probability at the time was probably closer to 40%, and definitely in the range of 30-46%.
What this means is that my two different offers should probably have been priced closer to €2.40 (“game will be cancelled”) and €1.70 (“game will go on”).
The majority was correct, the game went on
As you all know now, the game went on. As my survey had implied that was not so unlikely, but another unlikely event occurred instead. After being down 2-0, the English national team staged a magnificent comeback and won the game.
While the actual good news is that the game was played and millions of people around the globe got to enjoy an exciting game on that Saturday. For me personally, a small bonus was that I had just made €3.04 profit. For seven of my friends, they also made a modest profit of €0.40 from these good news, but for six pessimists were a €1.00 out of pocket (at least in accounting terms since I probably wont collect the money from my friends.
Thanks for reading,
*In order to avoid taking any money on the night from my friends, I deducted one euro from each offer and told them they would receive either €0.40 or €2.30 if they were right, but would have to pay me one euro if they got it wrong. So, I subtracted one euro from the napkin odds amount.