15 December: Mathematical models can predict a bit of everything
Today’s advent calendar researcher has a very definite grasp of probability, and among other things, applies his research to calculate lottery odds as well as how European Cup football matches affect the performance of Danish ‘Superliga’ teams.
Numerous everyday predictions are made possible with the help of mathematical theories and models – from finding out if interest rates will rise or fall, to predicting the number of goals in a football match.
Rolf Poulsen is a professor of mathematical finance at the Department of Mathematics. As someone who conducts research on financial markets, he is somewhat of an expert in probability. Much of his research can also be applied to other areas in society. For example, he has investigated whether Danish footballers’ Superliga play suffers if they have been playing European Cup matches.
"They don’t. My hypothesis is that when one says that playing European Cup matches comes at a cost, there is a post hoc ergo propter hoc effect. That is to say, if a team first plays a European Cup match and then performs poorly in the Danish Superliga, it becomes easy to conclude that the European Cup match was to blame for a subsequent Superliga failure. But, that’s just not the way it is.”
Football scores can be calculated
One mathematical theory, the Poisson distribution, can be used to calculate the probability of football results.
"By using the Poisson distribution, we can construct a mathematical model that takes a home field advantage and opposing team strengths into account, while also considering an independent modelling of a team’s defensive and offensive strengths. When the model is constructed, it can be used to come up with odds for bookmakers,” explains Rolf Poulsen, adding that it all gets rather technical quite quickly.
More questions than answers
His experience that more and more questions arise, as answers become fewer, is what prompted Poulsen down the research path.
“It was captivating that, the farther along I came in my education, it wasn’t the number of answers, but the number of questions that grew and grew. And within financial theory (and practice), the unanswered questions often deal with things that one would expect to have had “under control”.
While Rolf Poulsen’s research appears to be extremely theoretical, it can be applied to everyday matters. And this is precisely what Poulsen finds intriguing.
“Even the very theoretical quantitative finance models that we use are astoundingly useful.”