Quantitative analysts (quants) and statisticians are much in demand in a wide number of jobs and can command salaries within sports trading of between $50,000 and £750,000. For similar roles with banks and hedge funds, salaries can be significantly more than this when taking into account annual bonuses.

Statistical analysis is used widely in the planning of events such as natural disasters and their frequency of occurrence. By modelling such events it becomes possible to predict the most likely outcome of an event and to target resources where possible in an attempt to minimise the effects of the event. An event such as the Indian Ocean Tsunami that occurred on Boxing Day in 2004 was an unforeseen event and so was received with much shock as well as surprise, but other events in nature are more predictable and amenable to statistical modelling.

The insurance industry has to have some understanding of their likely exposure to risk – low risks may include paying out to homeowners when their homes are insured and there is a burglary or fire damage. Much more severe risks include paying out insurance on properties in regions that are annually hit by severe weather systems such as those that occur in the Caribbean and Gulf of Mexico. Investment banks rely on risk models to build the best portfolio of assets based upon historical returns on each stock in the portfolio. Portfolio theory is based upon the correlation of stocks within the portfolio and the objective is to produce a portfolio that will give maximum return for a given level of risk (volatility of a portfolio). Risk models are generated based upon the annualised performance of assets within a portfolio in terms of the correlation of each stock in the portfolio with all other stocks.

Monte Carlo simulations are often employed to model the various contributions that make up a single event. Each contribution can be appropriately weighted to reflect its contribution to the overall outcome. Monte Carlo models are stochastic models where random variables are used in the modelling process. A very simple example where Monte Carlo simulation is used is in the estimation of a value for pi. Consider a circle within a square; we can generate random variable pairs easily with a computer. If the magnitude of any pair falls within the circle we add this to the total of hits within the circle. The total number of points inside and outside the circle is also recorded and the ratio of number of points in the circle to the total number of points is proportional to the value of pi after many thousands of iterations.

Monte Carlo simulations are also applied to the modeling of financial risk and in physics to model a wide range of phenomena such as an estimation of the density of states of an amorphous solid in response to a laser pulse that generates free charges that decay with time.

Predicting the outcome of football matches is not necessarily about predicting the exact result of every match with a high degree of accuracy, but predicting the most likely outcome of a game based upon past performances of each team. Quantitative analysts are in great demand at the moment since predicting the most likely outcome of a sport’s competition gives those who set the odds for the match an edge over the people who gamble money on the outcome.

Professor David Spiegelhalter and his team of statisticians at Cambridge University have analysed many years of football results and applied a statistical analysis to the outcome of future games. In their analysis they calculate the average number of goals scored so far in a season and divide each team’s goals scored by this value – the teams at the top of the league will have a better goals scored to average number ratio than those at the bottom of the league.

They also determined the average goals scored for teams playing at home and the average goals scored by teams playing away from home. Thus, every team will be assigned an attack strength ratio (goals scored / goals scored) and a defensive weakness ratio (goals conceded / goals scored) and a weighting based on their home and away results – this weighting is the average number of goals scored per team at home and the average number of goals scored away from home.

In an example given in the paper Understanding uncertainty: Football crazy the Cambridge team analysed a match between Hull City v Manchester United.

The average number of goals scored by a home team in season (to March) 2008-09 was 1.36 and for an away team = 1.06.
Manchester United’s attacking strength = 1.46 and Hull’s defensive weakness = 1.37
Hull’s attacking strength = 0.78 and Manchester United’s defensive weakness = 0.52

The expected number of goals scored by Mancheter Utd = 1.06 x 1.46 x 1.37 = 2.12
And the expected number of goals scored by Hull City = 1.36 x 0.78 x 0.52 = 0.55

Additional factors that may affect the outcome of a match may also be taken into account; this requires a bivariate Poisson distribution to be used.

Since no team scores 2.12 goals, this is the average result if the match were to be repeated many times. To obtain the most likely number of goals Manchester Utd might be expected to score, we use the expected goals, 2.12, as the mean in the Poisson distribution. This gives a score of 2 goals (interestingly this is closely followed by the next most likely score of 1 goal – which was the actual number of goals scored by Manchester Utd in that game).

Sports trading is a growing industry with bookmakers amassing large profits from attracting clients to place bets with them. As with all businesses, they need to maximise profit and to do this they need to gain an advantage in the marketplace. In order to achieve this objective gaming companies are willing to pay up to £100,000 in salaries for quantitative analysts. A typical quant analyst that they would look to recruit would have commercial experience in statistical modelling and have an interest and knowledge of football. They would most likely have degrees in mathematics or physics and would ideally be educated to PhD level.