By Vince Ruscello
As the 2014 World Cup (Brazil) approaches, I think it is important to let the readers know that we at GPS can predict the results of each game, specifically the scores. This ability was especially important during the 2006 World Cup (Germany). (By the way, we can also predict hockey games & hurricanes.)
I was in Frankfurt trying to get a group of Master Black Belt candidates to ignore the Cup and to focus on a technical topic. The session was about using the Poisson & the related Exponential distributions to model event rates and the time between events. I think the initial example was about modeling calls to a call center. Even now, I can still feel the boredom of the class and their impatience to end the day.
Whether in the classroom, in a pulpit, or on stage, to command the attention of the audience, one requires a hook, an opening story, a compelling reason for the audience to continue to listen. Calls to a call center is not a gripping topic for most people. But high interest in World Cup Soccer in Europe, and especially in Germany in 2006, provided a perfect opening for a narrative on a topic that has many real-world applications. For World Cup fans, consider the following:
In the last six World Cup tournaments, from Italy in 1990 to South Africa in 2010, the goals/match has followed a near-perfect Poisson distribution – the average goals/match is 2.4. This fact provides a lot of predictive power. For example, the probability of 90-minutes of play ending in a 0-0 tie is around 9%. So, almost 1 in 10 games will be decided by goals only scored in overtime or a shootout. Relatedly, the probability of five or more goals scored in regulation play is also less than 10%, giving credence to some soccer critics’ complaints about the lack of action.
The time between goals can also be predicted with the Poisson-related Exponential distribution. In this example, the mean time between goals is the defining parameter of the Exponential. The mean is estimated by dividing the game time, 90 minutes, by the average goals/game, 2.4. Result: 37.5 minutes. This value can be confirmed with the actual goal times from data obtained from the FIFA website. Goodness-of-Fit tests confirm that the Exponential distribution is a good model of the shape of the inter-goal times.
How can we use predictions of the inter-goal times? As you are watching this year’s games, know that the probability of the final score remaining the same as the half-time score is only 30%. And, more importantly, there is still a 25% chance that the score will change in the last ten minutes. But with five minutes to go, there is only a little more than 10% chance of a score change. Of course it may change for the worse for your team…
For those who are not soccer fans, the sporting world and natural world are full of other examples. For hockey fans, for example, Wayne Gretzky’s performance as an Edmonton Oiler in points/game is easily modeled with a Poisson distribution. It is likely that many baseball statistics, walks, hits, runs, errors, home runs, etc. could be modeled the same way.
The Poisson distribution can also be used to characterize many natural phenomena. I live in Florida, and the beginning of June also brings the beginning of hurricane season. Since hurricane Katrina hit the Gulf Coast and Sandy hit the mid-Atlantic, interest in hurricanes has expanded well beyond Florida. The annual forecast for specific hurricane activity, that is, named storms, hurricanes & major hurricanes, varies year-to-year and has recently been released for 2014. The overall forecast for hurricanes that will make landfall in the US, however, has been unchanged for more than 160 years, climate change notwithstanding.
Like many other natural phenomena, the distribution of hurricanes that make landfall in the US follows a Poisson distribution with an average of about 1.8 hurricanes/year. So, we can predict the probability of a year with zero hurricanes – about 17%. Worried about another year like 2005 (six hurricanes including Katrina)? The probability is around 1%.
When training, of course the usual goal is to tie the use of the tools to industrial or managerial problems. It is much easier to do so, though, after the class has begun to learn the subjects from examples that generate more initial interest.
What about the MBB class in Frankfurt? We quit early and went to a pub to watch Germany play. We called it “Team Building.”
(Thanks to Singfat Chu (National University of Singapore) for the World Cup idea and Byron Schmuland (University of Alberta) for the Gretzky example. Any faults with the hurricane data are all mine.)