# Football’s a game of two halves

Ireland organise the greatest maths show on Earth! Maths Week Ireland. A week of mathematics lectures, shows, workshops, street maths and events happens every year around this time to link in with William Rowan Hamilton, the Irish mathematician’s discovery of Quaternions on the 16th October 1843. Quaternions are a strange kind of 4D algebra that did not have many uses until recently when Vodaphone used the algebra to improve data transmission. The rest is history and we now all benefit from ‘Hamilton super fast data’.

During Irish Maths Week I was invited to talk on the radio show “Savage Sunday” on Today FM. It’s never easy talking maths on the radio, as you usually find out pretty quickly that the presenter doesn’t like maths.

You need a hook. As always in teaching.

Later in the week there was a European Championship qualifying football game. Ireland was playing Germany away from home. I thought I’d make a prediction.

Mathematics cannot say for certain what the future will be but it can suggest possible outcomes that could occur, giving the probability that these may happen.

Predictions about how many goals could be scored in a match can be created by using the work of the 19th century mathematician Simeon Poisson.

The theory allows you to predict events that at first glance seem to be random or have little pattern. It is used, for example, to help to work out how many staff will be needed to work in a call centre at particular times in the day, or similarly to predict the size of queues at supermarkets checkouts.

For the football prediction you need Ireland’s past record against Germany as shown in the table below.

 Played W D L GS GA 18 5 4 9 22 34

From this information I worked out the average number of goals Ireland had scored as 1.22 and conceded 1.89. With these averages the Poisson Distribution gives the following probabilities for scoring and conceding goals.

 Goals 0 1 2 3 4 For 0.3 0.36 0.21 0.08 0.03 Concede 0.15 0.28 0.26 0.16 0.08

The mostly likely score for the Ireland Germany game works out to be a 1 -1 draw with a 10% chance of this happening. I checked my prediction by applying Poisson to all of Irelands games and felt confident.

You can hear my prediction on Savage Sunday TodayFM

On Tuesday night Germany scored first in the second half and things did not seem to bode well for my prediction, but then in the dying seconds of the match Ireland scored.

You might say I was lucky. I would say “Maybe, but luck can be helped along its way. By looking at chances, you can take certain actions to help make your good luck appear – well sometimes!”.

Steve Humble

### Collins Secondary

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