GPS Technology and Computerised analysis of the collected data has found its way into many sports, especially Australian Rules Football.
GPS units are sewn into players Football jumpers, and the players tracked during a game. All of their movements around the ground are mathematically captured onto computer storage.
This data is mathematically processed by computers and then used as a standard part of post match discussions with Players.
Here is a short video which shows a post match GPS report for Hawks player Stephen Gilham.
Knowing some mathematics and computing could be useful, especially if you are considering a career path into professional football.
In today’s computerised world, an understanding of mathematical principles has become more important than ever in everyone’s daily life.
“Learn Maths Through Footy”
Image Source: Herald Sun Newspapers
The Melbourne newspaper the “Herald Sun” produces a very reasonably priced “Learn Maths Through Footy” PDF booklet each year during the Football season.This is an excellent publication and we highly recommend it.
Unfortunately, this year’s booklet finished selling around mid August. So if you missed out, then keep an eye out for the booklet next year.
The Herald Sun “LMTF” workbook includes a wide variety of activities, which vary from graphing to problem solving and geometry.
Each worksheet provides links to current football statistics to increase interest and engagement among students.
Here is a list of the “LMTF” 2011 booklet’s Worksheets.
1 A new angle
2 Accurate kicking
3 Club membership
4 Compare height & weight
5 Complex areas
6 Cost of lunch
7 Energy to burn
8 Evacuating the MCG – circles
10 Football grounds & area
11 Football ladder spreadsheet
12 Goal-kicking percentages
13 Ladder logic
14 MCG facts & figures
15 Number lines
16 Player injuries
17 Player salaries
18 Predicting results
19 Problem solving
20 Problem solving with equations
21 Stem and leaf comparisons
22 Using calculators to compare
23 Using graphs to compare
24 What’s in a name – probability?
25 Who is the best player?
Worksheet 5 is on Player GPS, and covers Perimeter, Area, and Speed.
If you do not have the 2011 “LMTF” Workbook, then there are some Free Worksheets on topics other than GPS available on this site:
Note that in this diagram, the player starts in the middle cross shaped part of the diagram and does the top left hand path. He then runs back through the start to do the bottom right hand path, and ends up back at the middle start point.
If you are using this type of problem with students who do not know Pythagoras Theorem, then it will be necessary to calculate the two missing sides and supply these values to students.
Maths Questions which can follow on from the above diagram are as follows:
1. What was the total distance the player ran ?
2. What was the longest continuous straight line distance he ran during this passage of play ?
3. If the player’s average speed was 1.6 meters per second, How long did it take him to run through this passage of play diagram? (Give answer in both seconds and minutes).
4. Find the area of the ground enclosed by the path that he followed ?
5. What activities might the player have been doing along this path, eg. chasing an opponent, taking possession of the ball, kicking the ball, returning to his set position, and so on.
AFL GPS Detailed Report
“FitSense Australia” undertook a detailed study of Player GPS data for the AFL using data gathered during several recent football seasons.
This study was conducted by FitSense Australia as a funded project by the AFL Research Board.
Full details of the Fitsense report can be found at the Link below.
What follows is a summary of some key parts of the report.
The main mathematics involved is related to Poynomials, and so it needs to be mentioned here that Junior School students will not have studied these yet, as they are a Senior School maths topic.
All game files were analysed using a number of steady state and movement pattern variables:
Total distance (km)
Average speed (km/hr)
Exertion index per minute
Time spent in speed zones (min:sec)
Number of surges over specified speeds
Longest continuous time above specified speeds (seconds)
Acceleration / deceleration profile
The word “exertion” refers to the active use of strength, power, etc. in relation to exercise, energetic activity, and effort.
“Exertion Index” is a quantifiable level of physical load developed by FitSense Australia. This measure allows a relationship to be drawn between game load, fatigue, and the total load between players.
The exertion index used to assess GPS data in the Fitsense study is based on the sum of a weighted instantaneous speed, a weighted accumulated speed over 10 seconds, and a weighted accumulated speed over 60 seconds.
This ensures both short sharp efforts, and long sustained efforts are analysed equally.
The weighting is based on a Polynomial Relationship in which high speeds achieve a higher exertion value than lower speeds.
Exertion index is measured in arbitrary units.
The formula to determine exertion index is:
Exertion Index = (Sum of EI1 + Sum of EI10 + Sum of EI60) / 300
EI1 = (v4 x 0.000009) – (v3 x 0.001) + (v2 x 0.0356) – (v x 0.0596) – 0.0172
EI10 = (V104 x -0.00003) – (V103 x 0.0004) + (V102 x 0.0477) – (V10 x 0.0476) + 0.1056
EI60 = (V604 x -0.00003) – (V603 x 0.0004) + (V602 x 0.0477) – (V60 x 0.0476) + 0.1056
v = speed in kilometres per hour captured at 1 Hz.
V10 = average speed in kilometres per hour of the last ten 1 Hz speed samples.
V60 = average speed in kilometres per hour of the last sixty 1 Hz speed samples.
“Exertion Index Per Minute” is a measure of game intensity and is determined by dividing exertion index by playing time.
“Efficiency” is a measure of the work requirements for game involvement and game impact. Measured by dividing exertion index by total number of possessions.
Results of the Fitsense GPS Report
Some key findings of the Fitsense GPS Report were as follows.
The game intensity estimated from GPS monitoring has increased by 17% in the period from 2005-2010.
The most successful teams completed less overall work. This pattern was evident when comparing top 4 to bottom 4 placed teams as well as all teams’ finishing position on the ladder.
This finding has important implications for recovery and injury rates as it indicates that performance level (and the underpinning factors of skill, tactics and coaching of both teams) can influence physical demands of the players.
Workloads were substantially lower in rounds 18-22 compared with other stages of the season (home and away games, and the final series). This contradicts the 2009 finding, however it is likely this varies year to year depending on the competition for finals positions towards the end of the season.
There was a 15% reduction in workload from quarter 1 to quarter 4.
Here at Passy World we have always thought that the bottom teams started “slacking off” during the final few games of the season, and we were correct!
It has been mathematically proven by Fitsense that average AFL player exertion drops during Rounds 18 to 22.
The average workload for these rounds was over 5% less than the season average.
This is shown quite clearly in the following “Box and Whisker Plot” from the “Fitsense” Report.
This difference is attributed to the best teams having superior coaching, tactics, and skills; which forces the weaker teams to “give chase” far more.
GPS is an amazing technology that has a variety of data collection and tracking capabilities.
Many company vehicles are fitted with GPS, and head office can see where a vehicle is at any time.
Companies also get alerts automatically sent from malfunctioning machinery that are offsite at customer’s premises, with GPS location of the machine provided on a map.
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