# Maths in relation to Field Hockey

Hockey is a sport which I have played since I’ve been in primary 4. It’s something I train for 3 times a week whilst playing 2 games throughout the week. However, even though I’ve played this sport for many years I had never thought about the connection and relation it had to maths. Therefore, after being told to think about this before class I was very surprised how many links I found there were.

The Rules for hockey are as follows:

1. 1. It’s an eleven-sided game, meaning you are allowed to have a maximum of eleven players on each team playing on the pitch. Each team will have one goalkeeper and ten field players. Although only eleven players are allowed on the pitch, normally a hockey team will consist of fifteen players as subs will be needed.
2.  In hockey the ball is not allowed to hit your feet unless you are the goalkeeper. If the ball is kicked then it’s a foul and the opposition gets the ball.
3. To score you must be in the attacking “d”. This is a semi-circle around the goal.
4. Raised balls are not allowed above knee height as this is classed as a ‘dangerous ball’ and will be a foul. However, a raised ball called an Ariel is allowed. This is a very high ball which is above head height.
5. Stick tackles are not allowed in the game of hockey. If there’s a slap to a stick and a loud noise is made when a tackle is made, then that is a stick tackle. This will be a foul and the ball will be given to the opposition to take from where the stick tackle occurred.

Strategies

I then used my own knowledge of the game in finding strategies for playing hockey effectively. In field hockey they are different strategies and tactics both defensively and attacking to result in success.
The main strategies for hockey are formations. With a goalie in the goal defending at the back, there are ten outfield players. This means you have ten players to create formations with. Below are two common different starting formations. Obviously, these will change depending on what team you’re playing and where their strong players are on the pitch. The way the opposition presses against your team’s hit out can also be dependent on your team’s formation. It also depends on where your area of strength is in the players you have on the pitch within your own team as well.

Hockey in relation to Maths

After doing research I realised the many connections field hockey has to maths. The design of the pitch is in the shape of rectangle which is separated into four sections. There are 3 lines marked across the pitch marking the 25m line, the 50m line (half pitch) and the 75m line. A hockey pitch also consists of two semi circles that make out 180 degrees which is called the “d”.
After our lecture on chance and probability, it made me think of this topic in relation to the game of hockey. It made me question what’s the probability of a successful attacking 3v2 situation? Or what’s the probability of 5 average attacking hockey players beating 3 very strong defenders? Or what are the chances for a goal in a 1v1 situation with a striker and a goal keeper?

After reading articles online of maths in hockey it made me realise how the smallest of things in the sport are related to maths! For example, the different shapes we form when passing, eg. triangle passing. As a defender it made me think how far away the defensive line should be from one another when we are talking a defensive hit out for it to be successful. For the hit out to be successful then it must eliminate some of the attacking line in the opposition. This topic has made me want to investigate this further and in more technical terms by measuring out the distance of how far away we should be standing from each other.

More math related aspects to field hockey

1. The make of the ball, for example whether it’s a kukri or Slazenger ball. Each make of ball feels different to play with.
2. The surface of the ball – some balls have a smooth surface all around the ball, whereas some have little circular dips around it.
3. The speed of the ball when it is passed. The speed changes depending on if the ball was sent as a slap, a push pass, a sweep, a hit, a small raised ball or an aerial.
4. Position of hands on the stick, finger positions.
5. Angle and position of the stick when the ball is received and passed.
6. Angle and position of body and stick in a tackle.
7. Eye level behind the ball when passed/hit.
8. Body weight distributed between both feet whilst hitting the ball.
9. Motion of swing when hitting the ball.
10. The strength behind each pass.
11. The pressure of how tight you hold the hockey stick.