CONVERSION KICK

When a try is scored by putting the ball down behind the line, the scoring team gets to take a conversion kick. This kick must be taken in line with where the try was scored but it is up to the kicker how far away the kick should be taken. But how far back should the ball be taken to make the kick easiest?

Too close (red) and too far away (blue) will give small angles to aim at. Somewhere in the middle is needed (green).

Too close (red) and too far away (blue) will give small angles to aim at. Somewhere in the middle is needed (green).

One way to answer this question is to look to maximise the angle between the posts which the kicker will have to aim at: if the kick is taken too close to or too far from the goal line there will be a very thin angle to aim at. Somewhere between these extremes there will be a maximum angle to aim at.

When looking to maximise this angle, we can use one of the ‘circle theorems’ which have tormented many generations of GCSE maths students: ‘angles subtended by the same arc at the circumference are equal’. This means that if a circle is drawn going through both posts, then the angle made at any point on this circle will be the same.

The angles made by the red and blue lines are equal because 'angles subtended by the same arc at the circumference are equal'.

The angles made by the red and blue lines are equal because ‘angles subtended by the same arc at the circumference are equal’.

A larger circle drawn through the posts will give a smaller angle. If a vertical line is drawn which just touches the right of the circle, then the point at which it touches the circle will be the best place on this line to take a kick. This is because any other point on the line will be on a larger circle and so make a smaller angle.

Using this method for circles of different sizes leads to the following diagram, which shows where the kick should be taken for every position a try could be scored:

The best place to take a kick?

The best place to take a kick?

This, however, is not the best place to take the kick.

Taking Account of Height

When a try is scored near the posts, the above method recommends a position from where the ball must be kicked at an impossibly steep angle to go over. To deal with this problem, we are going to have to look at the situation from the side.

When kicked, the ball will travel along a parabola (ignoring air resistance and wind as their effects will be small[citation needed]). Given a distance from the posts, there will be two angles which the ball can be kicked at and just make it over the bar. Kicking at any angle between these two will lead to a successful conversion. Again, we have an angle which we would like to maximise.

The highest (blue) and lowest (red) the ball can be kicked while still going over the bar.

The highest (blue) and lowest (red) the ball can be kicked while still going over the bar.

However, the position where this angle is maximised is very unlikely to also maximise the angle we looked at earlier. To find the best place to kick from, we need to find a compromise point where both angles are quite big.

To do this, imagine that the kicker is standing inside a large sphere. For each point on the sphere, kicking the ball at the point will either lead to it going over or missing. We can draw a shape on the sphere so that aiming inside the shape will lead to scoring. Our sensible kicker will aim at the centre of this shape.

But our kicker will not be able to aim perfectly: there will be some random variation. We can predict that this variation will follow a Kent distribution, which is like a normal distribution but on the surface of a sphere. We can use this distribution to calculate the probability that our kicker will score. We would like to maximise this probability.

The Kent distribution can be adjusted to reflect the accuracy of the kicker. Below are the optimal kicking positions for an inaccurate, an average and a very accurate kicker.

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The best place to take a kick for a bad kicker (top), an average kicker (middle) and a good kicker (bottom). All the kickers kick the ball at 30m/s.

As you might expect, the less accurate kicker should stand slightly further forwards to make it easier to aim. Perhaps surprisingly, the good kicker should stand further back when between the posts than when in line with the posts.

The model used to create these results could be further refined. Random variation in the speed of the kick could be introduced. Or the kick could be made to have more variation horizontally than vertically: there are parameters in the Kent distribution which allow this to be easily adjusted. In fact, data from players could be used to determine the best position for each player to kick from.

In addition to analysing conversions, this method could be used to determine the probability of scoring 3 points from any point on the pitch. This could be used in conjunction with the probability of scoring a try from a line-out to decide whether kicking a penalty for the posts or into touch is likely to lead to the most points.

Although estimating the probability of scoring from a line-out is a difficult task. Perhaps this will give you something to think about during the remaining matches of the tournament.

MAKE A CONVERSION KICK

While scoring a try might look simple enough, scoring by kicking the ball in a game of rugby can be a lot trickier. It is an important aspect of rugby as there are several ways for players to score through kicking alone, such as the drop kick and conversion. Here are some tips and drills that you can do, to make sure you manage to score.


Warm Up 

While every sport requires you to warm up before participating, this is especially important for rugby as the game involves a high level of physical exertion and contact with other players. Be sure to do thorough warm up exercises, as ligaments and muscles can be strained while kicking since these kicks often require a lot of force and impact from the player. 

Drills such as squats and lunges are good for warming up the muscles in your legs to avoiding over-exerting them. 

Distance 

Kicking in rugby requires the player to be able to project the ball across great heights or distances. While strength is one very important factor when it comes to long distance kicking, players often do not realise that speed of kicking is another determining part of how far and high the ball travels. 

Take a few steps backwards and to the side from where the ball is, before running towards it in order to put in as much power as possible when kicking. Another useful tip is to keep your body straight, as well as to kick the ball with the knuckle of your foot directly above your big toe in order to ensure maximum power. The knuckle of the foot is the strongest part, and also tend to lower the risk of injury when kicking with that part. 

Accuracy 

After you’ve gotten sufficiently warmed up, the next most important thing is to make sure your accuracy is spot on in order to get the ball where you want it to be. One trick that many rugby players use to make sure of their accuracy is to align the seam of the ball to the spot they want it to be after kicking. For example, when placing the ball on a tee or on the ground before kicking, players should always try to position the pointed end of the ball upwards and towards their target. 

Follow Through 

While the main point of kicking is to try to score or to get the ball to a teammate, players should also pay attention to what comes after they kick the ball. For instance, the player should be mindful to follow through with the kick, meaning to let his leg complete the arc after making contact and kicking the ball, instead of abruptly stopping his leg mid-motion.