The forward pass

Last week I presented a workshop at conference and I promised to give a few details of an analysis of the forward pass that I did there. Here it is.

In rugby, the ball is moved by passing from player to player. When the ball is passed it must not travel toward the opposition dead-ball line or it is deemed to be a forward pass and a scrum may be awarded to the opposition (IRB Laws of the game 2005). By analysing video of the IRB seven-a-side tournament in Wellington in 2006 it was possible to see that almost half the passes between players running in open play actually travelled forward yet none of these was penalised. Similar analysis and observation of 15-a-side rugby show that a substantial proportion of passes between running players is similarly forward as defined by the rules. Below is an analysis of one such pass to show why this might have happened.
Using the field markings as reference points the player positions were noted for each frame of video at 1/24th second intervals and speeds calculated accordingly.
At the instant the pass was made the players were running parallel to one another at approximately 8m/s. They were 6m apart laterally and the receiver was 1.0m behind the passer. Between the pass being made and the receiver catching the ball took 0.30s.
The receiver remained 1.0m behind the passer when he caught the ball.
Using these figures we can see that between the release of the ball and the catch, the receiver travelled forward a distance:
d= 8.0 x 0.30 = 2.4m

The passer was initially only 1.0m ahead so that the ball must have travelled 1.4m forward.

The passer was clearly aiming the ball back to the receiver who receives it from in front so how does it travel forward?
The answer lies in Newton’s first law of motion. An object in motion remains in motion unless acted on by an outside force. As the ball is released it is moving forward with the passer at 8.0m/s. He, by throwing backward, gave it an additional 3.3m/s backward so that the net forward speed is now 4.7m/s. The speed across the field is 20 m/s. By vector addition we can show the situation as revealed by the camera or a stationary observer above the field.
The referee and linesman must keep up with the play as much as possible and, therefore relative to either of them, moving at the same speed as the players, the ball appears to travel backward – no infringement. (Rugby World 2005)
Let us now reconsider this pass to see how it could have been made legally. At the limit the ball must not travel forwards so that we shall assume that it travels straight across the field. The passer is travelling forward at 8.0m/s and thus must give the ball a rearward component of 8.0m/s to render it stationary. To reach the receiver before he is in front of the release point the ball must cover the 6.0m of their separation in the time it takes him to travel 1.0m. i.e. 0.125s. The ball must travel across the field at 48 m/s. Combining these results by Pythagoras’ for this one pass we get: 175 km/h for the pass
Clearly the passer will be unable to achieve this and the receiver would have difficulty surviving it.
Using the figures earlier can we determine how the players should be positioned to give a valid pass. We decided that the receiver travelled 2.4m during the pass so it would seem that he should run 2.4m back from the line of the passer. This will not actually work as the passer must aim much farther back. Using the need to have a rearward component of 8.0m/s and a speed of pass of 20m/s(as used above) we get 23 degrees back from the transverse line.
The transverse component of the velocity is therefore 18.33 m/s
At this speed the pass will take 0.327s in which time the receiver will travel 2.62m. He must be at least this far behind to receive a legitimate pass.
The farther the players are apart, the longer it will take for the pass and, therefore, the farther back the receiver will need to be to receive the pass before crossing the advantage line. Alternatively the receiver will need to slow down to avoid crossing the line and thus will lose the advantage of speed built up in the move.
In a recent test match a centre passed to the winger who carried on to score the try. There was no debate amongst either set of supporters that it was a forward pass despite the fact that it was released before the 22 and received after the 22 with a forward separation of 2.2m. Careful study of the video shows that the players had a lateral separation of 13.2m and longitudinal separation of 5.0m at the time the ball was released. The pass took 0.9s and the receiver was travelling at 8.0ms-1. The passer was slowing down at the time of the pass and his speed was approximately 5.5m/s. In this case, therefore, the pass was released at 15.0m/s in a direction which was ahead of the instantaneous position of the receiver (to allow for their speed differential). In actual fact the receiver still had to slow slightly to take the pass. To make the pass legitimate in this case it would have required the ball to be aimed at the receiver at 22.3m/s. This is an increase of about 50% on the actual pass, but it would have been flatter and take only 0.6s rather than 0.9s giving less risk. The key to this pass being possible legitimately is that the receiver was initially 5m behind the passer.