Random thoughts: Boyles law, pressure, space, and rugby-playing molecules

Have you ever have one of those nagging thoughts that won't quit you? Perhaps its the idle time cause by the rugby off season, perhaps it's some the reading i just did on game-theory, perhaps it's too much celebrity deathmatch.

I have in my head that perhaps we can find a way to problem solve in rugby mathematically. Perhaps we can use the laws that govern gases and pressure, coupled with the mathematics of economics, game theory, and competition, to find ways to score trys. Perhaps I'm insane.

Boyle's Law states, if you remember high school physics, that the relationship between the volume of a gas and the pressure of a gas is constant. There's a bunch of other scientists that piggy backed off of this, did the math, and ultimately the "combined gas law" was developed. Bottom line, when we're talking about gasses, pressure, volume, and temperature are all related.

Here's where I ask you to get in my head for a minute, and picture the following :

Every rugby player on the pitch is a molecule of gas. For the time being lets imagine that there are two types of molecules, which have approximately the same attributes. Let's call them Red and Blue.
The pitch itself is a bounding container.
The temperature, for now, is unchanging.

Back to high school physics: What happens when we heat a gas? The molecules move faster! And, as a result, the pressure increases. If the space is small, and the pressure increases enough, the molecules will start to collide, creating more heat and more pressure.

When i picture this, I can't help but see a rugby team. The blue team has worked it's way down into their green zone. I see that team attacking off the fringes, over and over and over, only to be stopped by the red team on defense.

What would happen if those rugby-playing molecules expanded to fill the available space (limited by the constantly shifting off-sides line)? Less pressure, less collisions, and voila - more trys.

This whole "attack space" thing is common sense, right? We all coach our teams and players to attack space, right?

Let's go back to HS physics. Can we change the volume of our container? We could use a balloon, or some other sort of expansion device, right? How about the pitch? Are there spacial variations that we can identify and apply these laws to? Can we predict where the logical attack point might be in different scenarios, based upon the space available?

There's a paper on the EPRU website written by Lee Smith, former NZ Director of Coaching, titled The Creation of Space at Phase Play, where he specifically discusses different spacial situations, and how pressure is impacted.

Consider these variations:

Lineout at the 50:

• Vertical distance between back lines - 22 meters (10 for each backline, one for the tunnel, 1/2 for each player in the lineout)


• Lateral distance available for attacking - 45 meters (assuming the lineout occupies the space up to the 15 meter mark)


• Minimum straight line distance to the try zone from the attacking #10 - 61 meters (1 meter for the lineout itself, 10 meters back, 50 meters from lineouts)


• Maximum straight line distance to the tryzone from the attacking #10 - 76 meters (from the attacking #10 to the opposite corner of the tryzone, using a²+b²=c² to solve for the hypotenuse of the triangle.
  


• Total strong side attacking Space (a x b) - 2745 square meters

Scrum center at the 50:

• Vertical distance between back lines - 11 meters (3 per scrum for the vertical space each scrum occupies, 5 for the depth of the attacking flyhalf from the attacking scrum.



• Lateral distance available for attacking - 29 meters to the left and to the right of the scrum (assuming the scrum itself occupies the 2 meters horizontally , and that it is dead center of a 60 meter pitch.



• Minimum straight line distance to the try zone from the attacking #10 - 58 meters (1 meter for the lineout itself, 10 meters back, 50 meters from lineouts)



• Maximum straight line distance to the tryzone from the attacking #10 - 65 meters (from the attacking #10 to the opposite corner of the tryzone.



• Total strong side attacking Space (a x b) - 1681 square meters

This diagram illustrates a lineout on the 50, and hopefully makes it clear where all the numbers come from. And before you start, NO, I didn't put down the tackle line, gain line, attack line, etc etc etc. I'm kind of free-wheeling it here, thinking out-loud if you will. Mock if you must.



Here, clearly, are two "yellow zone" situations with significant spacial differences. Again, OBVIOUS. Add the whole extra-man-on-the-right-offensively thing, and the situations become even more different.

So lets look at the match-ups of a less obvious, but more critical situation.

Attacking green zone lineout on the 22 ..

Attacking green zone lineout on the 5 ...

I specifically bring up these two situations because most coaches have some sort of plan - "we" do x from a lineout in the greenzone. These two scenarios, mathematically, couldn't be more different. Especially when you consider how the position of the wings and fullbacks shift as the attack approaches the tryzone.

Attacking lineout on the 22...

• Vertical distance between back lines - 22 meters (10 for each backline, one for the tunnel, 1/2 for each player in the lineout)


• Lateral distance available for attacking - 45 meters (assuming the lineout occupies the space up to the 15 meter mark)


• Minimum straight line distance to the try zone from the attacking #10 - 33 meters (1 meter for the lineout itself, 10 meters back, 22 meters to the tryzone)


• Maximum straight line distance to the tryzone from the attacking #10 - 55.5 meters (from the attacking #10 to the opposite corner of the tryzone.
  


• Total strong side attacking Space (a x b) - 1485 square meters

Attacking lineout on the 5 ...

• Vertical distance between back lines - 16 meters (10 for the attacking backline, 3.5 for the defending back line, one for the tunnel, 1/2 for each player in the lineout)


• Lateral distance available for attacking - 45 meters (assuming the lineout occupies the space up to the 15 meter mark)


• Minimum straight line distance to the try zone from the attacking #10 - 16 meters (1 meter for the lineout itself, 10 meters back, 5 meters from tryzone)


• Maximum straight line distance to the tryzone from the attacking #10 - 47.75 meters (from the attacking #10 to the opposite corner of the tryzone.


• Total strong side attacking Space (a x b) - 720 square meters

Let's put all this aside for a moment.

In order to score a try, we need to get the ball into the hands of a player who can attack. This player must be able to overcome pressure. If he or she cannot, than the player needs enough support to preserve possession and maintain continuity of attack. If we cannot strategically supply the support, then we need to make sure the player gets the ball under minimum pressure. That's assuming of course, that the skills of every player on the pitch are the same.

It's a bit of a conundrum.

Since pressure is directly equated to the number of molecules (players) in the designated space, its clear that attacking close to the set piece = attacking close to the most pressure. Not coincidentally, this is where the most support is.

If we attack away from the pressure, then our attacker is more often then not with limited support. Errors become turnovers.

In order for us to be successful, or players need to learn to recognize space, pressure, and support. We need to learn to look (to use an art metaphor) at the NEGATIVE spaces. Rather than seeing the defenders, we need to learn to see the lack of defenders. We need to learn, like the mindless gas, to expand to fill the container, and to go where the pressure is at it's lowest. And we need to do it fast - before the defense expands too, and everything is equal again.

In Mr Smith's article, he speaks specifically about phase play - where the pressure is even greater, and the quest for space so much more elusive.

It's probably worth noting at this point, that the "pitch map" is to scale. The little dots representing humans are the equivalent of two 1/2 feet wide. Imagine the average human, with about a meter and 1/2 wingspan. You could literally line up 70 people, shoulder to shoulder, along the 50 meter line. When you think about how many players are actually on the field, related to how much SPACE is on the field, it sure seems like mostly space, and not alot of human.

This is just the tip of the iceberg as far as how we can describe the pitch and the game. There's speed and acceleration of individual players, maximum passing distance, passing efficiency, the blind side, kicking - all of it can be described in numbers.

Here's something practical from this little ramble.

At a lineout in the 22, there is 1485 square meters of space on the strong side of the pitch. At the 5, there's 720. The closer we get to the tryzone, the closer the wings and fullbacks get to joining the first line of defense. Conclusion? The closer we get to the tryzone, the greater the pressure, both in terms of space and manpower.

Doesn't it suck to work your way all the way to the green zone, without coming away wiht trys? My suggestion - early in the season especially - spend time specifically coaching green zone attack, closer to the tryzone and further from it. Think hard about the tactics you employ in the green zone, and whether or not the space available merits them. Teach your players how the actions of one group effect space and pressure. Ie, if you drive that lineout at the 5, but get stopped at the 2, is there any space left out wide?

So before all you science geeks and teachers slam me, I know humans aren't gas molecules, and I know we don't behave like we are. I know that varying speeds, sizes, and skills add vast amounts of complexity. I know that weather matters. And friction. And gravity. And i know that human beings, put into a large room, will not expand to fill our surroundings - we will converge upon each other, social creatures that we are, and occupy only a small amount of space.

But I just can't help but wonder, and I KNOW that the people who author XBox and Playstation games think about this stuff ....

These are the ramblings of a rugby-deprived mind. Vacation can't come soon enough. For now, stop drop and roll Paris!!