Saturday, January 06, 2007

Chaos in rugby

From time to time I will probably jump on opportunities to related to rugby mathematically. I've always loved mathematics, and specifically I've always been awed by the ability of numbers to describe natural phenomena.

So - I just watched this indy film "Julie Johnson". It's about a stereotypical "poor white trash" woman, who has hidden talents. She reads Scientific American and a bevy of other science mags in secret, and eventually kicks out her husband so she can get her GED and go to college. There is of course a romantic storyline, but what intrigued me was the references the director makes to Chaos theory, and how it applies to human lives and experiences.

This isn't the first movie to do this. The Butterfly Effect did in 2004. Chaos theory, in summary, states that in certain non-linear systems,tiny, seemingly insignificant changes in one area result is massive changes somewhere else.

Let's see if we can't find applications of chaos theory in rugby.

Our team is attacking. We have a scrum on the left side of the pitch, 5 meters from the tryzone. Things look good for us, eh? A tight head wheel is on, and DUH, we're gonna run a back row move.

Keep that thought for a second.

Every player has what I'll refer to as "tolerances". A fly-half, for example, has among other things a "ball-catching tolerance" which varies from day to day, game to game. The vast majority of times, a given flyhalf, moving at a given pace, can catch a ball, moving at a given pace, in a certain area around the intended target area. If the pass TO the flyhalf is "out of tolerance", it is unlikely to be caught successfully.

So - lets pretend that a tiny thing happened. Our scrumhalf didn't put quite as much back spin on the ball as she usually does at the put in. As a result, when our hooker struck the ball, she did it one inch further out than she usually does. Instead of going straight through channel two (which was our plan), it bounced off the locks foot in an unpredicted way. The tight head wheel that was on (which we planned, because of where we were on the field) caused the ball to bounce around even more between the lock and the #8, eventually squirting out on the left side of the 8. The scrumhalf no longer has a solid weak side play.

She's a little flustered. IT happens, who can blame her? One minute, we're in a position to score an easy try. The next, CRAP!!! Suddenly the back row play to the weak side can't happen, the ball is loose, and she MUST do something. She scoops up the ball and moves it to our #10. And, since she's a bit flustered, under pressure from her opposite, the pass was just a smidge "out of tolerance".

Well, BECAUSE we did a tight head wheel on purpose, we put the opposite teams #7 much closer to our #10. By now, you're probably starting to see how what was a very good situation 10 seconds ago is turning ugly pretty quick.

Since we're in a 5 meter scrum situation, the defense's backline is as close to us as it's ever going to be. When the ball is not caught, they are all over us. Our fullback and weak side wing are up, because they were participating in the back row move. When the #7, #8, #9 and #10 turn over the ball and counter attack (as a result of our wheel they are in a great position to do so), they kick the ball way down field and the chase is on. We are F'd.

Chaos - a small, seemingly insignificant change in one area results in a large, very significant change in another.

The rugby related lesson? Our players need to always be prepared for change - we need to coach them to be cool in the head, and to make quick, smart decisions on the fly. We need to insure that our sub-units function as part of the larger TEAM. Scrum wheels, largely coached in the vacuum of forward play, have a massive impact on our back line's ability to attack successfully. Errors and events that seem insignificant to one player (the hooker who struck the ball an inch to wide) are catastrophic to others (the flyhalf who got gang-raped).

We are butterflies, flapping our wings all over the pitch. Every one of us - the team with the ball, the team without it, the referee who did or didn't hustle to see the play, the coach who shouted on the sidelines, the touch judge who sets and holds the mark - we are all butterflies. At any second something we do can change the tide of the game. Without the luxury of time-outs, free subs, line changes, huddles, and downs, we are at the mercy of the chaos.

The team that recognizes the chaos in action, and actively works with it, is likely to have and effectively use more possession than the team that sticks to a script. If we work WITH the chaos, instead of against it, we will be brilliant.


Anonymous said...

This "butterfly effect" is very similar to Ito's Lemma. Ito's Lemma is a diffusion function with a stochastic (random) component. Think of how smoke goes out of a smoke stack. At first the stream of smoke is narrow and then, with time, it defuses wide. On a windy day (eg the wind being the stochastic component) the smoke spreads out even more with time.

When describing combinatorial scenarios, ie a 9-10-12-13-11 passing chain, it means that the longer(in time) the ball moving from player-to-player then the chances of something going wrong are higher. When a bigger stochastic/random component is added (ie wet ball, hung-over players) then, with time, the error margin widens. To tactically reduce the randomness maybe occasionally skip passing the weakest player would both reduce the time the ball is the air and avoid the player adding the most variability. Teaching good passing & catching skills doesn’t hurt either since it too reduces the overall variability.

In finance a similar concept applies to why banks change more money for longer term loans. They figure that the longer their money is in someone else's hands then the chances of something going wrong are higher. So they charge more money. Of course Murphy’s Law is woven through all of this.


OBG said...

Love this post and the response. As a coach, it's something that I remind myself of often. That's why we rarely practice a ploy with more than 3 passes. It's why we practice ploys rarely actually, because I think that teaching decision-making in chaotic situations pays more dividends in the long run.

I had a London Irish coach ask me, to set an example in front of a group of people, how many lineout calls our small club has. My answer was "essentially three." Because we have just three how-many-in variations, three where-to-throw variations and three what-happens-after-the-catch variations. Now, putting them all together gives you three-cubed options, or 27, if my math is right, but there's not a lot to remember. The coach scoffed a bit and said how many the Irish had (can't remember the number but it was something like 100). My point in all of this is that we minimize the variety (or the variability). On purpose. To minimize the butterfly effect.

A LOT of times, that's not popular with players who want to do a 1-2 dummy, loop 3, skip to the wing with a crash back to the looper or some such. But a well-executed skip 2 that puts a player in space is appreciated.

I imagine as a coach, our tolerance for ... tolerance ... gets higher as the skills of the players do.