Some might say (where have I heard that phrase before?) that I was pretty dumb about choosing an area of maths in which to specialise. With a bit more forethought I might have spent my career cheerily doing sums on something nicely esoteric like, say, Non-Commutative Geometry (don’t worry, there won’t be questions!). That would have allowed me to claim I was close to discovering the Secret Of The Universe (it’s 42, of course) whilst remaining confident that even an improbably snazzy bit of kit like the Large Hadron Collider wouldn’t be able to prove me right or wrong until well after I had ceased to care.
As it was, though, I foolishly spent a large part of my working life telling people what exactly I expected to happen to the bit of metal they were about to launch into the stratosphere. Which gave me plenty of scope for immediately looking like a turniphead if it didn’t.
And now, even though I’ve long retired from such things, I haven’t made life any easier for myself with my involvement in darts. OK, the bits of metal are smaller and the distance they might miss by is measured in millimetres rather than kilometres, but the turnip risk factor is still present. Not only present, greatly amplified by the fact that the launcher is a human.
Make an aerodynamic improvement to the darts of a player who’s having an off day and he will probably still have an off day, even if not as off as it might have been. But if he then wakes up the next morning feeling good and throws a nine-darter with an old set of brass arrers he found in the garage, he may well draw an understandably vegetably conclusion.
That may not have happened to me yet (as far as I know!), but if and when it does I’ll just have to regard it as a risk of the job. The reward is when those improved darts do actually help the player get out of their bad patch, or, better still, raise their game to a new standard. And for me that reward more than outweighs the risk.
Which brings me (sort of) to my main topic for today. I’m about to provide a scientific reason why round-the-board practice routines are important, thereby running the risk common to all scientific conclusions relating to easily-understandable everyday subjects (ie ones entirely unlike Non-Commutative Geometry). And that risk is simply this: if the scientific conclusion disagrees with common sense, people simply won’t believe it. On the other hand, if it does agree, phrases such as “Well, no spit, Sherlock” (this is a respectable blog), are likely to appear as quickly as the research budget disappears.
That risk duly acknowledged, here goes!
I mentioned last time that gravity will make a dart drop maybe 50cms on its way to the board. That figure varies with the time of flight squared, and thus, for a fixed throw speed, is closely related to the distance to the board squared. Let’s suppose that 50cms is indeed the drop a player has to allow for when aiming at the bull, which is 2m from, in line with, and at the level of, their release point. As I also said last time, they won’t consciously aim 50cms above the bull, they’ll rely on their subconscious to do the trajectory sums for them – even though their subconscious is not a mathematician, just empirically trained by practice and experience to “know” how much to aim up.
OK, so we’ll now suppose that the player changes his aimpoint to a double, 165mm away from the bull. Pythagoras (remember him?) tells us the 2m distance to the target will now have increased by just under 7mm. Not much, you may think, but when 2.007m is squared the difference with 2m is enough to make that 50cm gravity drop increase by over 3mm. Enough to mean a double top, say, is wired - and maybe a tournament is lost.
Of course that geometry is over-simplistic, but it’s hopefully rather more understandable than the non-commutative sort and does give the general idea. A proper trajectory computation would show that moving the aim point from the bull to most doubles without an individual allowance for the different gravity drop would often result in a miss. And although that may not be the case for vertically-oriented doubles like 6 and 11, we still haven’t considered variations in the throw itself and the yawing motion of the dart.
So the best way to give your subconscious a fighting chance of getting the trajectory calculation right wherever you’re aiming on the board is to provide it with lots of data. A scientific conclusion that may be, as Sherlock himself might agree, “Elementary”, but is no less worth stating for that.
In other words, if “practice, practice, practice” is how an American gets to Carnegie Hall, then “practise, practise, practise” is how a Brit gets to Alexandra Palace!
Q&As
No actual questions this time, but an opportunity to thank Pete and Jeff for their “sporting legend” nominations and take a quick look at them.
Pete goes with The Power and the unarguable call of the great Rocky Marciano, but then throws an interesting curve ball with multiple World Speedway and Long Track Champion Ivan Mauger. Certainly a fantastic rider, and also a talented all-round sportsman, but if we’re going to accept Ivan as a legend I think we should at least mention Tony Rickardsson.
Jeff, meanwhile, has taken a commendably patriotic approach with his nomination of the multi-divisional Filipino boxing World Champion Manny Pacquiao. Maybe Boxing World Championships have suffered a bit image-wise since Marciano’s days, but Manny is certainly a worthy nominee – especially since he’s so into his darts!