A big moment; the deciding leg in your first match in your first serious steel-tip tournament. You’re on 138 with your opponent on 167. Your mind goes worryingly blank before you vaguely remember a checkout table’s suggestion and hit treble 20, followed by treble 16. Then, even as that dart is on its way to the board, the memory of Keith Deller slotting in treble 18 then double 12 in 1983 suddenly returns – too late now! You take a deep breath to compose yourself, then decisively miss the double 15 by half an inch into the single.
As you collect your darts and walk back, nagging doubts arise. With the Crafty Cockney waiting on 32, it was hardly relevant that Keith missing that treble 18 into the single would have left 60. For you, however, that would have been much better than the awkward 62 that would have resulted from you missing your treble 16. So doesn’t that mean that checkout table was wrong and the Deller route is always better than the one it recommended? What’s more, having started on that one, should you even have gone for that double 15, or aimed for single 14 to leave you 16 in three darts next go, if you get the chance, that is? Or maybe it would have been less risky to go for single 6, leaving 24?
Even away from the heat of battle, answering such questions is not straightforward, depending as it does not only on the scores of both players but also their levels of ability. Standard checkout tables and apps may tell you how to achieve the arithmetical goal and give preferred routes amongst a number of options, but I haven’t yet found one that properly takes into account such complexities. Moreover, there are even inconsistencies in the recommendations of different tables. Take that above 138 finish, apart from the T20, T16, D15 and T20, T18, D12 “Deller” routes mentioned, I’ve also seen T20, T14, D18.
For some years I have thus pondered on producing a checkout app to address this gap in the market. My original idea was that the User would input their and perhaps their opponent’s standard, defined in terms of a 3-dart scoring average (as is already used in UniLab), together with both their scores, and the app would then output estimated probabilities for the best theoretical routes to a win.
A new motivation to revisit this idea, incidentally, could be the recent launch of the Unicorn Smartboard with its auto-scoring app-based technology. This could, in theory at least, provide those probabilities based on a player’s scoring history without the need for manual data input.
One possible basis for the calculations required in such an app would be for me to repeat the somewhat cavalier use of what statisticians call “The Central Limit Theorem” which featured in my “Everything is Normal” blog (July 2011). This assumed a dart player’s accuracy can be modelled by a mathematical entity called a “normal distribution”. Unfortunately, although this approach was pretty much OK for my earlier usage, it would have some potentially serious drawbacks when used as the basis for a checkout app
An obvious problem here is that there would be no allowance for psychological effects or individual preferences for certain areas of the board. However, I don’t see these as show-stoppers because a player would at least get an idea of the statistical disadvantage they were under when, say, preferring a scoring route that led to double 18 rather than to double 16.
Another potential issue is allowing for the advantage of “marker” darts and the flip-side disadvantage of needing to aim consecutive darts at widely separated targets. Admittedly this could be allowed for through a semi-empirical correction, but this would be in danger of being just an arbitrary generalisation, for one thing irrespective of any relevance there might be in whether the player is a quick-fire muscle-memory thrower or an “aimer”.
But probably the biggest problem is presented by what are known in the world of statistical distributions as “outliers”.
Pretty much every day of late I have been making the short trek to the purpose-built fortress of darting solitude which stands at the bottom of my garden. Once there, I determinedly work my way through a variety of practice routines which, whilst having the collateral damage of demonstrating my dismaying lack of any real talent, can serve the purpose of putting any new ideas for dart innovations to some sort of a test.
One such routine ends in throws at the bull, and a not atypical one from this very morning is shown in the photo above. Yep, one dart on target, one in the outer, and one missing by maybe three inches (sorry the photo is blurry, although looking at it does remind me to blag a new board off Unicorn sometime, the one shown has come out of 20+ years’ storage!).
Whilst me throwing a wayward dart is certainly no surprise, the fact is they’re also not that unusual even for top players. We’ve all seen World Champions, for whom 100+ averages and even 9-darters are regular occurrences, miss a bull checkout by a millimetre and then miss the entire expanse of the single 9. The problem is, if we take that normal distribution formula to be strictly applicable, such things should almost never happen.
Using that formula, the chances of someone like me, with a 3-dart scoring average of maybe 60 on a very (very) good day missing by more than 3 inches is maybe 1 in a 1000, as is the similarly calculated chance of a professional with an average of 90+ missing by more than 1 inch. As both I and the pros miss by those respective amounts a lot more often than that, justifiably to apply the formula in a checkout app would require another fairly arbitrary allowance for “outliers”, meaning the odd wayward darts that don’t sit within the distribution.
Which is one fairly arbitrary allowance too many for me to justify sacrificing many hours of pleasantly indolent retirement in the pursuit of producing the app. Of course, should you feel that this is all just an excuse for laziness on my part and such an app is high on your wish list, you can always try nagging/encouraging me via a reply to this blog, but even so I fear the UniBoffin Checkout App may still always remain “in the post”.
Well, that’s it from me this time. I’m going to leave you to decide what happened in that match of yours that began this blog. Luckily your opponent didn’t checkout out 167, but only by a millimetre, leaving 25 which my crystal ball tells me will definitely go next time.
So, when you next get the chance to throw three darts at a board, you have 15 to finish for your first win on a big stage. No pressure…..
If you have any comments or questions for UniBoffin, please do so through the website link below.