As I think I've mentioned a couple of times on this blog, I'm a fairly big fan of American football, and naturally the things that it has in common with darts jump off the screen right at you. But, joking aside, one thing that happened in the NFL draft recently (for the uninitiated, the event where college players wanting to turn pro are selected by professional teams) which made me think a little.
The Denver Broncos, with the fifth pick of the draft, selected Bradley Chubb, widely considered to be the best defensive end (the primary players that attempt to sack the opposition quarterback) prospect in the draft. This is interesting for two reasons - firstly, they already had excellent players in that position - primarily Von Miller amongst others, and secondly, with multiple possible quarterbacks available (Josh Allen, Josh Rosen, Lamar Jackson), they could have filled a position which they have been lacking in since before the retirement of Peyton Manning, easily the most important position on the field (I'm aware they picked up Case Keenum, who despite playing well last year is hardly a long term solution and certainly doesn't prevent the Broncos from selecting a quarterback, even if he sits behind Keenum for most of his rookie season).
There's a few things that are going on here - the Broncos could just have been taking who they think is the best player available, which Chubb arguably was at the time and many mock drafts didn't see going past Cleveland with the fourth pick. They may not have liked any of the quarterbacks that were available at the time (for those not interested, quarterbacks were taken by Cleveland and the New York Jets with the first and third picks, who Denver might have taken if available). Or they may simply have thought that they can create a huge strength in their side by exaggerating what is already quite a good part of their lineup.
This is where it comes to darts, four paragraphs into the post. There's plenty of players who have an imbalance in certain aspects of their game. The obvious example is Dave Chisnall - he's amazing at scoring, probably one of the best in the world, but he's not the best at doubling. If you could give Chizzy an extra 5% on either checkout percentage or accuracy on big trebles, conventional wisdom would be to say give it to his doubling. But is that the right thing to do?
In an actual real life situation, might it be better to further improve Chisnall's scoring, and put him further ahead of his opponent in the game, giving him more darts at a double? There's a couple of things we can't measure here - firstly Chisnall's opponent may feel more pressure from Chisnall's increased scoring power and his game may be affected as a result. Secondly Chisnall's doubling percentage may get better as he knows he has more opportunities and can relax a little. As we can't realistically model either, we'll ignore those, but with some simplification we can certainly look to model the rest of it. If we consider that we need, to use cricket language, 24 marks in order to reach a finish, then we can look to use a binomial/cumulative distribution to work out how often this happens within any given number of darts, if we just use a simplification of getting three if Chisnall hits a treble, or one if he doesn't. From there, we can just pick a checkout percentage and calculate the number of darts it takes to finish a leg - if we say that Chisnall has a 30% checkout rate, and he's on a double after 12 darts, he'd finish in 13 darts 30% of the time, 14 darts 21% of the time, 15 darts around 15% of the time, etc etc.
Once we have this set up as a model, it's pretty easy just to tweak our initial probabilities and see how Chisnall's speed of killing the leg gets altered. That's something for me to do on another day, but for now, if you've been watching the World Cup, doesn't it annoy you how Gurney, against Poland, did exactly what I said was idiotic in the previous post by, with 82 left and Ratajski ready to step in on 85 for the match, going for bull? As he hit it and then double 16 it'll never be mentioned again, and I'm sure they will go on to have a long and successful run in this tournament.
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