Fix your problems or improve your strengths 2 - Electric Boogaloo

So I played with the binomial function on Google Sheets and it does exactly what I want it to do. If we take the assumptions that we did in the previous post, then if we assign a player a probability of hitting a treble 45% of the time, and a double 30% of the time, this is how often they finish a leg at certain speeds:

Now let's opt to give our player an extra 5% on the doubles:

That's a bit better, isn't it? Getting more than half our legs in under 15 darts and cutting our awful leg stat down to less than one in six. But here's the question - do we do better by improving our scoring? Let's give our player an extra 5% on treble scoring instead:

That's, oddly enough, quite a lot better again - we're now up over 55% of legs in under fifteen darts, although we do have about the same number of really bad legs, give or take a fraction of a percent.

What can we make of this? It's kind of obvious if you think about it - what percentage of darts that you throw in a leg of 501 are at trebles, and how many are at doubles? That should give you a clue - while giving yourself a better chance of hitting a double is nice, a small improvement in scoring power will allow you that many more shots that it more than compensates for it. It's all well and good if you go 100-100-100-100-69 and know that you will check out 32 with complete certainty in the next visit, but if your opponent goes 140-140-140-T19 first dart, he's got five shots to finish you off before you can even step up to try to pin double 16. He only needs to have a 13% checkout percentage to win the leg more often than not, a rate most pub players would be disappointed with.

What I can do is throw these stats into the master computer, and see how often different skill sets would win against each other - but that'll have to wait for another day. It was kind of amusing to see that Chisnall, who kind of inspired this piece, helped to knock England out earlier - not because his finishing was comical, three from five isn't bad at all, but because his scoring went to pieces, second leg excepted. Weird how that works out, isn't it?

Fix your problems, or improve your strengths?

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.

Clarity of thought

Something that I'm a bit lacking in, having delayed by commute home due to Northern Rail going full Northern Rail and not fancying two train journeys today in conditions that would make animal rights activists lose their shit if we were transporting chickens in such conditions, and the only way to properly wait an hour for a later train is in licensed premises.

So anyway, suppose we're stepping up to take on a fairly high outshot, where there's possibilities of routes we can take. It's important to know what we're doing when we step up and how to adapt to each dart in the sequence. Let's say we've left ourselves on 132 for whatever reason, and the opposition is on a low score so we really want to go out in this turn. We've either done our maths and, somehow, the maths on our particular skill set suggests going bull first is optimal (or, more likely, we use conventional bad wisdom and just fire away at bull because keep visit alive at all costs aaaaaargh). We hit the bull. Now we go for bull again.

NO NO NO. Why are you doing that? You have 82 left, and the premise of the visit is to go out in this visit. It had better be a fucking great marker on the smallest target on the board to justify going for the smallest target in the board again, rather than going for treble 14 to leave tops.

But wait FRH Towers, why do we start on bull on 82? Because we have three darts, and doing so will allow us a dart at a double assuming we hit a minimum of 25 with the first one. Similar if we have one dart in hand, we either return on double 16 or big number for tops. We do not care what we might leave ourselves with two darts on 82, because the whole purpose of the visit is to go out - we are not expecting to return. If you're solely interested in finishing in six darts, just try to hit a straight ton.

There's similar applications on something like 121 or 161. Let's say the opponent is not really in range to kill, so we just want to not mess up setting it up, so in the first instance we'll go for bull if we hit two singles and leave 81 (if we stay upstairs) or 84 (if we switch, because we might go for it, who knows). 161's a similar discussion if we hit one treble.

Now this line of thinking to leave yourself an easier two darter when we return is fine. I've no problem with it. But if you're going to do this, there's two things you could do. Let's just consider the 121. On our second dart, why don't we switch to 19's if we're not fussed about going out this visit? If we hit, we're on 44, we've got a choice of singles to leave a preferred double. If we miss, we leave 82 - now this makes no real difference if we hit 25, it's still a single for tops. But it makes a huge difference if we hit bull - we're now on double sixteen, rather than on 31 (not ideal, we have to waste a dart), or 34 (not the best double in the world).

Or why not just shoot at bull on the second dart? We're then leaving 51 if we hit, easy single for a choice of whatever double, if we hit 25 we're leaving 76, which can set up double 8 or double 14, depending on whether you're Mensur Suljovic or a normal darts player. Or even on the first dart? 71 or 96 in two is fine and sets up pretty well whichever way you want to look at it. The general point is that if you're going to go for the bull to take advantage of leaving an easier shot if you hit 25, then do so at such a point in the visit where it doesn't leave you with more troubles than you need to when you return if you don't hit exactly 25.

Couple of events going on today. The World Trophy has started in the BDO, looks like they're posting up Darts for Windows PDF's so I can get some lovely data. Deta's already out, sigh. I didn't actually realise until today that this is actually a five day event, which seems incredibly excessive. I'm sure they could have trimmed it down to four and had a Friday afternoon session - surely the players that are playing today that wouldn't return until Saturday would appreciate being able to work a hotel schedule better, there's one less day's venue rental and it's not as if you're going to get noticably smaller crowds on a Friday afternoon than a Wednesday evening at a BDO event. Could even give them away to local schools or something, have them learn maths by doing the scoring for them. It's also a couple of Euro Tour qualifiers tonight, the second one is either still going strong or the results aren't on Twitter yet, but it looks as if Wattimena, Hopp, Reyes and van der Voort have got through the first one amongst others, surprising again that de Zwaan didn't get through, but we'll wait and see if he can make it through the second one.

More on averages versus money earned

A quick one:

https://i.imgur.com/nCBHngr.png

I've taken the average points per turn of everyone that's played at least three Players Championship events (didn't want outliers like Colin Osborne squashing the chart even more than it is on the lower end) and plotted them against the average money players have earned in the Players Championship series to date.

You'll note there's no Anderson or van Gerwen. I've omitted them as I needed to splice two charts together just to get it not quite so clustered as it already is. It's obviously too big to post as normal in the Blogger template so I've added it as a link (should be able to zoom it to about 1400x1400). Ando's on just short of £3.5k/tournament at just under 95 points per turn, van Gerwen's at over £7k/tournament on a shade under 96.5 points per turn.

There's some interesting things to note on this one. Firstly, while there's some obvious correlation between averaging and money earned, it's not the be all and end all - look at that cluster of Lennon/Nicholson/Searle at just over 92ppt and around £400 per tournament. They're all averaging more than Gerwyn Price, who's making more than a grand a tournament, and they're all making less than Benito van de Pas who's averaging over 8 points lower per turn. If you imagine a banana running from around the Part/Temple/Dudbridge section through to the Evans/Lowe/Price section capturing where the bulk of the players are, you can say anyone to the bottom right is playing better than their results suggest, and anyone to the upper left is running hot (relatively speaking). Anything above around 1k/tournament is almost certainly going to be affected by one or more very deep runs into a tournament so it makes sense to ignore them when looking for a trend curve.

Interesting to see several players not cashing once. Huckvale's only played three, which is fair enough, but Darbyshire's played 10 and Dootson and Groen have played all twelve and not won a single game. That's quite incredible given that Groen has previously qualified for the World Championship and Dootson's previously outright qualified to the money for the UK Open then made the last 16. The main three's results:

I don't know if I want Dootson to draw Groen in round one of the next Players Championship, or if we can get some sort of last longer betting going. Scary that Dootson got his tour card on day one, beating Harris (who's been playing great), Goldie (who was at least doing that earlier on), Pallett (who we all saw at the UK Open), Preston (who's won on the Challenge Tour this year) and then Aspinall to win the card. That's not a bad line up. Such a sharp contrast to Corey Cadby, who won the other half of the draw and has won almost twice as much in one tournament this year as Dootson has in his whole career.

Some speed of killing stats

Bored. Sunday with no darts, what is this? So, some graphics:

A count of all players that have won 250 or more legs in the PDC this year, ordered by legs won. Green segment of the bar = legs won in 12 or less darts, black = 13-15 darts, red = 16-18 darts, yellow = 19 or more darts. No real reason for posting it, just something people might like to see.

Schalke Shootout and other random thoughts

I watched a bit of this last night. I don't normally watch unranked events, but there was nothing better on after getting back from the pub, so why not. It's an interesting set up, it seemed to go on so, so late (I forget exactly when it finished, but the semi finals didn't start until 11pm local at the earliest), I'm not sure that was the greatest idea but at least it was in a bit of the country that's really close to lots of major cities (for those that don't know, Schalke's ground is in Gelsenkirchen, very close to Dortmund, Düsseldorf, Duisburg, Köln being a bit further away but still doable) with decent transport links - although I don't know how many trams back to GE-Hbf there'd be at that time of night and it's a fair old trek.

Obviously the big story, other than the Germans not winning anything and only the one guy that I didn't really know taking his opponent to a final leg and getting a match dart, was that Dimitri van den Bergh announced himself on the world stage. Beating van Gerwen and then Anderson, even if he did run out of steam in the final against Suljovic, is likely to correct lines featuring him to something more accurate. This happening in an unranked exhibition is annoying, as I'm not going to bet on it - if these results had happened on, say, the European Tour, then I'd likely have been on Dimitri in every match. Oh well. Good to see Mensur throwing well, should set him up nicely as we approach the Matchplay.

Elsewhere, in a sign that the PDC has not learned slightly from the clusterfuck of last year, there is still no indication that they've worked out how many players they're going to have in it. As we're more than half way through the Players Championship series and one short of half way through the European Tour (so, in total, we've played 22/41 floor events), you would think they'd have got a move on. At least they should say we're having 96 players, consisting of 32 seeds, 32 from the Pro Tour rankings and 32 invites from international tours/qualifiers/PDPA qualifier etc. Then at least people will have some sort of idea as to what they need to do, even if they really don't have a clue how a lot of the invites will work.

I really hope they don't go for any more than that. There was something that I saw that indicated that they were looking at 128 which would be hilariously bloated. 96 would be a nice number as it'd give the seeds a first round bye, but what do you go with outside of that? You could go with:

- Top 20 in the Pro Tour rankings not already qualified
- Top 4 non-UK/Ireland players in the Pro Tour rankings not already qualified
- Top 4 in the Challenge Tour not already qualified
- Top 4 in the Development Tour not already qualified
- 28 international invites (ideally primarily from their affiliated tours, with qualifiers where a tour doesn't exist)
- 4 from a last gasp PDPA qualifier

This would likely suit everyone - really pushes the minor tours, bumps the general Pro Tour places, and bump up the international nature of the tournament.

Finally, it's a week before the BDO's first major of the year, and apparently as of yesterday they've sold a grand total of nearly 200 tickets. Across all sessions. Preston's fairly local to me, so I could easily get up there if I wanted to, but over twenty quid for six games? In the last sixteen? Two of which are women's matches? In comparison, the next European Tour in Hamburg costs either 16 or 24 euros. For eight games. With an ever so slightly higher quality of play. The place has got to be pretty much close to dead as a professional tour. Barry could probably kill it overnight by, if he does expand the PDC worlds as we reckon he will, just directly invite the top 8 in the BDO rankings. In terms of the qualifiers for the World Trophy, it's a shame that Pallett lost in the last round. He'd probably have won the whole thing. Was quite a lot of Challenge Tour players there, Worsley qualified, Kellett made the last eight, two of the other qualifiers played the Development Tour, Padgett made the last 16... shame that more couldn't punch through but with just four spots it's pretty difficult. Oh well.

Well that was an interesting winner

Josh Payne won a second tournament. Didn't particularly see that coming, he's been in and around the top 32 for overall average so is probably playing a little better than his ranking suggests, and he made the world youth final so should be trending back up, but still a surprise. It's encouraging to see - too often you see someone win a title out of nowhere, but can never follow it up, he's done that now so it's interesting to see where he'll go from here. He's put himself into the Matchplay equation at least, although the Grand Prix could be a bit more realistic.

Also had surprising deep runs from a couple from across the sea in Dolan (semi final) and Mansell (quarter) - neither throwing amazingly well (Dolan with an adjusted average of just over 90, the same as Payne, Mansell was a shade under 89) but getting enough done. There were a few weird oddities - Luke Woodhouse made the last 16 despite an adjusted average of 85 and not winning a single of his twenty won legs in twelve darts, whereas Mervyn King had an adjusted average of 96 but ended up being eliminated at the same stage without winning a leg. Across the weekend as a whole, your top five averages came from Peter Wright, Mervyn King, Gary Anderson, Ian White and... Paul Nicholson. Nice return from Nicho, but inconsistent, averaging 88 in his losing legs, he managed to get over 70% of legs won in fifteen darts to get up there.

Latest FRH rankings:

1 Michael van Gerwen
2 Rob Cross
3 Peter Wright
4 Gary Anderson (UP 1)
5 Phil Taylor (DOWN 1)
6 Daryl Gurney
7 Michael Smith
8 Mensur Suljovic
9 Simon Whitlock
10 Gerwyn Price
11 Dave Chisnall
12 Ian White
13 James Wade
14 Darren Webster
15 Raymond van Barneveld
16 Jonny Clayton
17 Kim Huybrechts
18 Alan Norris
19 Joe Cullen
20 Jelle Klaasen

Payne is up in the top 60 following his win. All of Taylor's winnings are now being degraded, so he can't mathematically rise at all now. Clayton's barely a ton behind Barney and may have overtaken him by the time we play again. Klaasen is hanging on, with Lewis (both of them) and King within three grand. Dolan's good performances see him solidify a top 50 place which was under threat, Ricky Evans making two quarter finals sees him up into the top 64, while Clemens is just outside the top 70. Ryan Joyce continues his rise, two grand over the weekend putting him up to number 90, and the same amount for Michael Barnard lifts him into the last spot in the top 100.

Final words goes to Keith Deller - stating Adie has been to the last sixteen in the last five Pro Tour events, whilst accurate, is just asking for him to be knocked out early, which Arron Monk did in the first round. Top bokking.