TESTING OUT THE HEART OF DARTNES – IMPROVING DARTS WITH A.I

Darts is all about the numbers, and for most games, having a higher score than your opponent each round greatly increases your chances of winning. You should know already that the highest score on the dartboard that can be made with a single dart is the triple 20, giving you 60 points, but is this really the best place to aim on the board? Well, if you are a professional, of course that’s the best spot. But what about the rest of us who are looking for the upper hand?

Throwing 20s and hopefully hitting a few triple twenties is a great way to go about things as long as you don’t miss the target. The problem is, most of us think we are a lot better than we actually are, and if we are being honest, we actually hit a lot of 5s, 1s, and other numbers due to our inconsistency. I fancy myself as a bit of a dart player, and I can usually beat all my friends. But the truth is, I’m not that great. I can throw some wonderful darts that impress people, and quickly follow it up with darts all over the place. So is there a spot on the board you can throw that will increase your score over a game of darts?

Well, yes, it’s the bullseye! Conventional darting wisdom suggests that if you want to score more points and you are not that great, you are more likely to pick up a lot more points aiming for the bullseye than you would aiming for triple 20s. The difference is not about hitting the targets—it’s your misses that should give you a higher score. This was something I was planning to write about, along with understanding dart averages, until a friend sent me a link to The Heart of Dartness.

The Heart of Dartness is a neat web applet designed to help you determine exactly where on the board you should be aiming every single dart to maximize your dart score. The applet was dreamt up by three young Stanford boffins, Rayn J. Tibshirani, Andrew Price, and Jonathan Taylor as a way to help them take all the glory at their local tavern, and no doubt impress the ladies in the process.

How it works is, you throw up to 50 darts at the board and log the score of each dart. When you have entered all the numbers, you click the “Create heat map!” button. The applet runs some complicated mathematics (believe I tried to read the research paper), and then draws a heat map of your throws and suggests the optimal area you should aim at to maximize your score.

Well, that sounds pretty cool, so let’s give it a whirl and see what it does for me. Warning! My approach to this this applet is based more on me making stuff up as I go than any scientific reasoning.

First off, the principle behind this is that we all suck at triple 20s. So instead of throwing at the bullseye, I’m going to throw 50 darts at triple 20, and then 50 darts at the bull, and then compare the two and have a good laugh at how badly I scored. Aiming for triple 20 I scored 772 which is an average of 15.44 per dart. Throwing at the bull I scored 621, an average of 12.42 per dart. Wow! I scored 151 more points going for triple 20, and I had one bounce-out that I put down as zero. Very unexpected. I must be a darting god! That result was unexpected, but I guess you can’t account for flukes. I’m sure if I ran through this more than once, I’d get much different results.

The next step is to enter all the numbers from my throws at the bull and see if we can improve that score.

As we can see from the screenshot above, after I have entered my scores a heat map is created and a small dot it is placed on the dart board to show the best spot to aim for. In this case, the best spot to aim for me the single 7 just inside the triple ring. If I try and aim here, my maximum expected score should be 13.72. You can also mouse over the heat map and see what your expected score would be anywhere on the board. This is displayed below the heatmap, and in this case it shows that if I aimed for triple 20, I could expect to score 12.31 points.

Before I go on to see how I score, I thought I’d enter all my scores from aiming at triple 20 for no other reason than I already had the numbers. So you could say this a test using numbers a bit more randomly as they weren’t thrown at the bull.

This shows I should be aiming for the single 8 close to the bullseye. I could expect to score 12.05.

The next step now is to actually throw some darts at my my newly assigned number and see if my scores improve any.

First I’ll throw 50 darts at the single 7 just inside the triple ring as suggested by the first image:

Success! Aiming at this new target, I’ve increased my average per dart score by over 1.5 points. I’ve scored higher than my maximum expected score, and I even had two bounce-outs.

Now let’s see what happens if I readjust for my triple 20 scores:

Well, that was a disaster! I didn’t expect much as I wasn’t aiming at the correct target to get my new suggested score, although I did manage to score better than my maximum expected score. One interesting thing, though, is my score from aiming at this new target is slightly better than the score I got when I threw my first 50 darts at the bull.

I’m close to making a wishy-washy conclusion. The Heart of Dartness seems to work and has increased my scores a little, although I was expecting a huge jump in scores.

It’s all very well me standing at the dartboard and firing off a bunch of darts in the name of science while everyone else is is doing real work. What we need to do is apply this to some real games of 501 to see if I can crush the competition with my new aiming spot.

We will play four games of 501. In the first, I’ll be shooting for triple 20s; in the second I’ll shoot for bulls; the third game, I’ll aim for my suggested single 7 target; and in the last game, I’ll throw for silly single 8 target. I’ll record the scores from each round until I reach a finishing score (yeah I won’t finish, but I’ll get distracted and try and hit it):

Well, I managed to win two out of four games. Unfortunately, I didn’t win that all-important “Single 7” round. While I had greatly improved my average score under test conditions in the heat of the battle, I managed to show how bad my dart throwing can get.

Testing out The Heart of Dartness was good fun and was a great excuse to throw a bunch of darts in the office instead of doing any real work. I’m not convinced it has helped me to get any better scores, but I’ll be testing it out a bit more on my own time as the test conditions suggest I should have done better. The one thing I don’t get about it is, if I’m aiming for the bull, and my darts are landing outside the triple ring, how would it know?

I also know for a fact I throw better darts after a couple of beers (or at least that’s what I always tell myself), so these results may be a little skewed due to the lack of ale.

I would have liked to test out The Heart of Dartness with a non-dart player to see if we could improve their score. But I think my throwing was embarrassing enough throughout the test to show me I need to practice a hell of a lot more.

I’m kind of on the fence about The Heart of Dartness, but that’s because I only ran through it once and rather quickly. I think over the course of thousands of throws, you would see a marked improvement in your scores. I’m definitely going to try it out a bit more on my own time to see if I can’t win a few more games applying this data. Hopefully this post wasn’t too dry what with all those numbers. If you did take the time to study my scores, I hope at least they gave you a good laugh.