Different Levels of Players

[article from The Dart Book]

In every sport there are those who win championships. Then there are those who are in it as a hobby. There are many different levels and many ways to throw darts. There are those who make a living with it and those who just enjoy the social life that darts provides - and usually spend their salary in places where they meet. Both players - in my opinion - live a very full life and probably die with a big smile on their face.

For the lesser players, as in every sport, it's almost impossible to beat a master. This is also true in darts. However, it's typical of darts that the game is interesting even if the players are of different levels. With a little luck a beginner can beat an average player. But what's also typical of darts is that there are not many sports where players of different levels can and should do so much so differently from each other. The right choices depend on the level you are playing at. This is if you want to win the game.

It's very useful to watch the decisions masters make and learn from them. But when for example speaking about finishes in 501, all the masters have their own favourite finishes. Preferences speak more loudly when you try to find the best 'out', and there is not one objective player in the world to say which 'out' is the best. So this is not the way you can find the best finishes for your level. There is only one way to solve the problem. You must programme the computer to throw with the different - but exact - sprays of darts.

At first we must learn the figure of the dispersion. There is one old dart-player (there is no historical basis for this), Carl Friedrich Gauss (1777-1855), who helped us in this enormous task. Without his discovery of normally diversed phenomenon, it would be hard to calculate the probabilities exactly. Gauss's dispersion proved to depict the most natural symptoms in life. So we chose it to depict the distribution of dart shots.

Levels of players

After solving how the darts are spread around the aiming point you must decide which kind of players you want to take into your calculations. I decided to use four different levels of players. Just to make it easier for you to know what level I am talking about, I have named these levels: professional, expert, average and beginner.

Since the dispersions of darts should be exact for finding the exact percentages for these levels, there must be something that makes them exact. I have chosen the probability of hitting the treble-bed. The 'professional's' probability of hitting the treble is hereby always 46.42% in the book. An expert can hit the treble with the probability of 21.54%. For an average player the same figure is 10.00% and for the beginner only 4.64%.

I have not chosen these numbers randomly: the percentage of a professional raised to the third power makes exactly 10%. You can thus say that a 'pro' can get 180 points - three darts to treble-bed - every tenth time he tries. As you may already have guessed an expert can score 180p every 100th time and so on.

probability of probability of
hitting the scoring 180
treble points
------------------------------------------------------
professional (pro) 46.42% 1 to 10
expert (exp) 21.54% 1 to 100
average (ave) 10.00% 1 to 1000
beginner (beg) 4.64% 1 to 10000
------------------------------------------------------

You must, however, notice that the probability of getting 180 points is only theoretical: (46.4%^3 = 10%). After the first two darts there is already considerably less space on the treble-bed for the third dart. Therefore you often have to change your aiming point. Thus the 'right' probability of scoring the maximum score may be one-to-twenty or even less.

Then there is the mental pressure, which may be enormous. If you have never reached 180 points before, your hands may start to tremble. If you have practiced darts for many years already and have never scored 180, it is probably the biggest reason for this. It doesn't mean that you must now rank yourself in the 'beginners' group. In fact, even if you try to test the level of your play to find it out, there is no reason to start calling yourself 'an expert' or 'an average player'. As mentioned earlier, the names are used only because it's much easier to understand what kind of sprays I'm talking about. However, the test can help you to see what level you should be interested in.

On the other hand, after the first dart the beginner e.g. might have a good 'sighter' for his next shots, and the probability of throwing the remaining darts into the target can be much bigger than before. So, it's very hard to tell the exact level of scoring 180 points.

It would be more correct to say that an expert can hit three different trebles, for example T20, T15 and T16, every hundredth time. Since the theoretical probability is approximately right, it's easier to say that an expert can get 180 points every tenth time.

The Exact Dispersions of Darts

The next task is to iterate the dispersions to receive the exact required percentage. Compared to the first book there are many minor improvements. First, the probabilities are calculated much more accurately; instead of using circles of four millimetres, the areas around the aiming point are divided into parts smaller than 0.05 mm. The difference is significant for example in the bull's-eye, the smallest target on the board.

The computer is programmed to imitate the real world as closely as possible. For example, the wires hamper the players. The critical wire width is programmed to be 0.2 mm. This means that an expert aiming at the centre of a treble-bed loses 1.7% of his shots as 'wire-darts'. In the bull's-eye the probability of wire-darts is already 3.1% for the expert.

Note that the wires are, of course, wider than the given 0.2 mm, but if the dart hits a bit on the side of a wire it still goes in. It is not possible to know the exact percentage of wire-darts, but it is important to tell the computer that it's more probable in some areas - like in the bull's-eye - than in the centre of singles. Nowadays technology makes darts more flexible and the percentage of wire-darts is getting smaller.

When the term 'professional player' (pro) is used in the book it means a player who can throw (theoretically) 180 points every 10th time. The dispersion of darts is thus very small. You can hear the great 'one-hundred-and-eightyyy...' shouted at the biggest tournaments often enough to know that this level is not just theoretical. However, there aren't many players in the world who represent this honourable level of play.

Professional Player

As you can see in the picture, the area of possible hits is small, when a 'pro' aims at the centre of a treble-bed. The dispersion of this level is programmed to the computer, and it uses exactly the same spray of darts when aiming at any point on the board. When the dispersion is estimated to be normally divided, you can calculate the exact probabilities for this level.

Expert Player

Expert The spray of darts is still quite small. If an 'expert player' aims at the middle of triple-20, no darts are missed over sectors 1 and 5. The possibility of throwing 180 points is one in a hundred (1:100). The player of this level most certainly plays in a darts-league. Since this level is already represented by a much greater amount of players - and is still a very high level - I have tried to mention the 'expert' player often.

The spray of darts around treble-20 already looks more human and possible to reach than the one of a 'professional player'. Already 16% of his darts fly to the adjacent sectors. The average scoring is still very high: 74.7 points with three darts (without doubling). This level can be the result of a great deal of practice and years of social life in local pubs.

Average Player

Average The level of an average player can be very near the next one. The spray of hits is already quite large. Only one tenth of the darts hit triple-20 when aiming at the middle of it. Theoretically an average player (ave) is projected to throw 180 points every 1000th time. A few darts already miss over one sector and when for example trying the heart of treble-20, one dart in every thirteenth turn hits sector 18 or sector 12.

Only one tenth of the shots at a treble are successful. Note that the aiming point often has to be on the other side of a treble, when the bed is already crowded. Move the same spray of darts only one centimetre to the right and already every 26th dart (3.8%) hits sector 18 - meaning one dart every ninth turn. Does this look more like your play?

Beginner Player

Beginners are the group of players where levels vary the most. But when using the word 'beginner' (beg) in the book, it means that the spray of darts draws quite a large pancake around the aiming point. The 'beginner' finds it difficult to hit the same sector that he aims at and thus the average score is not much different in any area of the dart-board. 180 points is almost never achieved (1:10000).

A beginner finds it very frustrating to aim at a double-band. At first only one shot in fourteen will score. And then there is the baby in the next room who starts to cry every time you hit the enclosure cabinet. And these total misses are not few at the beginning of your road to the championship tournaments. Just a little practice and you will improve your play a great deal.

Theory

Note that in the 'real world' the dispersion of darts isn't usually exactly a circle, but an ellipse. This due to the way one throws darts at the dart-board. It's often more difficult to release the darts at the same point every time than to keep the same vertical line. This means the spray is more often high than wide. Of course there are players who do the opposite - they are the ones who are more likely to hit the single of sector six (and double-top) than the single-20.

To be more exact the ellipse may not be exactly vertical. For the right-handed players the figure usually leans a bit to the left. This comes from the motion of the hand when throwing. It also gives one more reason to use double-16 (and double-8) in doubling out.

For master players, however, the dispersion is closer to a circle and for them every area on the dart-board is quite as good.

Probabilities

As you have noticed, everything in darts has something to do with probabilities. When you choose the way of finishing you just try to find the best probability to win the game. The probability of the opponent finishing the next turn is also important. You can estimate these probabilities in your head or you can even calculate them mathematically, as you have seen done in the book first time ever.

At first you must find out the dispersions of darts for the player. You can do that with a test, but that would require a lot of throws to be reliable. Or you can do it purely mathematically when you know the theory of normal dispersion. Since we want to make the results of optimal play as general as possible, we must use a circle as the form of the dispersion. One way or another you have to know what the player's probability of hitting for example a double is, how many darts then fly to a single, which percentage to the sector beside and so on. These probabilities have to be known for every aiming point you want to calculate.