Validation # 2

Let’s consider the case where a player with a DA Rating of 90 has a score of 2 at the start of his turn. Therefore he needs a double ‘1’ to go out. What points should he aim at with his first, second and third dart?

This case is simple enough for it to be answered using a spreadsheet program.

  1. Please refer to Fig. 2 in the paper. This figure shows the locations of the target points in a sector, and it assigns an index to each target point. In our simple example, the only points a player might reasonably aim at are the points 21, 22, 23 and 24 in the ‘1’ sector. To aim at any other point would clearly be illogical.
  2. For this example, the Darts Assistant recommends that the player should aim at point 22 with his first two darts, and point 21 with his third dart. (You can confirm this by playing an artificial darts game on the app itself: set your DA Rating to 90 (by Direct Setting) then arrange for your score to drop to 2.)
  3. Use DACheck1.xls to estimate the probability of hitting Double ‘1’ if the player aims at each of the four possible target points 21, 22, 23 and 24. In the same way, estimate the probabilities that he will miss the board (i.e. not score anything) if he aims at those four points. This gives these results:
    Target point # in the '1' sector Distance from centre, r Probability of missing the board Probability of hitting Double '1'
    21 6.4375 0.36492000 0.28669178
    22 6.625 0.51477347 0.26451904
    23 7.0 0.78868162 0.14818055
    24 7.375 0.94141227 0.04746863
  4. Now prepare a list of all combinations of the four possible target points. For example, the player could aim at point 21 on each of his three throws. Or he could aim at point 21 with his first dart, point 21 with the second dart, and point 22 with the third dart. The list would look like this:
    1st target point 2nd target point 3rd target point
    21 21 21
    21 21 22
    21 21 23
    21 21 24
    21 22 21
    21 22 22
    21 22 23
    21 22 24
    21 23 21
    21 23 22
    21 23 23
    21 23 24
    21 24 21
    21 24 22
    21 24 23
    21 24 24
    22 21 21
    22 21 22
    22 21 23
    22 21 24
      Etc.  
  5. Figure out for each combination of target points the probability that the player will go out in one turn.
  6. You can download an Excel file that performs these calculations if you right-click (option-click on the Mac) on this link DACheck2.xls, and then choose “Save As …”.
  7. Notice that this workbook has two tabs: Unsorted and Sorted. They are identical except for the fact that the Sorted sheet is sorted according to the probability of going out in one turn. You can see that the best combination of target points is 22, 22 and 21 on the 1st, 2nd and 3rd throws, respectively – which is exactly what the Darts Assistant recommended.
  8. Notice that even a small change in the target points can make a big difference. If you aim at 22, 22, 21 you will go out in 2.10 turns, on average. If you aim at 21, 21, 21 (only 3/16th of an inch difference on the first two darts) it will take you 2.33 turns – about 10% longer.