## Any Three Darts

Since I bought my dartboard, I’ve been trying to find a yardstick for my own performance at 301. Three-dart average scores for pros are easy to find, but I haven’t come across any kind of guide for beginners.

Nor, I should say, am I convinced that a three dart average is the best way to track one’s progress at the start; something like triple-20s per round might be better. And T20 is just the beginning—closing is a different story altogether.

Despite these concerns, desperate for procrastination, I decided to calculate the average score for three darts thrown at random (not that the notion of a random throw makes much sense).

Please, let me know in the comments if you see any mathematical…er…improprieties.

### Assumptions

Each of these assumptions corrupts my calculations in some way.

• An equal distribution of probabilities across all points on the face of the board. Basically, I discount gravity as a factor.
• The absence of metal rings on the board. In my measurements of the board, I measure to and from the center of each metal ring. I do have one of those boards with thin wire and no staples, but I still occasionally get some bounceback. I’m pretending otherwise.
• 100% success at hitting the board. In my figures, no dart misses the board entirely. But in my living room, one wall is covered with a two-foot-wide strip of thick, blue high-density foam.

### Method

1. Find the total area of the board.
2. Calculate the area of each of the five scoring sections (double bull, single bull, triple ring, double ring, singles).
3. Calculate each area as a percent of the whole
4. Determine the average score for one dart across each section.
5. Multiply each average score times each area percentage, and add the five products. The result is the average score for a random dart, of which there is, of course, no such thing.

### Calculations

Note that I never multiply out all the πs. Since I’m ending with percentages (which are just ratios of x:100), I don’t really need to. I’ve also rounded everything to reasonable decimal places.

1. Total area = πr2 = π16.8cm2 = 282.24π cm
2. Areas of individual sections :
• Double bull: = π1.4 cm2 = 1.96π cm
• Single bull: = total single bull area – double bull area
= π3.4 cm2 – 1.96π cm
= 11.56π cm – 1.96π cm
= 9.6π cm
• Triple ring:
= area of outer triple circle – area of inner triple circle
= π10.5 cm2 – π9.5 cm2
= 110.25π cm – 90.25π cm
= 20π cm
• Double ring:
= area of outer double circle – area of inner double circle
= π16.8 cm2 – π15.8 cm2
= 282.24π cm – 249.64π cm
= 32.6π cm
• Singles: = Total board area – the other areas
= 282.24π cm – 9.6π cm – 20π cm – 32.6π cm
= 218.08π cm
3. Areas as Percentages
• Double bull: = (100 x DB area) / total area
= 196π cm / 282.24π cm
= .68%
• Single bull: = 960π cm / 282.24π cm
= 3.4%
• Triple ring: = 2000π cm / 282.24π cm
= 7.09%
• Double ring: = 3260π cm / 282.24π cm
= 11.55%
• Singles: = 21808π cm / 282.24π cm
= 77.27%
4. Average scores:
• Singles: 10.5 (average of the sum of all whole numbers from 1 to 20)
• Triple ring: 31.5 (singles average x 3)
• Double ring: 21 (singles average x 3)
• Single bull: 25 (can’t score anything else)
• Double bull: 50 (exactly)
5. Areas x Scores = (.0068 x 50) + (.034 x 25) + (.0709 x 31.5) + (.1155 x 21) + (.7727 x 10.5)
= 13.96 points

### Discussion

So, barring typos, miscalculations, and flawed assumptions of which I’m unaware, a dart hitting a board in a random spot will yield, on average, 13.96 points. Any three such ideal darts will yield just under 42 points.

In a game of 301, 42 points per turn would get you down under 60 (which is where I can start thinking about closing) in six turns, or 18 darts.

What should you conclude about your own game? Probably not much. For my part, I’m just noting that, as long as I’m shooting for T20, I’m doing a better than random, mostly getting down under 60 in 4, 5 or 6 rounds. That makes me, I would say, and average 301 player.

However, once it’s time to close, I’m not as good—and I don’t even play by the real rules, where you must close with a double. So, time to play some ‘Round the Clock.

### 2 thoughts on “Any Three Darts”

1. magnetic dartboard December 8, 2009 / 8:44 am

Great posting. Thanks for useful information.

Like

2. devan December 8, 2009 / 10:07 am