The Science behind the Ringer

Why is it so hard to throw a ringer?

This is a more complex question that expected. In the most simple form, the pole is 1” in diameter, and the quoit has a 3” diameter hole. Thus, for the quoit to not catch the top of the pole, the center of the quoit must pass through an area 2” in diameter, at the height of the top of the pole. This is equal to 3.1415 in². However, since no one throws quoits so that the ring is perpendicular to the trajectory of the quoit at the post (the quoit is not traveling straight down, instead it is on a low arc), the 2” diameter is reduced to an amount that varies with the angle of attack of the quoit and the trajectory of the arc at the height of the top of the pole. In a rough sense, this cuts the margin of error in half (different for each person). That means you have to get the center of your quoit to pass through an imaginary spot in the air, of approximately 1.57” in area. However, there is also an increase in chances based on non-exact hits that still stay on the pole. As any experienced pitcher will tell you, this really doesn't happen that often. Most of them end up bouncing several feet away. Field research models on this aspect are not yet finished.


Are there any formula's for working out the odds of a ringer?

If you know your CEP (Circular Error Probable), it's straight forward. CEP is a ballistics term. It is the radius of the circle that roughly half your quoits will land inside, and half will land outside. The smaller the CEP, the more accurate your toss. Define it in inches for simplicity. The other needed item is the area of the swath of air the hole in the quoit makes as it passes the top of the pole. If unsure, use 1.6

Chance of Ringer=SWATH/(2*∏*CEP²)

As an example, if my CEP is 14”, and I throw an average quoit, my odds are:

~1.57/(2*3.1415*14²)=.0125% chance on any given toss.

That's 800 quoit tosses per ringer.

However, if I am deadly accurate, throw a flat quoit, and my CEP is a meager 5” (I'm pretty much hitting the top of the pole every other toss):

~2.1/(2*3.1415*5²)=2.6% chance on any given toss.

Now it's a meager 74 tosses per ringer.


How can I increase my odds of throwing a ringer?

Just like getting to Carnegie Hall: practice, practice, practice. Also, the flatter your quoit on it's toss (the closer the quoit is to parallel to the ground while flying in the air), the greater your target area. A higher toss will also increase this, but higher tosses will also decrease your accuracy. You must find a balance that works for you.

Is it worthwhile to try to throw a ringer in competition?

No! The odds of having your quoit hit the pole and bounce far away greatly exceed your odds a getting the quoit on the pole. Thus, you are likely to give up the opportunity to both win points and prevent your opponent from winning points by going for a ringer. Roughly 1 in 9 quoits that hit the top of the pole will end up a ringer. You also suffer because your misses are now from an aimpoint 8-10" above the ideal aim point. Thus you tend to throw too long.