Interactive Roquet Probability Calculator

The math in the Interactive Roquet Calculator application was developed with the help of Wolfram|Alpha GPT and is based on probability and statistical modeling. Here's Wolfram's simplified explanation:

• Baseline Probability: The calculator starts by using your baseline accuracy, which is the chance of hitting a fully visible ball from 13 yards away. This is expressed as a percentage, calculated by your successful hits divided by total attempts (e.g., 12 hits out of 20 shots = 60%).
• Distance Scaling: The probability of hitting a ball changes with distance. The calculator uses a logistic distribution to model this. A parameter called 𝜙, derived from your baseline accuracy, determines how your success rate decreases with distance.
• Visibility and Lawn Quality Adjustments:
  • Visibility: The more of the target ball that is visible (not partially blocked by another ball or a wicket), the higher your chance of hitting it. This is modeled with a simple scaling factor that adjusts the base probability.
  • Lawn Quality: A better lawn makes shots more predictable, while a poor lawn increases the difficulty. The effect is modeled with a quadratic formula that either adds or subtracts from your probability.
• Critical Distance: The critical distance is where your probability of hitting remains consistently high. This is calculated as a direct multiple of your baseline accuracy.
• Probability Chart: The calculator generates a graph showing your probability of hitting the ball at various distances. This helps visualize how changes in baseline accuracy, visibility, and lawn quality impact your performance.

In six-wicket croquet, a 13-yard shot is intermediate—not as easy as a short shot (like 8 yards), but not as challenging as a longer one (18 yards). This makes it a balanced starting point, allowing the results to be easily extrapolated to both shorter and longer distances.

Mathematically, using 13 yards provides a convenient benchmark for scaling probabilities. From the logistic distribution, probabilities for other distances and target widths can be derived using simple scaling formulas. This makes the calculations consistent and straightforward.

The critical distance is the maximum range at which your probability of successfully hitting a target ball remains consistently high. It depends on your baseline accuracy and reflects the distance at which you can reliably make shots during gameplay.