Squash PAR-15 Rally Win Probability
Solve bounded caller PAR target/win-by scoring state under independent constant rally probability, including analytic deuce; no universal PAR-15 rules, forecast calibration or betting advice.
Description
A point-a-rally game model combines score, target and win-by rules.
A point-a-rally game model combines score, target and win-by rules. An independent constant rally probability permits a finite recursion with an analytic deuce tail.1
The returned values include Modeled game win probability. The How section below explains the calculation, input rules and interpretation.
When to use Squash PAR-15 Rally Win Probability
Use Squash PAR-15 Rally Win Probability when you need to evaluate the supplied records under the calculation and evidence rules below. No universal PAR15 rules, calibrated forecast or betting recommendation is supplied.
Prepare the observed race, match or training records and the stated units. Supply independently verified rule editions, calibration tables and targets where requested.
How to use Squash PAR-15 Rally Win Probability and understand its results
- Prepare the observed race, match or training records and the stated units. Supply independently verified rule editions, calibration tables and targets where requested.
- Enter callerIndependentRallyWinProbability, observedPlayerScore, observedOpponentScore, callerTargetScore, callerWinByPoints using the field table and calculation rules, then run the tool.
- Read modeledGameWinProbability. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| callerIndependentRallyWinProbability | Caller independent rally win probability | number | Required |
| observedPlayerScore | Observed player score | number | Required |
| observedOpponentScore | Observed opponent score | number | Required |
| callerTargetScore | Caller target score | number | Required |
| callerWinByPoints | Caller win by points | number | Required |
Enter probability 0–1, integer target 1–50, win-by exactly 1 or 2, and integer active scores 0–100. Reject an already completed game. Memoize score-state transitions; use the analytic tied/advantage deuce solution for win-by-two and handle p=0/1 endpoints. Return modeled game-win probability.
deuceWin=p²/(p²+(1−p)²) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| modeledGameWinProbability | Modeled game win probability | number |
{
"input": {
"callerIndependentRallyWinProbability": 0.5,
"observedPlayerScore": 14,
"observedOpponentScore": 14,
"callerTargetScore": 15,
"callerWinByPoints": 2
},
"output": {
"modeledGameWinProbability": 0.5
}
}Limitations and assumptions
No universal PAR15 rules, calibrated forecast or betting recommendation is supplied.
Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Rugby Goal Kick Success Percent: Goal-kick success is conditional on actual kick opportunities. Pooling counts avoids equal weighting of unequal match exposures. For a complementary task, use Padel Average Rally Length Calculator: A rally-length mean requires observed evidence. Unknown rallies should not enter as zero-shot observations.
References
-
Squash PAR-15 Rally Win Probability — tool.io
Similar or alternative tools
- Rugby Goal Kick Success Percent
Goal-kick success is conditional on actual kick opportunities. Pooling counts avoids equal weighting of unequal match exposures.
- Padel Average Rally Length Calculator
A rally-length mean requires observed evidence. Unknown rallies should not enter as zero-shot observations.