Capturing a wild Pokémon involves a complex mathematical formula that takes several variables into account. Unlike many RPGs where success is a flat percentage, Pokémon games (Generation 3 through 8) utilize a modified catch rate algorithm. This calculator uses the standard Generation 6+ formula to estimate your success rate.
The Primary Variables
To maximize your efficiency in completing the Pokédex, it is crucial to understand the four main pillars of the catch formula:
Species Catch Rate: Every Pokémon species has a base catch rate ranging from 1 (hardest) to 255 (easiest). For example, a basic Pidgey has a rate of 255, while a Legendary like Mewtwo often has a rate of 3.
HP Factor: Lowering a Pokémon's health is the most reliable way to increase your odds. The formula compares Current HP to Maximum HP; the closer the current HP is to 1, the higher the multiplier.
Ball Multiplier: Different Pokéballs apply different multipliers. A standard Pokéball has a 1x multiplier, whereas an Ultra Ball provides a 2x multiplier. Conditional balls like Dusk Balls or Quick Balls can offer up to 4x multipliers under specific circumstances.
Status Conditions: Inflicting status ailments significantly boosts catch rates. Sleep and Freeze provide the highest bonus (2.5x), while Paralysis, Poison, and Burn offer a smaller but substantial bonus (1.5x).
How the Math Works
The core calculation determines a "modified catch rate" (a) based on the variables above. The probability of a successful capture is roughly equivalent to a divided by 255. However, the game visually represents this through the "shake check." The ball must pass four random number checks (shakes) to succeed. If the ball shakes three times and clicks, the Pokémon is caught.
Tips for Capture
False Swipe is Essential: This move leaves the target with exactly 1 HP, maximizing the HP factor in the formula without making the target faint.
Prioritize Sleep: Since Sleep provides a 2.5x multiplier compared to the 1.5x of Paralysis, moves like Spore or Hypnosis are statistically superior for difficult catches.
Turn 1 Strategy: The Quick Ball offers a massive 4x multiplier but only on the very first turn of battle. It is often the most efficient way to catch wild Pokémon quickly.
function calculateCatchProbability() {
// 1. Get Input Values
var rateInput = document.getElementById('speciesRate').value;
var ballMod = parseFloat(document.getElementById('ballType').value);
var hpMax = parseFloat(document.getElementById('hpMax').value);
var hpCurr = parseFloat(document.getElementById('hpCurrent').value);
var statusMod = parseFloat(document.getElementById('statusAilment').value);
// 2. Validation
if (!rateInput || !hpMax || !hpCurr) {
alert("Please enter values for Catch Rate and HP.");
return;
}
var speciesRate = parseFloat(rateInput);
// Validate Logic ranges
if (hpCurr > hpMax) {
hpCurr = hpMax;
document.getElementById('hpCurrent').value = hpMax;
}
if (hpCurr < 1) hpCurr = 1;
if (speciesRate 255) speciesRate = 255;
// 3. Master Ball Check
if (ballMod === 255) {
displayResult(100);
return;
}
// 4. Calculate Modified Catch Rate (Gen 3-7 Formula Standard)
// Formula: a = ( ( (3 * HPmax – 2 * HPcurrent) * Rate * BallMod ) / (3 * HPmax) ) * StatusMod
// Note: The position of StatusMod varies slightly by Gen, but generally applies to the whole.
// We will use the Gen 6+ linear approximation structure.
var numerator = (3 * hpMax – 2 * hpCurr) * speciesRate * ballMod;
var denominator = 3 * hpMax;
// Prevent division by zero
if (denominator === 0) denominator = 1;
var a = (numerator / denominator) * statusMod;
// 5. Convert 'a' to Percentage
// If 'a' >= 255, catch is guaranteed.
// Probability approx = a / 255
var probability = 0;
if (a >= 255) {
probability = 100;
} else {
probability = (a / 255) * 100;
}
// Cap at 100%
if (probability > 100) probability = 100;
// 6. Display Results
displayResult(probability);
}
function displayResult(percent) {
var resultContainer = document.getElementById('resultContainer');
var probDisplay = document.getElementById('probabilityResult');
var ballsDisplay = document.getElementById('ballsNeededResult');
var meter = document.getElementById('probabilityMeter');
resultContainer.style.display = 'block';
// Format percentage
var finalPercent = percent.toFixed(2);
if (finalPercent.endsWith('.00')) {
finalPercent = Math.round(percent);
}
probDisplay.innerHTML = finalPercent + "%";
meter.style.width = finalPercent + "%";
// Calculate Expected Balls (Geometric Distribution Mean = 1/p)
if (percent >= 100) {
ballsDisplay.innerHTML = "1";
meter.style.background = "#4dff4d"; // Green
} else if (percent <= 0) {
ballsDisplay.innerHTML = "Infinite";
meter.style.background = "#ff4d4d"; // Red
} else {
var pDecimal = percent / 100;
var expected = 1 / pDecimal;
ballsDisplay.innerHTML = "~" + expected.toFixed(1);
// Color coding
if (percent < 10) {
meter.style.background = "#ff4d4d"; // Red
} else if (percent < 50) {
meter.style.background = "#ffa64d"; // Orange
} else {
meter.style.background = "#4dff4d"; // Green
}
}
}