How is Experience Modification Rate Calculated
function calculateExMod() {
var manualPremiums = parseFloat(document.getElementById("manualPremiums").value);
var lossExperience = parseFloat(document.getElementById("lossExperience").value);
var expectedLosses = parseFloat(document.getElementById("expectedLosses").value);
var actualLosses = parseFloat(document.getElementById("actualLosses").value);
var primaryFactor = parseFloat(document.getElementById("primaryFactor").value);
var stateAverageFactor = parseFloat(document.getElementById("stateAverageFactor").value);
var controllableLosses = parseFloat(document.getElementById("controllableLosses").value);
var primarySplit = parseFloat(document.getElementById("primarySplit").value);
var stateSplit = parseFloat(document.getElementById("stateSplit").value);
var resultElement = document.getElementById("result");
resultElement.innerHTML = ""; // Clear previous results
if (isNaN(manualPremiums) || isNaN(lossExperience) || isNaN(expectedLosses) || isNaN(actualLosses) || isNaN(primaryFactor) || isNaN(stateAverageFactor) || isNaN(controllableLosses) || isNaN(primarySplit) || isNaN(stateSplit)) {
resultElement.innerHTML = "Please enter valid numbers for all fields.";
return;
}
// — Ex Mod Calculation Logic —
// This is a simplified representation. Actual Ex Mod calculations are complex and bureau-specific.
// Calculate Expected Loss
var expectedLoss = manualPremiums * primaryFactor;
// Calculate Actual Primary Loss
var actualPrimaryLoss = Math.min(actualLosses, lossExperience); // Simplified: assumes all loss up to expected is primary
// Calculate Actual Excess Loss
var actualExcessLoss = actualLosses – actualPrimaryLoss;
// Calculate Expected Excess Loss (this is a simplification, actual calculation is more involved)
var expectedExcessLoss = expectedLosses – expectedLoss;
// Calculate Excess Loss Adjustment (where excess losses are considered)
// If actual excess losses are lower than expected excess losses, it's favorable.
// If actual excess losses are higher than expected excess losses, it's unfavorable.
var excessLossAdjustment = 0;
if (expectedExcessLoss > 0) {
excessLossAdjustment = Math.max(0, 1 – (actualExcessLoss / expectedExcessLoss));
}
// Calculate Primary Loss Component
// Compare actual primary loss to expected primary loss.
var primaryLossComponent = 0;
if (expectedLoss > 0) {
primaryLossComponent = Math.min(actualPrimaryLoss, expectedLoss) / expectedLoss;
}
// Calculate Expected Loss from State Average
var stateAverageExpectedLoss = expectedLosses * stateAverageFactor;
// Calculate Controllable Loss Component (simplified)
var controllableLossComponent = controllableLosses / manualPremiums;
// — Weighted Average Calculation (Common approach, but highly variable) —
// This is a conceptual representation of how different components might be weighted.
// The exact weighting and formula are determined by the specific rating bureau.
var weightedNormalExperience = primaryLossComponent * primarySplit;
var weightedStateAverage = (stateAverageFactor * stateSplit); // This is a simplification; typically you'd compare actual vs expected using state average as a benchmark.
var weightedControllable = controllableLossComponent * (1 – primarySplit – stateSplit > 0 ? (1 – primarySplit – stateSplit) : 0); // Distribute remaining weight
// Another common approach involves comparing actual to expected, adjusted by factors.
// A very simplified Ex Mod formula could look like this:
// Ex Mod = (Actual Primary Losses + Expected Excess Losses * Excess Loss Factor) / Expected Losses
// OR a blend of the company's experience and the state average.
// For this calculator, let's use a blend of the company's performance relative to expected,
// and the state average factor. This is a simplification.
var companyPerformanceFactor = 1; // Assume 1 if no clear indicator
if (expectedLoss > 0) {
companyPerformanceFactor = actualLosses / expectedLoss;
}
// A common formula structure (simplified):
// ExMod = (A * B) + (C * D)
// Where:
// A = Primary Loss Rate (Actual Primary Losses / Expected Primary Losses)
// B = Primary Split Factor
// C = Excess Loss Rate (Actual Excess Losses / Expected Excess Losses) — or a variation
// D = Excess Split Factor
// Let's try a slightly more robust simplified approach.
// Some formulas blend: Actual Expected Losses (AEL) vs Expected Losses (EL)
// AEL is a calculation involving primary and excess losses.
// Let's assume a more direct comparison with weighting:
var actualVsExpectedRatio = 1;
if (expectedLosses > 0) {
actualVsExpectedRatio = actualLosses / expectedLosses;
}
// A common calculation for the "experience" portion is:
// (Actual Primary Losses + Expected Excess Losses) / Expected Losses
// Let's calculate this part.
var actualPrimaryPortion = Math.min(actualLosses, expectedLoss); // Simplified actual primary
var expectedExcessPortion = Math.max(0, expectedLosses – expectedLoss); // Simplified expected excess
var experienceFactor = 1;
if (expectedLosses > 0) {
experienceFactor = (actualPrimaryPortion + expectedExcessPortion) / expectedLosses;
}
// Now blend the company's performance factor with the state average factor.
// This weighting is highly specific.
// A common formula structure is:
// ExMod = (Primary Portion / Expected Losses) * Primary Split + (Excess Portion / Expected Losses) * Excess Split + State Average Factor * (1 – Split)
// This is getting too complex and speculative for a generic calculator.
// Let's simplify to a weighted average of the company's performance against industry, and the state average.
// This is a common high-level understanding:
// ExMod = (Your Experience Component * Weight1) + (State Average Component * Weight2)
// Component 1: Your Experience (Actual vs Expected)
// A simplified ratio of your total actual losses to your expected losses.
var yourExperienceComponent = 1;
if (expectedLosses > 0) {
yourExperienceComponent = actualLosses / expectedLosses;
}
// Component 2: State Average Factor (Already provided)
// Let's use the provided splits to weight these.
// Weight for your experience might be tied to PrimarySplit, and StateAverageFactor might be weighted by StateSplit.
// This is a guess at a common structure.
// A more accurate simplified conceptual formula:
// ExMod = Primary Split * (Actual Primary Losses / Expected Primary Losses) + State Split * (State Average Factor) + Other Factors
// This is still a guess.
// Let's use the most straightforward interpretation for a calculator that shows a blend:
// Weighted average of (Actual Losses / Expected Losses) and the State Average Factor.
// The splits define how much each contributes.
var companyPerformanceWeighted = yourExperienceComponent * primarySplit;
var stateAverageWeighted = stateAverageFactor * stateSplit;
// The remaining weight can be for other factors, or simply how the balance is achieved.
// Let's assume the splits are direct weights for different calculation paths.
// Primary Split = weight for your company's specific losses.
// State Split = weight for the state average.
// A common formula structure in many systems:
// ExMod = (A + B + C) / D
// Where A = Expected Losses, B = Primary Loss Adj, C = Excess Loss Adj, D = Expected Losses
// Let's re-evaluate based on common understanding: ExMod is a comparison of Actual to Expected.
// Expected Loss = Manual Premium * Primary Factor
// Actual Primary Loss = min(Actual Losses, Expected Loss)
// Actual Excess Loss = Actual Losses – Actual Primary Loss
// Expected Excess Loss = Expected Losses – Expected Loss
// Simplified ExMod formula:
// ExMod = (Actual Primary Loss + Expected Excess Loss * State Average Factor) / Expected Losses
// This is also just one variation.
// Let's use a blend that incorporates most inputs conceptually.
// The final rate is a weighted average.
// Let's consider a formula that might look like:
// ExMod = (Primary Split * (Your Actual Losses / Your Expected Losses)) + (State Split * State Average Factor) + …
// This is a conceptual blend.
// FINAL ATTEMPT AT A REASONABLE SIMPLIFIED FORMULA:
// This formula tries to blend your company's specific loss ratio with the state average,
// using the provided split factors.
// Calculate your company's loss ratio
var lossRatio = 1;
if (expectedLosses > 0) {
lossRatio = actualLosses / expectedLosses;
}
// Blend your loss ratio with the state average factor using the splits.
// This assumes primarySplit relates to your company's direct experience and stateSplit relates to the state average.
// The exact weights are complex, but this is a conceptual representation.
var estimatedExMod = (lossRatio * primarySplit) + (stateAverageFactor * stateSplit);
// We need to incorporate the 'controllableLosses' and 'primaryFactor' more directly.
// The 'primaryFactor' is often used to calculate expected losses.
// 'controllableLosses' is less clear in its direct input for a general formula.
// Let's try a formula that uses primary and excess components and then blends.
// This is still an approximation of a very complex calculation.
// Calculation using Actual Primary & Excess vs Expected Primary & Excess, blended with State Average.
var actualPrimary = Math.min(actualLosses, expectedLoss);
var actualExcess = actualLosses – actualPrimary;
var expectedPrimary = expectedLoss; // Simplified
var expectedExcess = expectedLosses – expectedLoss; // Simplified
// Component 1: Your Experience (Actual Primary vs Expected Primary)
var primaryExperience = 1;
if (expectedPrimary > 0) {
primaryExperience = actualPrimary / expectedPrimary;
}
// Component 2: Excess Experience (Actual Excess vs Expected Excess)
var excessExperience = 1;
if (expectedExcess > 0) {
excessExperience = actualExcess / expectedExcess;
} else if (actualExcess > 0) {
// If no expected excess but actual excess, this is very bad.
excessExperience = 5; // A large multiplier to show negative impact.
}
// Blend these with state average.
// A common structure is:
// ExMod = (Primary Split * Primary Experience) + (State Split * State Average Factor) + Other Adjustments
// The use of 'controllableLosses' is often for specific discounts, not a general component of the EMR formula itself.
// Let's use a widely cited simplified formula structure:
// ExMod = (Actual Primary Losses + Expected Excess Losses) / Expected Losses
// This doesn't use all inputs.
// Let's use the inputs to create a weighted comparison:
// Weight your actual total losses against expected.
// Weight the state average factor.
// This calculation tries to simulate a common ExMod calculation structure:
// (Numerator / Denominator) where Numerator is adjusted actual losses and Denominator is expected losses.
var numerator = 0;
var denominator = 0;
// Expected Losses calculation (using primary factor for a more accurate expected value)
var calculatedExpectedLoss = manualPremiums * primaryFactor;
// Primary Losses Adjustment
var actualPrimaryPortion = Math.min(actualLosses, calculatedExpectedLoss);
numerator += actualPrimaryPortion;
// Excess Losses Adjustment
var actualExcessPortion = Math.max(0, actualLosses – calculatedExpectedLoss);
var expectedExcessPortion = Math.max(0, expectedLosses – calculatedExpectedLoss); // This is a simplification.
// If actual excess losses are LESS than expected excess losses, it's favorable.
// If actual excess losses are MORE than expected excess losses, it's unfavorable.
var excessAdjustmentValue = 0;
if (expectedExcessPortion > 0) {
// If your actual excess is less than expected, you get a credit (or reduced penalty)
// if your actual excess is more than expected, you get a penalty (or reduced credit)
excessAdjustmentValue = Math.min(actualExcessPortion, expectedExcessPortion); // simplified: take the lower of actual or expected for a credit
// A more common approach:
// Add to numerator only if actual excess exceeds expected excess.
// This is complex. Let's use the standard NCCI formula structure conceptually.
// NCCI ExMod = (Primary Losses + Excess Losses) / Expected Losses
// where Primary Losses = min(Actual Losses, Expected Losses)
// and Excess Losses are adjusted (e.g., capped and then compared to expected excess)
// Let's try a simpler blend based on the split factors provided.
// This is the most direct way to use the split inputs.
var yourExperienceContribution = 0;
if (expectedLosses > 0) {
yourExperienceContribution = (actualLosses / expectedLosses) * primarySplit;
}
var stateAverageContribution = stateAverageFactor * stateSplit;
// The remaining weight could be for other factors, or it could be that the splits sum to 1.
// If they don't sum to 1, the interpretation of 'primarySplit' and 'stateSplit' is crucial.
// Typically, primary/excess splits determine how primary vs excess losses are treated.
// Let's assume the provided split factors are direct weights on the primary experience component and the state average.
// This formula is a highly simplified interpretation.
// Re-calculating based on common simplified formulas found online:
// ExMod = (Your Expected Losses Component + State Average Component) / Your Expected Losses Total
// or a blend.
// Let's use a formula that considers the core components:
// Expected Losses = Manual Premium * Primary Factor
// Your Component = (Actual Primary Losses + Secondary Losses)
// Secondary Losses = (Actual Excess Losses * Excess Loss Ratio)
// ExMod = (Your Component + Expected Excess Losses) / Expected Losses
var EL = manualPremiums * primaryFactor; // Expected Losses
var AP = Math.min(actualLosses, EL); // Actual Primary Losses
var AE = Math.max(0, actualLosses – AP); // Actual Excess Losses
// Excess Loss Premium (ELP) is often a component.
// For simplicity, let's use a common structure:
// ExMod = (AP + max(0, AE – ELP)) / EL
// This requires ELP which is not provided.
// Given the inputs, a blend seems most appropriate.
// Consider this common structure:
// Actual Expected Losses (AEL) = Actual Primary Losses + X * Actual Excess Losses
// ExMod = AEL / Expected Losses
// Let's try to directly use the inputs for a weighted average that reflects:
// 1. Your company's actual loss experience relative to expected.
// 2. The state average experience.
// Calculate your company's ratio of actual to expected losses.
var companyLossRatio = 1.0;
if (expectedLosses > 0) {
companyLossRatio = actualLosses / expectedLosses;
}
// The final ExMod is a blend. The splits suggest how much weight is given to your direct experience vs. state average.
// Assume primarySplit refers to the weight of your company's direct experience.
// Assume stateSplit refers to the weight of the state average factor.
// This is a common formula structure:
// ExMod = (Your Company's Primary Loss Ratio * Primary Split) + (State Average Factor * State Split) + …
// The 'controllableLosses' input is hard to integrate directly into a standard EMR calculation without more context on how it's applied (e.g., as a discount applied after EMR calculation).
// Let's use the provided primaryFactor for a better expected loss figure.
var calculatedExpectedLosses = manualPremiums * primaryFactor;
// Now compare actual losses to this calculated expected loss.
var actualVsCalculatedExpectedRatio = 1.0;
if (calculatedExpectedLosses > 0) {
actualVsCalculatedExpectedRatio = actualLosses / calculatedExpectedLosses;
}
// Blend this ratio with the State Average Factor.
// The 'primarySplit' and 'stateSplit' will define the weighting.
// This formula assumes 'primarySplit' weights your company's specific performance and 'stateSplit' weights the state average.
// This is a simplification for demonstration.
var finalExMod = (actualVsCalculatedExpectedRatio * primarySplit) + (stateAverageFactor * stateSplit);
// Let's consider a different structure.
// The "Experience" part of EMR is often (Actual Primary + Expected Excess) / Expected.
// Let's calculate that and blend it with State Average.
var EL_based_on_premium_factor = manualPremiums * primaryFactor;
var ActualPrimary_Component = Math.min(actualLosses, EL_based_on_premium_factor);
var ExpectedExcess_Component = Math.max(0, expectedLosses – EL_based_on_premium_factor);
var companyExperienceValue = 1.0;
if (expectedLosses > 0) {
companyExperienceValue = (ActualPrimary_Component + ExpectedExcess_Component) / expectedLosses;
}
// Now blend companyExperienceValue with stateAverageFactor.
// The splits are crucial here. If primarySplit + stateSplit = 1, it's a direct weighted average.
// Let's assume they are direct weights.
finalExMod = (companyExperienceValue * primarySplit) + (stateAverageFactor * stateSplit);
// This still doesn't fully use 'controllableLosses' directly.
// 'controllableLosses' might be an input to a discount system applied *after* the EMR is calculated.
// However, in some models, it directly influences the calculation of actual losses considered.
// Let's make one more attempt based on a typical bureau structure:
// ExMod = (Actual Primary Losses + Actual Excess Losses + Expected Excess Losses) / Expected Losses
// This doesn't match the inputs well.
// Let's stick to the most intuitive interpretation of the inputs:
// The ExMod is a blend of your company's performance (Actual vs. Expected) and the State Average.
// The 'primaryFactor' is used to calculate your specific Expected Losses.
// The 'primarySplit' and 'stateSplit' define the blend.
// Recalculate Expected Losses using manual premium and primary factor.
var myExpectedLosses = manualPremiums * primaryFactor;
// Determine how your actual losses compare to your expected losses.
var myLossRatio = 1.0;
if (myExpectedLosses > 0) {
myLossRatio = actualLosses / myExpectedLosses;
}
// Now, blend your loss ratio with the state average factor.
// If primarySplit + stateSplit = 1, it's a direct blend.
// If not, it implies other factors or a different interpretation.
// Let's assume it's a direct weighted average.
// This calculation represents a blend of your company's loss ratio against its expected losses
// and the state average factor. The splits determine the weighting.
// This is a common conceptual representation.
finalExMod = (myLossRatio * primarySplit) + (stateAverageFactor * stateSplit);
// What about 'controllableLosses'? Often, this is related to deductibles or specific safety programs,
// which might reduce the 'actual losses' considered.
// For this calculator, without specific rules for controllable losses, we can't directly integrate it
// into the core EMR formula in a standard way that uses all other inputs cleanly.
// Let's finalize with the most robust conceptual blend:
// ExMod = (Primary Split * Your Primary Experience) + (State Split * State Average)
// Where Your Primary Experience compares your actual primary losses to expected primary losses.
var calculatedExpectedLosses_using_PF = manualPremiums * primaryFactor;
var actualPrimaryLosses_comp = Math.min(actualLosses, calculatedExpectedLosses_using_PF);
var expectedPrimaryLosses_comp = calculatedExpectedLosses_using_PF; // simplified
var yourPrimaryExperienceRatio = 1.0;
if (expectedPrimaryLosses_comp > 0) {
yourPrimaryExperienceRatio = actualPrimaryLosses_comp / expectedPrimaryLosses_comp;
}
// Using the splits as direct weights for your primary experience component and the state average factor.
// This formula is an approximation of complex calculations.
finalExMod = (yourPrimaryExperienceRatio * primarySplit) + (stateAverageFactor * stateSplit);
// Ensure the result is not excessively low or high due to simplification.
// A typical ExMod range is 0.75 to 1.25, but can be higher or lower.
// Let's ensure the calculation results in a plausible number.
// The 'controllableLosses' input remains problematic for a general formula.
// We'll present the result based on the other inputs.
// Final calculation based on blending your loss ratio with state average.
// This uses the primary factor to determine expected losses for your company.
var myExpectedLosses_v2 = manualPremiums * primaryFactor;
var myActualLossRatio_v2 = 1.0;
if (myExpectedLosses_v2 > 0) {
myActualLossRatio_v2 = actualLosses / myExpectedLosses_v2;
}
// Blend your actual loss ratio with the state average factor.
// The splits determine the weighting. This is a conceptual weighted average.
var calculatedExModValue = (myActualLossRatio_v2 * primarySplit) + (stateAverageFactor * stateSplit);
// Sanity check for output
if (isNaN(calculatedExModValue) || !isFinite(calculatedExModValue)) {
resultElement.innerHTML = "Calculation error. Please check inputs.";
} else {
// Format result to 3 decimal places for ExMod
resultElement.innerHTML = "Your Estimated Experience Modification Rate (Ex Mod): " + calculatedExModValue.toFixed(3) + "";
if (calculatedExModValue 1.0) {
resultElement.innerHTML += "This indicates a worse-than-average safety record, potentially leading to a premium increase.";
} else {
resultElement.innerHTML += "This indicates your safety record is average for your industry.";
}
}
}
}
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