Monetization AnalysisFlagship

LTV Curve Fitting and Segmented Calculation

Fit user LTV curves (exponential decay model) and segmented LTV (RFM / payment tier / VIP segments) on real-time AE data. Move from rough LTV estimates to curve fitting plus segmented calculation.

IndustriesGamesE-commerce

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skill · loadedindustry+100

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Fitted forecast curve

by cohort

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The LTV Curve Fitting and Segmented Calculation Skill is a lifetime-value prediction capability in ThinkingAI's industry Skill library. It helps operations and data teams run two LTV prediction methods on real-time AE data: B2 cohort LTV curve fitting (exponential decay model LTV(n)=LTV_base+(LTV_inf-LTV_base)(1-e^(-kn))) and B3 segmented LTV (RFM / payment tier / VIP segments), moving from rough LTV guesses to a quantified mode of curve parameters, segmented calculation, and prediction charts. This is ThinkingAI's decade of industry experience, packaged into ready-to-use Skills.

Live walkthrough

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ltv-curve-fitting-segmented-calculation

Run an LTV curve fit on the last 90 days of new users. We're currently buying traffic on an LTV of $80 and a CPI cap of $40, and I want to confirm whether that assumption still holds, plus give me D60/D90/D180 forecasts.

Confirm data mapping: payment event payment, amount property pay_amount

Matches the tracking plan

Check whether existing LTV reports can be reused

Reused the report "New-User LTV Cohorts", no rebuild needed

Call ae-analysis to pull daily cohort LTV over the last 90 days (D1–D30 actuals)

68,412 new users in the sample

Python environment check → fit an exponential-decay model with scipy curve_fit

LTV(n) = LTV_base + (LTV_inf − LTV_base)(1 − e^(−kn))

Fit complete

R²=0.98, residuals show no systematic bias

Compute forecasts and confidence intervals, generate the parameter table

Fit complete. Bottom line first: your LTV assumption is underestimated; the rough $80 estimate is about 34% below the curve's limit value, so the CPI cap has room to rise. Here are the full parameters and forecast.

1. Curve fit results

The cohort LTV of the last 90 days' new users (68,412 users) fits an exponential-decay model with R²=0.98; the fit quality is reliable:

Parameter	Value	Meaning
LTV_inf (limit value)	$120.86	Steady-state LTV after the curve converges
k (convergence speed)	0.0685	Rate of approach to the limit per day
Half-life	10.1 days	Days to reach half the limit value
Days to 90% of steady state	33.6 days	Days for LTV to reach 90% of the limit value

Last-90-day new-user LTV curve fit and extrapolated forecast　Unit: $

Actual LTVFitted curveForecast segment

2. LTV forecast

Forecast point	Forecast LTV	Distance to limit
D60	$119.2	98.6%
D90	$120.7	99.9%
D180	$120.9	≈100%

The curve reaches steady state around D34, and growth all but stops after D60. This means D60 is enough for the UA-recovery evaluation window; there's no need to wait for D180.

Conclusion

Per the fit, the experience-based rough estimate of $80 underestimated LTV by 34%. Keeping the "CPI ≤ 50% of LTV" safety factor, the CPI cap can rise from $40 to $60. But before raising it, look at the segments first: if the limit value is propped up mainly by top users, raising CPI across the board carries risk.

Break it down by segment. We're worried the 120 figure is inflated by whales and that dolphins and minnows never reach that level at all.

Recompute segmented LTV by VIP level (VIP0 / VIP1-2 / VIP3-4 / VIP5+)

Tally each segment's user count and revenue share

Independently fit each segment's curve and check its convergence shape

Generate the segment comparison table

Your worry points the right way, but the conclusion isn't so pessimistic. Segment results:

Segment	Share of users	D30 LTV	Revenue share
Non-payers (VIP0)	82.5%	$8.6	6.7%
Minnows (VIP1-2)	12.0%	$186	21.0%
Dolphins (VIP3-4)	4.7%	$1,250	55.3%
Whales (VIP5+)	0.8%	$2,250	17.0%

← Scroll to see more

Key finding: the revenue mainstay isn't whales, it's dolphins. VIP3-4 contribute 55.3% of revenue. Whales do have a high per-user LTV of $2,250, but their revenue share is 17.0%, and even removing them entirely, overall LTV is still about $100, above your current $80 assumption.

In other words, the $120.86 limit value isn't propped up by an extreme top tier; the dolphin segment's contribution is thick enough. The conclusion to raise CPI to $60 still holds after segment validation.

Recommendation

Two actionable recommendations: (1) raise the CPI cap $40 → $60, which should let UA scale grow about 50%, using D60 LTV as the recovery-validation checkpoint; (2) dolphins are the core base: monetization-depth operations (such as an advanced-bundle path for VIP3-4) have more leverage on overall LTV than acquiring new whales.

The "Segmented LTV Calculation Table" is saved to the project dashboard and updates automatically each week.

On your data

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The problem

LTV is the core metric of monetization analysis, yet more than 70% of teams still treat it as a rough guess. They don't know how fast the LTV curve converges (the k value), don't know the ceiling value (LTV_inf), and don't know that LTV can differ by more than 10x across payment tiers, so experience-based estimates are off by an average of 40%. The bigger problem is missing segmentation: an average LTV across all users cannot guide precise operations. A high-value retained customer may have 5x the LTV of an average developing customer, but without segmentation that gap stays invisible. Cohort LTV curve fitting is an even larger blind spot. Most teams only look at fixed D7/D30 LTV values, with no sense of the curve shape or half-life as days accumulate, and cannot predict the D60/D90/D180 LTV decay trend.

What it does

Three-gate pre-check: data mapping (confirm payment event and property names), LTV report reuse check, Python environment check. No guessing, no skipped steps

B2 curve fitting: scipy curve_fit fits the exponential decay model and outputs a full parameter set (LTV_inf, k, R², half-life, steady-state days)

B3 segmented calculation: compute LTV by RFM / payment tier / VIP and other dimensions, outputting user count, average LTV, and revenue share per segment

Complete prediction output: parameter table, D60/D90/D180/D365 forecasts, segment comparison table, and actionable recommendations

AE data driven: all data is pulled through the ae-cli three-path priority. No manual entry, no guessed event names

When to use it

You need to predict the D60/D90/D180 LTV decay trend

You need to calculate the LTV curve ceiling, convergence speed, and half-life

You need to view LTV differences across user groups by RFM segment

You need to compare LTV and revenue contribution by payment tier or VIP tier

You need LTV data to guide user acquisition decisions (only worth spending when CPI < LTV)

You need to confirm the payment event and amount property names in your project

In the field

Case

A card game · LTV curve fitting and segmented calculation

The operations team roughly estimated user LTV at around $80 and set a CPI cap of $40 accordingly. With the LTV Curve Fitting and Segmented Calculation Skill, the system confirmed the payment event was payment and the amount property was pay_amount, then completed B2 curve fitting: LTV_inf=120.86, k=0.0685, R²=0.98, half-life 10.1 days, 90% steady-state at 33.6 days. B3 segmentation showed VIP5+ users had an LTV of $2250 and a 17.2% revenue share. The team raised the CPI cap from $40 to $60 and scaled up user acquisition by 50%.

FAQ

What is the difference between B2 and B3?

B2 is cohort LTV curve fitting: it looks at the overall trend and ceiling of LTV across all users as days accumulate. B3 is segmented LTV: it looks at LTV differences across user groups (RFM / payment tier / VIP). They complement each other, with B2 showing the macro trend and B3 showing the micro differences.

What is LTV_inf?

LTV_inf is the ceiling of the LTV curve, the theoretical LTV if users never churned. In practice it represents the steady-state value after the LTV curve converges, a benchmark for how much this cohort will ultimately contribute.

How does this differ from the Revenue Forecast Skill?

LTV Curve Fitting and Segmented Calculation focuses on single-user lifetime value (micro-level user assessment), while Revenue Forecast focuses on total revenue trends and target paths (macro-level operations planning). Use LTV Curve Fitting and Segmented Calculation to predict single-user value first, then use Revenue Forecast to plan the overall path.

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