Timothy Solomon | Builder, Thinker, Systems Architect

Here's something your CRM isn't telling you: your entire pipeline is decaying right now.

Every lead that was active yesterday is slightly colder today. Every opportunity that seemed urgent last week has lost a little momentum. Every contact who was engaged three weeks ago is now wondering who you are.

This isn't metaphorical. It's mathematical. And understanding the math changes how you should think about—and respond to—your pipeline.

The Decay Function

In physics, there's a phenomenon called exponential decay. It describes how quantities decrease over time—radioactive particles, temperature differentials, drug concentrations in the bloodstream.

Lead health follows the same pattern.

Without any intervention, a lead's "health"—their engagement, readiness, and likelihood to act—decreases over time. Not linearly, but exponentially. Today's hot lead is tomorrow's warm lead is next week's cold lead.

The basic formula:

H(t) = H₀ × e^(-t/τ)

Where:

H(t) is health at time t
H₀ is initial health (after last engagement)
τ (tau) is the "time constant" or contact lifespan
e is Euler's number (~2.718)

This equation says: health decays exponentially, at a rate determined by τ. A larger τ means slower decay (leads stay warm longer). A smaller τ means faster decay (leads go cold quickly).

Why "Derivative" Matters

The title of this essay claims lead health is a "derivative." Let me explain what that means and why it matters.

In calculus, a derivative measures rate of change. If position is where you are, velocity is the derivative—how fast you're moving. If velocity is how fast you're moving, acceleration is the derivative—how fast your speed is changing.

Lead health is a derivative in this sense: it measures how a lead's engagement is changing over time.

Score is like position—a point-in-time assessment of fit
Health is like velocity—how fast they're moving toward (or away from) action
Health change is like acceleration—is engagement speeding up or slowing down?

Most CRMs only track position (score). They're missing velocity (health) entirely. It's like trying to predict where a car will be in an hour when you only know where it is now—not how fast it's going or which direction.

The Differential Equation

For the mathematically inclined, lead health can be modeled as a differential equation:

dH/dt = -H/τ + A(t)

Where:

dH/dt is the rate of change of health
-H/τ is the decay term (health decreases proportionally to current health)
A(t) is the activity injection function (engagement boosts health)

This says: health is always decaying (first term), but activities can inject new health (second term).

Every email opened, page viewed, form submitted, or meeting held injects some amount of health. Between activities, health decays toward zero.

The equilibrium state—when a lead maintains constant health—requires ongoing engagement at a rate that exactly offsets decay. This is why leads go cold when you stop nurturing them: the decay continues but the injection stops.

What This Means Practically

Okay, enough math. What does this mean for how you actually manage your pipeline?

1. Time is Always Working Against You

Every day you don't engage a lead, they get colder. There's no "stable" state where a lead stays equally warm without input. The default trajectory is decay.

This creates urgency where urgency might not be obvious. A lead scored at 85 three weeks ago might look great—but if they haven't engaged since, their health is cratering even if the score hasn't changed.

2. Different Businesses Have Different τ

The time constant τ varies dramatically by industry, product, and buyer type:

B2C impulse purchase: τ might be days. A lead who doesn't buy in 72 hours is probably gone.
B2B SaaS: τ might be weeks. Leads stay warm for 2-4 weeks without re-engagement.
Enterprise sales: τ might be months. Long sales cycles mean slower decay.
High-consideration consumer: τ might be variable depending on the purchase cycle.

You need to know your τ. If you don't, you're treating all leads with the same urgency—which means under-serving fast-decaying leads and over-serving slow-decaying ones.

3. Health and Score Are Orthogonal

This is crucial and almost universally missed: lead health and lead score are independent dimensions.

Score (fit) asks: How well does this lead match our ideal customer profile?

Health (urgency) asks: How recently have they engaged, and how fast is their interest decaying?

A lead can be:

Score	Health	What this means
High	High	Ideal lead. Great fit, actively engaged. Prioritize!
High	Low	Great fit but going cold. Re-engage immediately before you lose them.
Low	High	Poor fit but very active. Disqualify gracefully—don't waste their time or yours.
Low	Low	Poor fit and disengaged. Let them go.

Most CRMs collapse these into a single dimension. High-score low-health leads look the same as medium-score medium-health leads. But they require completely different responses!

4. Health Enables Proper Re-engagement

When you track health explicitly, you can build re-engagement campaigns that actually make sense:

Health-based workflow:

IF health < 30 AND score > 70 THEN
    Trigger re-engagement sequence
    (Great fit going cold → bring them back)

IF health < 20 AND last_activity > 30 days THEN
    Move to long-term nurture track
    (Gone too cold for immediate action)

IF health > 80 AND qualification_stage = 'MQL' THEN
    Alert sales for immediate follow-up
    (Hot lead ready to move)

These workflows can't exist if health isn't tracked. You're left with crude rules like "email everyone who hasn't engaged in 14 days"—which treats high-score and low-score leads the same.

5. Health Decay Varies by Channel

Not all engagement decays at the same rate:

Website visit: Fast decay. Anonymous browsing fades from memory quickly.
Content download: Medium decay. They have your content, which persists.
Webinar attendance: Slower decay. Active participation creates stronger memory.
Demo request: Very slow decay. Explicit intent persists longer.
Meeting held: Slowest decay. Human connection maintains interest.

You might model this as different initial health injections:

Website visit: +10 health
Content download: +25 health
Webinar: +40 health
Demo request: +60 health
Meeting: +80 health

The higher the injection, the longer before decay brings health back to baseline.

Implementing Health in Your CRM

Here's how to actually build this:

Step 1: Define Your τ (Time Constant)

Analyze your historical data:

How many days between last touch and closed-lost, on average?
At what point do leads "go dark" and never return?
What's the typical sales cycle for deals that close?

A reasonable starting τ is: (typical_sales_cycle_days) / 3

If your typical deal takes 45 days, τ might be 15 days. This means a lead loses about 63% of their health in 15 days without activity (that's how exponential decay works).

Step 2: Define Activity Injections

Catalog all the ways a lead can engage and assign health values:

Activity	Health Injection
Email open	+5
Email click	+15
Page view	+10
Content download	+25
Form submission	+30
Demo request	+60
Meeting scheduled	+50
Meeting held	+80
Proposal viewed	+40

These numbers are illustrative—calibrate to your business.

Step 3: Build the Calculation

Option A: Batch recalculation (simpler)

Every night, recalculate health for all contacts
new_health = old_health × decay_factor + recent_activities
Decay factor for daily calculation: e^(-1/τ)

Option B: Event-driven calculation (more accurate)

Update health whenever an activity occurs
Decay from last activity time, then add new injection
More complex but reflects reality better

Step 4: Surface Health in Your UI

Don't bury health in a field nobody sees. Surface it:

Color-code leads by health band (green/yellow/red)
Sort views by health to prioritize urgent action
Alert on health drops for high-score leads
Include health in lead handoff information

Step 5: Build Health-Based Automations

Once you're tracking health, use it:

Re-engagement campaigns triggered by health drops
Escalation to sales when health + score both exceed thresholds
Archival workflows when health stays low for extended periods
Win-back campaigns for previously healthy leads that went cold

The Lyapunov Interpretation

For those interested in the deeper mathematics, lead health can be understood through the lens of Lyapunov stability.

In dynamical systems, Lyapunov functions measure how far a system is from equilibrium and whether it's moving toward or away from stability. Lead health serves as a kind of Lyapunov function for engagement:

Stable engagement: Health stays high, injections balance decay
Decaying engagement: Health drops, system moving away from active state
Recovery: New injections push health back up, approaching stable engagement

The equilibrium point (H = 0, no engagement) is a stable attractor—without input, all leads eventually reach it. Active engagement is an unstable state that requires constant energy to maintain.

This framing has practical implications: maintaining a healthy pipeline isn't a one-time achievement but an ongoing energy expenditure. You're fighting entropy.

Health Across the Pipeline

Health matters differently at different stages:

Early stage (Lead → MQL):

Health indicates general interest and engagement
Low health here is normal; leads often browse before engaging deeply
Focus on score to identify fit, use health to prioritize nurture

Mid stage (MQL → SQL → Opportunity):

Health becomes critical; these leads have expressed intent
Low health is a warning sign—intent is fading
Immediate re-engagement needed when health drops

Late stage (Opportunity → Close):

Health is paramount; deals die when momentum stops
Every day without engagement increases close uncertainty
Sales should track health obsessively

The further a lead has progressed, the more important health becomes. Losing a cold lead is cheap; losing a cold opportunity is expensive.

Why This Isn't Standard

Given how important health is, why don't most CRMs track it?

It requires calculus. Most CRM designers don't think mathematically about decay functions and derivatives.
It's computationally nontrivial. Calculating decay for millions of contacts requires infrastructure.
It's not in the standard model. The "lead score" paradigm dominates, and health doesn't fit neatly into it.
It reveals uncomfortable truths. Once you track health, you see how much of your pipeline is actually cold. That's not a report most CMOs want to present.

But the organizations that do track health operate at a different level. They catch decaying opportunities before they're lost. They prioritize truly urgent action. They stop wasting resources on zombie leads that look good but are actually cold.

Conclusion: Urgency is Temporal

The core insight is this: urgency is fundamentally temporal. It's about when, not just what.

A perfect-fit lead (high score) is worthless if they've gone cold (low health). A mediocre-fit lead (medium score) might close if they're red-hot (high health).

Lead score tells you about fit. Lead health tells you about urgency. You need both, and you need them separate.

Your pipeline is decaying right now. The question is whether you're tracking it—and whether you're doing anything about it.

This essay is part of the CRM Framework series. For implementation in software, see Oblio. For strategic consulting, see Hire Timothy Solomon.

Related Reading:

Lead Health is a Derivative