n = 25 reps
Q = $1,000,000/yr
t = 3 yrs
t/2 = 1.5 yrs
Standard Ramp (t = 3 yrs)
Year 1 β Reps in early back-weighted ramp. Contribution = 1/(2t) of full quota:
ΞSβ = n Γ Q Γ 1/(2t)
= 25 Γ $1,000,000 Γ 1/(2Γ3)
= 25 Γ $1,000,000 Γ 0.167
= $4,166,667
Back-weighted assumption: reps produce ~1/3 of output in first half of ramp, ~2/3 in second half. Averaged across Year 1, this nets to 1/(2t) of annual quota.
Year 2 β Reps still in ramp (t > 1). Late-ramp contribution = 1 β (tβ1)/(2t):
ΞSβ = n Γ Q Γ (1 β (tβ1)/(2t))
= 25 Γ $1,000,000 Γ (1 β (3β1)/(2Γ3))
= 25 Γ $1,000,000 Γ 0.667
= $16,666,667
In Year 2 the reps are in the back-weighted (high-output) phase of their ramp, producing proportionally more than Year 1.
Accelerated Ramp (t/2 = 1.5 yrs)
Year 1 β Ramp time is t/2, so contribution = 1/t of full quota:
ΞSβ = n Γ Q Γ 1/t
= 25 Γ $1,000,000 Γ 1/3
= $8,333,333
Halving ramp time exactly doubles Year 1 contribution β the entire acceleration benefit is front-loaded here.
Year 2 β Reps finish ramp mid-year (t/2 β€ 1 or t/2 β€ 2), fully productive by Year 2:
ΞSβ = n Γ Q
= 25 Γ $1,000,000
= $25,000,000
All reps hit full quota during or before Year 2 β Year 2 captures the full potential of the cohort.
Acceleration Lift
Additional revenue generated by halving ramp time:
ΞYear 1 Lift = $8,333,333 β $4,166,667 = $4,166,667
ΞYear 2 Lift = $25,000,000 β $16,666,667 = $8,333,333
Total 2-yr Lift = $12,500,000