Choosing a Forecasting Model

Key takeaways

• Start a prelaunch estimate with a Monte Carlo simulation using beta distributions. There is no empirical proof that it outperforms complex models, but its assumptions are visible and easy to revise.
• BG/NBD forecasts noncontractual repeat purchases. It does not suit subscriptions or predict first conversion.
• The widely cited Bass averages p=0.03 and q=0.38 are secondary citations, potentially dominated by durable goods; do not apply them directly to SaaS.
• MMM requires at least two years of weekly data. It does not suit new-channel forecasts or early startups.
• An agent-based model remains an illustrative toy until its inputs and outputs have been validated.

Which Model Fits?

Bass Diffusion

The innovation coefficient $p$ and imitation coefficient $q$ describe a new product's adoption curve.

$$f(t) = [p + qF(t)][1 - F(t)], \quad F(t) = \frac{1 - e^{-(p+q)t}}{1 + (q/p)e^{-(p+q)t}}$$ $$t^* = \frac{\ln q - \ln p}{p + q}$$

The averages $p\approx0.03$ and $q\approx0.38$ are widely cited. Secondary literature attributes them to Sultan, Farley, and Lehmann (1990; 213 applications), noting substantial variation. The original is paywalled and was not checked (grade D). These parameters imply a peak around 6.2 years (calculated). The equations were also checked through a secondary source rather than the original paper; only internal consistency was checked through numerical differentiation.

• Use for: an outline of new-product or feature adoption, especially products driven by word of mouth.
• Do not use for: applying durable-goods average parameters directly to SaaS or apps, short-term campaign conversion, or estimating market size from a few observations before the peak.

BG/NBD and Pareto/NBD

These models describe active-customer transactions with a Poisson process and dropout with a separate process. BG/NBD assumes dropout happens only immediately after a transaction; Pareto/NBD allows it at any time.

Inputs are each customer's transaction count $x$, last transaction time $t_x$, and observation period $T$. Fader, Hardie, and Lee (2005) trained on 39 weeks of data from 2,357 CDNOW customers and forecast another 39 weeks. BG/NBD underpredicted by 4% and Pareto/NBD by 2% (model paper).

• Use for: noncontractual repeat purchases, transaction and CLV forecasts for existing customers, and cohort comparisons.
• Do not use for: subscriptions with observed churn (consider shifted-beta-geometric models), prelaunch forecasts, or first conversion.
• We found no official minimum-data threshold.

Agent-Based Models

Use these when interactions between individuals generate the aggregate outcome. Rand and Rust (2011) identify conditions including intermediate scale, complex local interactions, and heterogeneity. Validation involves:

Do not use one merely to estimate an aggregate conversion rate. Without real data to compare against the outputs, its numbers are not trustworthy.

Marketing Mix Modeling

MMM decomposes revenue into a baseline and channel advertising effects, transformed for carryover and saturation.

Meridian offers calibration using past experiments as priors. Saturation curves are model assumptions, not measurements; without experimental calibration, similar problems to attribution can arise. These are documentation sources from the companies that built the tools.

• Use for: budget reallocation by organizations already spending across multiple channels.
• Do not use for: forecasting a new channel before spending, early startups, or campaign- and creative-level decisions.

The Complexity Trap

More complex models require more input assumptions. When most inputs are benchmarks, precise-looking outputs are an illusion. Start with a simple model and wide intervals; add complexity as real data accumulates.