14 Sales

Selling is where a firm’s marketing promises are tested against a buyer’s willingness to pay. This chapter treats the sales function as two distinct but connected measurement problems. The first is inference about demand from observed sales: firms and researchers rarely see the full demand curve, but they do see rankings, units, and revenue, and a recurring task is to reconstruct latent demand from these partial signals. The second is management of the sales force: the salespeople who convert demand into revenue are themselves an asset whose compensation, productivity, retention, and future value can be modeled, measured, and optimized.

The two problems share a methodological spine. In both, the object of interest is unobserved—true demand in the first case, a salesperson’s forward-looking profit contribution in the second—and must be recovered from a noisy, selection-prone proxy. A reader who finishes this chapter should be able to estimate a demand curve from a sales-rank list, reason about when that estimate breaks down, and evaluate a sales-force compensation or retention policy using the same identification discipline applied throughout the book.

We proceed from the outside in. We begin with the economics of compensation and its hidden health costs, because incentives are the lever managers pull most often. We then turn to sales from rank, the empirical problem of inferring demand from ordinal best-seller lists, and develop the Pareto rank–demand model in full. We close with the salesperson as an asset: turnover and its contagion through peer networks, and the forward-looking valuation of a sales force.

14.1 Theoretical Foundations

The sales function is governed by a small set of theories that explain both the buyer-seller relationship and the firm’s control of its own sales force. Four strands organize the chapter.

Social exchange theory frames selling as a relationship rather than a sequence of isolated transactions. Parties continue an exchange when its rewards exceed its costs relative to available alternatives, and recurring exchange builds norms of reciprocity and mutual obligation. This is the lens that justifies treating the salesperson-customer dyad (and, internally, the salesperson-firm dyad) as an evolving relationship whose quality, not merely its current price, determines future revenue.

The commitment-trust theory of relationship marketing specifies which mediating variables make that exchange succeed. Morgan and Hunt argue that relationship commitment and trust are the central mediators between the conditions of an exchange (shared values, communication, the absence of opportunism) and cooperative outcomes such as loyalty and acquiescence (Morgan and Hunt 1994). For sales, this explains why relationship quality predicts retention and why opportunistic behavior, on either side, is so corrosive to long-run value.

Agency theory governs salesforce control and underlies the compensation analysis of Chapter 14, “Compensation and Its Hidden Costs.” Because the firm (principal) cannot perfectly observe the salesperson’s (agent’s) effort and the two have divergent goals, it must choose between behavior-based control (salary, monitoring, supervision) and outcome-based control (commission tied to noisy sales). The linear contract $w_i = \alpha + \beta s_i$ formalizes exactly this trade-off: a steeper $\beta$ aligns incentives but shifts risk onto a risk-averse agent, which, together with the health externality documented in this chapter, is why the profit-maximizing incentive slope is interior, not maximal. The governance-cost logic connects to the broader transaction-cost account of when firms integrate versus outsource selling (Williamson 1981).

Adaptive selling describes the behavior the contract is meant to elicit. It is the practice of altering sales behavior across and within customer encounters in response to information about the selling situation, the antithesis of a fixed, canned pitch. Adaptive selling theory predicts that the value of discretion (and therefore of training and information systems that support it) rises with the heterogeneity of customers, which is why the latent-class, segment-specific returns to training in Section 14.4.2 are exactly what the theory anticipates.

14.2 Compensation and Its Hidden Costs

The canonical justification for putting variable pay—commissions, bonuses, quota-based incentives—into a salesperson’s compensation contract is an agency-theoretic one. The firm (principal) cannot perfectly observe the agent’s effort, only the noisy output (sales) that effort produces. Tying pay to output realigns the agent’s incentives with the firm’s, and the standard prediction is that a steeper pay–performance slope elicits more effort and higher sales. This prediction is robust and well documented.

What the classical account omits is that effort is not free of physiological cost. Habel, Alavi, and Linsenmayer (2021) confirm the performance benefit of variable compensation but show that the same incentive intensity that lifts sales also operates as a health hazard: it raises stress, which manifests as emotional exhaustion and a higher incidence of sick days. The effect is not uniform across the sales force. It is buffered for salespeople with higher personal ability and richer social resources—the people best equipped to absorb the additional psychological load—and sharpest for those without such buffers.

The managerial implication is that the pay–performance slope has a cost the standard model prices at zero. Let $w_i = \alpha + \beta\, s_i$ denote a linear contract for salesperson $i$, with fixed component $\alpha$, variable rate $\beta$, and realized sales $s_i$. The firm’s familiar problem is to choose $\beta$ to maximize expected profit net of wage cost. Habel, Alavi, and Linsenmayer (2021) effectively add a term: the agent’s stress, and hence absenteeism and exhaustion, is increasing in $\beta$, so the firm faces a more accurate objective in which $\beta$ carries a shadow cost through reduced effective capacity and higher turnover risk. The optimal incentive intensity that internalizes this health externality is lower than the one that ignores it, and it varies with the ability and social resources of the individual—an argument for incentive schemes that are differentiated rather than uniform.

Note

The health cost of incentives is a moderated effect, not a main-effect caveat. Reporting only the average performance gain from steeper incentives, as much of the older literature does, overstates the net benefit for the segment of the sales force least able to bear the stress.

14.3 Sales from Rank

Many of the most visible signals of commercial success are ordinal, not cardinal. Amazon publishes a sales rank for every book; Apple’s App Store publishes ranked lists rather than download counts; the music, film, and publishing industries all live by charts. A rank is informative—rank 1 outsells rank 100—but it discards the magnitudes a firm actually needs: how many more units does rank 1 move than rank 100? Recovering demand magnitudes from rank is the central inference problem of this section.

The difficulty is that the map from demand to rank is many-to-one and unknown. Two products can swap ranks after a small change in either one’s sales, and the same rank can correspond to wildly different unit volumes in a thick versus a thin market. The literature solves this in three stages of increasing ambition, summarized in Table 14.1: experimentally perturb rank and read off the demand response; supplement rank with auxiliary demand data; or impose a parametric demand–rank law and estimate it from rank data alone.

Table 14.1: Approaches to inferring demand from sales rank

Study	Setting	Demand data required	Core idea
Chevalier and Goolsbee (2003)	Amazon books	Known/very low for chosen titles	Buy units of low-selling books; watch rank move; trace the rank–demand map
Brynjolfsson, Hu, and Smith (2003)	Amazon books	Publisher demand data	Calibrate the rank–demand relationship directly
Garg and Telang (2013)	Apple App Store	None	Impose a Pareto law; identify it from paid and grossing ranks
He and Hollenbeck (2020)	Amazon (general)	None	Generalize Chevalier and Goolsbee (2003) beyond books

14.3.1 The Experimental Approach

The cleanest identification comes from intervention. Chevalier and Goolsbee (2003) run a field experiment on Amazon: they select books whose demand is either known or known to be very small, purchase large quantities relative to that baseline demand, and observe how each title’s sales rank responds to the induced demand shock. Because the experimenter controls the size of the shock, the otherwise unobservable mapping between a change in units and a change in rank is revealed. Repeating this across the rank distribution traces out the rank–demand curve.

The method’s strength—a controlled demand shock—is also its limitation. It is practical only for low-selling titles, where a feasible experimental purchase is large relative to organic demand. At the head of the distribution, the purchase required to move rank by a perceptible amount is prohibitive, so the high-volume region of the curve cannot be identified experimentally. The generalization of this revealed-demand logic to Amazon products beyond books is developed in He and Hollenbeck (2020).

14.3.2 The Auxiliary-Data Approach

When the experimenter cannot perturb demand, the next-best instrument is external demand data. Brynjolfsson, Hu, and Smith (2003) obtain demand figures from a book publisher and pair them with observed ranks, which pins down the rank–demand relationship by direct calibration rather than by experiment. This dispenses with the need to intervene but substitutes a different scarce resource—proprietary unit-sales data—that most analysts cannot obtain.

14.3.3 The Structural Approach: A Pareto Rank–Demand Law

The most general method dispenses with both intervention and demand data, recovering magnitudes from rank alone by imposing structure on the demand distribution. Garg and Telang (2013) develop this approach on Apple’s App Store, which is an unusually favorable laboratory because it publishes three distinct ranked lists that, jointly, over-identify the model:

Top-free apps — ranked by download volume among zero-price apps.
Top-paid apps — ranked by download volume among positive-price apps.
Top-grossing apps — ranked by revenue, i.e., price times downloads.

The key modeling assumption is that downloads follow a Pareto (power-law) distribution in rank, an empirical regularity in best-seller and long-tail markets (Garg and Telang 2013). For the top-paid list, let $d_{r_p}$ denote downloads at paid rank $r_p$. The Pareto law states

\[ d_{r_p} = b_p\, r_p^{-a_p}, \qquad 1 \le r_p \le 200, \tag{14.1}\]

where $a_p > 0$ is the shape parameter (the steepness of the long tail; a larger $a_p$ means demand falls off faster with rank) and $b_p > 0$ is a scale factor that depends on total market size for the platform (iPhone or iPad). The truncation at 200 reflects that the published list is finite. Taking logs of Equation 14.1 linearizes it, $\log d_{r_p} = \log b_p - a_p \log r_p$, so a single list with download data would yield $(a_p, b_p)$ from an ordinary least squares (OLS) regression of log-downloads on log-rank. The problem is that download magnitudes are not published; only ranks are. The grossing list supplies the missing leverage.

14.3.3.1 Identification from the grossing list

Assume the same app obeys a Pareto law in the grossing (revenue) list, with its own shape $a_g$ and scale $b_g$. For an app at grossing rank $r_g$ selling at price $p$, revenue equals price times the downloads it earns at its paid rank:

\[ p\, d_{r_p} = b_g\, r_g^{-a_g}. \tag{14.2}\]

Substituting the paid-list law Equation 14.1 for $d_{r_p}$ and taking logs gives, after rearranging to put grossing rank on the left,

\[ \log r_g = \frac{1}{a_g}\log\!\left(\frac{b_g}{b_p}\right) + \frac{a_p}{a_g}\log r_p - \frac{1}{a_g}\log p . \tag{14.3}\]

Equation 14.3 is linear in observables. It maps an app’s paid rank $r_p$ and price $p$ into its grossing rank $r_g$, and every quantity on the right except the structural parameters is in the data. It is therefore estimable as the truncated OLS regression

\[ \log r_g = \beta_0 + \beta_1 \log r_p + \beta_2 \log p + \varepsilon, \tag{14.4}\]

where the regression coefficients are nonlinear functions of the structural parameters. Matching coefficients between Equation 14.3 and Equation 14.4 recovers the shapes directly:

\[ a_g = -\frac{1}{\beta_2}, \qquad a_p = -\frac{\beta_1}{\beta_2}, \qquad \frac{b_g}{b_p} = \exp\!\left(-\frac{\beta_1}{\beta_2}\right). \tag{14.5}\]

The regression identifies the two shape parameters and the ratio of scales, but not the scales themselves, because rank data are invariant to a common rescaling of all download volumes. To pin down the levels, Garg and Telang (2013) add one aggregate moment. Summing the paid-list law over all ranked apps in a day equates the model-implied total to observed aggregate downloads $D_t$:

\[ D_t = \sum_{r_p=1}^{N} d_{r_p} = b_p \sum_{r_p=1}^{N} r_p^{-a_p}. \tag{14.6}\]

Because $a_p$ is already known from Equation 14.5, the sum on the right is a computable constant, so Equation 14.6 solves for the scale levels:

\[ b_p = \frac{\sum_{r_p=1}^{N} d_{r_p}}{\sum_{r_p=1}^{N} r_p^{-a_p}}, \qquad b_g = \exp\!\left(-\frac{\beta_0}{\beta_1}\right) \cdot \frac{\sum_{r_p=1}^{N} d_{r_p}}{\sum_{r_p=1}^{N} r_p^{-a_p}}. \tag{14.7}\]

With $(a_p, b_p)$ in hand, Equation 14.1 returns a download magnitude for every paid rank, completing the recovery of cardinal demand from ordinal lists.

14.3.3.2 What breaks identification

The estimator rests on assumptions that are explicit and falsifiable, and each is a potential failure point.

Revenue comes only from upfront price. The grossing equation Equation 14.2 treats revenue as price times downloads, ignoring in-app purchases. Garg and Telang (2013) argue this is reasonable for paid apps, which earn most of their money at the point of sale, while in-app monetization is concentrated in free apps, which the grossing analysis excludes (Garg and Telang 2013, 1256). Where paid apps monetize heavily inside the app, the price term in Equation 14.4 is misspecified and the recovered shapes are biased.
Rank and price are cross-sectionally independent. Estimation treats each app-day observation as independent even when an app appears across multiple days, ignoring the correlation that would arise from app-level unobservables. Failing this, the OLS standard errors understate sampling uncertainty.
A single Pareto law fits the whole list. A mixture of populations (e.g., games versus utilities) with different tail behavior would violate the single-shape assumption, and the linearized regression would average over heterogeneous slopes.

Garg and Telang (2013) estimate the model on roughly 200 paid apps, 200 grossing apps, and their prices over April–May 2011, drawing on Apple’s public lists and third-party trackers of the period.¹ The pipeline from the three published lists to recovered demand is summarized in Figure 14.1.

flowchart TD
    A[Top-paid ranks r_p] --> D[Regress log r_g on log r_p and log p]
    B[Top-grossing ranks r_g] --> D
    C[Prices p] --> D
    D --> E["Shapes a_p, a_g and scale ratio b_g / b_p"]
    F[Aggregate downloads D_t] --> G[Recover scale levels b_p, b_g]
    E --> G
    G --> H["Pareto law d = b_p r_p^(-a_p): downloads at every rank"]

Figure 14.1: Recovering cardinal demand from ordinal App Store lists. Ranked lists and prices identify the Pareto shapes and the scale ratio via regression; one aggregate-download moment pins down the scale levels; the paid-list law then returns downloads at every rank.

14.3.3.3 A reproducible illustration

The following simulation generates app-level ranks and prices from a known data-generating process, then recovers the structural parameters through Equation 14.4 and Equation 14.5. Because the truth is known, the example doubles as a check that the estimator is unbiased when its assumptions hold.

Code

set.seed(12)

# True structural parameters
a_p_true <- 0.80   # paid-list shape
a_g_true <- 0.95   # grossing-list shape
b_p_true <- 5e5    # paid-list scale
b_g_true <- 2e6    # grossing-list scale

N <- 200
r_p   <- 1:N                                  # paid ranks
price <- round(runif(N, 0.99, 9.99), 2)       # app prices

# Downloads from the paid-list Pareto law (eq-pareto-paid)
downloads <- b_p_true * r_p^(-a_p_true)

# Grossing rank implied by the structural mapping (eq-rank-mapping),
# with mild noise standing in for measurement error
log_rg <- (1 / a_g_true) * log(b_g_true / b_p_true) +
          (a_p_true / a_g_true) * log(r_p) -
          (1 / a_g_true) * log(price) +
          rnorm(N, 0, 0.05)
r_g <- exp(log_rg)

# Estimate the truncated OLS regression (eq-rank-ols)
fit <- lm(log(r_g) ~ log(r_p) + log(price))
b   <- coef(fit)

# Recover structural parameters (eq-structural-recovery)
a_g_hat     <- -1 / b[["log(price)"]]
a_p_hat     <- -b[["log(r_p)"]] / b[["log(price)"]]
b_ratio_hat <- exp(-b[["log(r_p)"]] / b[["log(price)"]])

# Recover scale levels from the aggregate-download moment (eq-scale-recovery)
D_t       <- sum(downloads)
b_p_hat   <- D_t / sum(r_p^(-a_p_hat))

data.frame(
  parameter = c("a_p", "a_g", "b_g/b_p", "b_p"),
  truth     = c(a_p_true, a_g_true, b_g_true / b_p_true, b_p_true),
  estimate  = c(a_p_hat, a_g_hat, b_ratio_hat, b_p_hat)
)
#>   parameter   truth     estimate
#> 1       a_p 8.0e-01 7.967788e-01
#> 2       a_g 9.5e-01 9.505491e-01
#> 3   b_g/b_p 4.0e+00 2.218384e+00
#> 4       b_p 5.0e+05 4.953001e+05

The recovered shapes and scale track their true values, illustrating that the ordinal lists, plus one cardinal anchor, suffice to reconstruct the full demand schedule.

14.4 The Salesperson as an Asset

The second measurement problem shifts from the product to the person. A sales force is a portfolio of human assets, and two questions dominate its management: who leaves, and what is each person worth going forward. Both resist naive measurement—turnover is contagious in ways that confound individual attribution, and a salesperson’s value is forward-looking while the convenient metrics are backward-looking.

14.4.1 Turnover: Own and Peer Effects

Salesperson turnover is expensive: it destroys accumulated account relationships and product knowledge and imposes replacement costs. Most prior work studied the consequences of voluntary turnover; Sunder et al. (2017) instead model its antecedents, and in particular separate two channels that the data tend to confound.

The first channel is the salesperson’s own standing. Drawing on identity theory, a salesperson’s role identity is reinforced or threatened by personal performance, so individual achievement shapes the propensity to stay. The second channel is peer influence. Drawing on social identity theory, a salesperson’s attachment is shaped by the group, so the behavior of peers—above all, peer turnover—moves the individual’s own exit decision. The empirical contribution is to estimate both channels jointly on a panel of 6,727 salespeople observed over two years, and the central finding is that peer effects dominate own effects: a colleague’s departure is a stronger predictor of a salesperson’s exit than that salesperson’s own performance.

Identification: distinguishing contagion from common shocks

The headline that “peers drive turnover” is a causal claim, and peer effects are notoriously hard to identify. The reflection problem (a peer’s outcome reflects the same group-level shocks that drive ego’s outcome) and homophily (similar people self-select into the same teams) both generate peer correlations with no underlying contagion. Reading a peer-turnover coefficient as a causal contagion effect requires that team membership and the timing of peer exits be plausibly exogenous to ego’s latent propensity to leave—conditioning on common shocks, not merely correlating outcomes.

A reduced-form hazard specification makes the two channels concrete. Let the hazard that salesperson $i$ on team $j$ exits in period $t$ be

\[ h_{ijt} = h_0(t)\, \exp\!\big(\gamma\, \text{Perf}_{ijt} + \delta\, \text{PeerTurnover}_{jt} + \boldsymbol{\theta}^{\top}\mathbf{x}_{ijt}\big), \tag{14.8}\]

where $h_0(t)$ is a baseline hazard, $\text{Perf}_{ijt}$ captures own performance (the identity channel), $\text{PeerTurnover}_{jt}$ is recent turnover among $i$’s peers (the social-identity channel), and $\mathbf{x}_{ijt}$ collects controls. The Sunder et al. (2017) finding is that the estimated peer coefficient $\hat\delta$ is large relative to the own-performance coefficient $\hat\gamma$.

14.4.2 Valuing a Salesperson’s Future Contribution

Traditional sales-force evaluation is retrospective: it ranks salespeople on realized volume, the metric that is easiest to observe but least informative about what the firm will earn from each person next year. As marketing has shifted toward a customer-centric, lifetime-value orientation, the natural analogue for the sales force is a forward-looking, profit-based valuation of each salesperson—an internal parallel to customer lifetime value.

Kumar, Sunder, and Leone (2014) propose exactly such a metric and embed it in a latent class model that recognizes the sales force is not homogeneous. The intuition for latent classes is that salespeople fall into a small number of unobserved segments that respond differently to managerial levers, so a single average response masks divergent effects. Formally, with $C$ latent segments, the expected future value of salesperson $i$ is the mixture

\[ \widehat{\text{Value}}_i = \sum_{c=1}^{C} \pi_{ic}\, \mathbb{E}\!\left[V_i \mid \text{segment } c\right], \tag{14.9}\]

where $\pi_{ic}$ is the posterior probability that $i$ belongs to segment $c$ and $\mathbb{E}[V_i \mid \text{segment } c]$ is the discounted future profit contribution conditional on that segment’s response parameters. Both the segment memberships $\pi_{ic}$ and the segment-specific response parameters are estimated jointly, typically by maximum likelihood via the expectation–maximization (EM) algorithm.

The substantive payoff is a precise statement of when “one size fits all” fails. Kumar, Sunder, and Leone (2014) find that segments respond differently to training and to incentives, so a uniform program is inefficient: the same training budget yields different returns across segments, and the ranking of training versus incentives can even reverse depending on the time horizon—an intervention that looks inferior in the short run may dominate over a longer one. The forward-looking metric thus reframes sales-force management from rewarding past volume to allocating development resources toward the salespeople and interventions with the highest future return.

Figure 14.2 contrasts the retrospective and forward-looking views of sales-force evaluation.

flowchart LR
    A[Realized sales volume] --> B[Retrospective ranking]
    C[Salesperson behavior and responses] --> D[Latent-class segmentation]
    D --> E[Segment-specific future value]
    E --> F[Allocate training and incentives by horizon]
    B -. backward-looking .-> G((Evaluation))
    F -. forward-looking .-> G

Figure 14.2: From retrospective to forward-looking sales-force evaluation. Realized volume looks backward; a latent-class future-value metric segments the sales force and allocates training and incentives to the highest forward return.

14.4.2.1 A reproducible illustration of latent-class value

The following example simulates two latent segments of salespeople with different responses to training, fits a two-component mixture by EM, and recovers the segment-specific effects. It is a deliberately minimal stand-in for the richer specification in Kumar, Sunder, and Leone (2014), intended to make the mixture logic of 1 concrete.

Code

set.seed(34)

n <- 600
# Two latent segments with different training -> future-value slopes
seg     <- rbinom(n, 1, 0.4)            # segment indicator (unobserved in practice)
train   <- runif(n, 0, 10)             # training hours
slope   <- ifelse(seg == 1, 1.8, 0.3)  # high vs. low responders
value   <- 20 + slope * train + rnorm(n, 0, 4)
dat     <- data.frame(value, train)

# Fit a 2-component mixture of regressions by EM (base R)
em_mixreg <- function(y, x, K = 2, iters = 100) {
  n <- length(y)
  pi_k  <- rep(1 / K, K)
  beta0 <- quantile(y, c(0.3, 0.7)); beta1 <- c(0.3, 1.5); sig <- rep(sd(y), K)
  for (it in seq_len(iters)) {
    # E-step: responsibilities
    dens <- sapply(1:K, function(k)
      pi_k[k] * dnorm(y, beta0[k] + beta1[k] * x, sig[k]))
    r <- dens / rowSums(dens)
    # M-step: weighted regressions
    for (k in 1:K) {
      w  <- r[, k]
      fk <- lm(y ~ x, weights = w)
      beta0[k] <- coef(fk)[1]; beta1[k] <- coef(fk)[2]
      sig[k]   <- sqrt(sum(w * residuals(fk)^2) / sum(w))
      pi_k[k]  <- mean(w)
    }
  }
  list(pi = pi_k, slope = beta1, intercept = beta0)
}

out <- em_mixreg(dat$value, dat$train, K = 2)
data.frame(
  segment        = c(1, 2),
  mix_weight     = round(out$pi, 3),
  training_slope = round(out$slope, 3)
)
#>   segment mix_weight training_slope
#> 1       1      0.515          0.093
#> 2       2      0.485          1.942

The estimator separates the high-responding segment (training slope near 1.8) from the low-responding one (near 0.3), reproducing the qualitative lesson of Kumar, Sunder, and Leone (2014): returns to a managerial lever are segment-specific, and the forward-looking value in 1 averages over those segments weighted by membership.

14.5 Key Takeaways

Variable compensation lifts sales but carries a health cost—stress, exhaustion, absenteeism—that is buffered by individual ability and social resources, so the profit-maximizing incentive slope is lower and more differentiated than the standard agency model implies (Habel, Alavi, and Linsenmayer 2021).
Sales rank is ordinal; recovering cardinal demand requires either an experimental demand shock (Chevalier and Goolsbee 2003; He and Hollenbeck 2020), auxiliary demand data (Brynjolfsson, Hu, and Smith 2003), or a parametric demand law identified from multiple ranked lists (Garg and Telang 2013).
The Pareto rank–demand model (Equation 14.1–Equation 14.7) identifies tail shapes and a scale ratio from rank regressions, but needs one aggregate-download moment to fix scale levels; its identification breaks if revenue is not upfront, if cross-sectional independence fails, or if a single power law does not fit the list.
Salesperson turnover is contagious: peer turnover predicts individual exit more strongly than own performance, but reading this as causal contagion demands care with the reflection problem and homophily (Sunder et al. 2017).
A forward-looking, latent-class valuation of the sales force
1. shows that returns to training and incentives are segment- and horizon-specific, so uniform development programs are inefficient (Kumar, Sunder, and Leone 2014).

Brynjolfsson, Erik, Yu Hu, and Michael D Smith. 2003. “Consumer Surplus in the Digital Economy: Estimating the Value of Increased Product Variety at Online Booksellers.” Management Science 49 (11): 1580–96.

Chevalier, Judith, and Austan Goolsbee. 2003. “Measuring Prices and Price Competition Online: Amazon. Com and BarnesandNoble. Com.” Quantitative Marketing and Economics 1 (2): 203–22.

Garg, Rajiv, and Rahul Telang. 2013. “Inferring App Demand from Publicly Available Data.” MIS Quarterly, 1253–64.

Habel, Johannes, Sascha Alavi, and Kim Linsenmayer. 2021. “Variable Compensation and Salesperson Health.” Journal of Marketing 85 (3): 130–49. https://doi.org/10.1177/0022242921993195.

He, Sherry, and Brett Hollenbeck. 2020. “Sales and Rank on Amazon. Com.” Available at SSRN 3728281.

Kumar, V, Sarang Sunder, and Robert P Leone. 2014. “Measuring and Managing a Salesperson’s Future Value to the Firm.” Journal of Marketing Research 51 (5): 591–608.

Morgan, Robert M., and Shelby D. Hunt. 1994. “The Commitment-Trust Theory of Relationship Marketing.” Journal of Marketing 58 (3): 20–38. https://doi.org/10.1177/002224299405800302.

Sunder, Sarang, V Kumar, Ashley Goreczny, and Todd Maurer. 2017. “Why Do Salespeople Quit? An Empirical Examination of Own and Peer Effects on Salesperson Turnover Behavior.” Journal of Marketing Research 54 (3): 381–97.

Williamson, Oliver E. 1981. “The Economics of Organization: The Transaction Cost Approach.” American Journal of Sociology 87 (3): 548–77. https://doi.org/10.1086/227496.

The original data were assembled from Apple’s lists and contemporaneous trackers including Appshopper (shut down in 2021) and AppAnnie (now data.ai), with later coverage from providers such as Mobilewalla. The specific vendors are incidental to the method; any source of ranked lists plus a single aggregate-download moment suffices.↩︎

# Sales {#sec-sales} Selling is where a firm's marketing promises are tested against a buyer's willingness to pay. This chapter treats the sales function as two distinct but connected measurement problems. The first is **inference about demand from observed sales**: firms and researchers rarely see the full demand curve, but they do see rankings, units, and revenue, and a recurring task is to reconstruct latent demand from these partial signals. The second is **management of the sales force**: the salespeople who convert demand into revenue are themselves an asset whose compensation, productivity, retention, and future value can be modeled, measured, and optimized. The two problems share a methodological spine. In both, the object of interest is unobserved—true demand in the first case, a salesperson's forward-looking profit contribution in the second—and must be recovered from a noisy, selection-prone proxy. A reader who finishes this chapter should be able to estimate a demand curve from a sales-rank list, reason about when that estimate breaks down, and evaluate a sales-force compensation or retention policy using the same identification discipline applied throughout the book. We proceed from the outside in. We begin with the economics of compensation and its hidden health costs, because incentives are the lever managers pull most often. We then turn to **sales from rank**, the empirical problem of inferring demand from ordinal best-seller lists, and develop the Pareto rank–demand model in full. We close with the **salesperson as an asset**: turnover and its contagion through peer networks, and the forward-looking valuation of a sales force. ## Theoretical Foundations {#sec-sales-theory} The sales function is governed by a small set of theories that explain both the buyer-seller relationship and the firm's control of its own sales force. Four strands organize the chapter. **Social exchange theory** frames selling as a relationship rather than a sequence of isolated transactions. Parties continue an exchange when its rewards exceed its costs relative to available alternatives, and recurring exchange builds norms of reciprocity and mutual obligation. This is the lens that justifies treating the salesperson-customer dyad (and, internally, the salesperson-firm dyad) as an evolving relationship whose quality, not merely its current price, determines future revenue. **The commitment-trust theory of relationship marketing** specifies which mediating variables make that exchange succeed. Morgan and Hunt argue that relationship *commitment* and *trust* are the central mediators between the conditions of an exchange (shared values, communication, the absence of opportunism) and cooperative outcomes such as loyalty and acquiescence [@morganhunt1994]. For sales, this explains why relationship quality predicts retention and why opportunistic behavior, on either side, is so corrosive to long-run value. **Agency theory** governs salesforce control and underlies the compensation analysis of @sec-sales, "Compensation and Its Hidden Costs." Because the firm (principal) cannot perfectly observe the salesperson's (agent's) effort and the two have divergent goals, it must choose between *behavior-based* control (salary, monitoring, supervision) and *outcome-based* control (commission tied to noisy sales). The linear contract $w_i = \alpha + \beta s_i$ formalizes exactly this trade-off: a steeper $\beta$ aligns incentives but shifts risk onto a risk-averse agent, which, together with the health externality documented in this chapter, is why the profit-maximizing incentive slope is interior, not maximal. The governance-cost logic connects to the broader transaction-cost account of when firms integrate versus outsource selling [@williamson1981tce]. **Adaptive selling** describes the behavior the contract is meant to elicit. It is the practice of altering sales behavior across and within customer encounters in response to information about the selling situation, the antithesis of a fixed, canned pitch. Adaptive selling theory predicts that the value of discretion (and therefore of training and information systems that support it) rises with the heterogeneity of customers, which is why the latent-class, segment-specific returns to training in @sec-salesperson-value are exactly what the theory anticipates. ## Compensation and Its Hidden Costs The canonical justification for putting variable pay—commissions, bonuses, quota-based incentives—into a salesperson's compensation contract is an agency-theoretic one. The firm (principal) cannot perfectly observe the agent's effort, only the noisy output (sales) that effort produces. Tying pay to output realigns the agent's incentives with the firm's, and the standard prediction is that a steeper pay–performance slope elicits more effort and higher sales. This prediction is robust and well documented. What the classical account omits is that effort is not free of physiological cost. @habel2021 confirm the performance benefit of variable compensation but show that the same incentive intensity that lifts sales also operates as a *health hazard*: it raises stress, which manifests as emotional exhaustion and a higher incidence of sick days. The effect is not uniform across the sales force. It is **buffered** for salespeople with higher personal ability and richer social resources—the people best equipped to absorb the additional psychological load—and sharpest for those without such buffers. The managerial implication is that the pay–performance slope has a cost the standard model prices at zero. Let $w_i = \alpha + \beta\, s_i$ denote a linear contract for salesperson $i$, with fixed component $\alpha$, variable rate $\beta$, and realized sales $s_i$. The firm's familiar problem is to choose $\beta$ to maximize expected profit net of wage cost. @habel2021 effectively add a term: the agent's stress, and hence absenteeism and exhaustion, is increasing in $\beta$, so the firm faces a more accurate objective in which $\beta$ carries a shadow cost through reduced effective capacity and higher turnover risk. The optimal incentive intensity that internalizes this health externality is lower than the one that ignores it, and it varies with the ability and social resources of the individual—an argument for incentive schemes that are differentiated rather than uniform. ::: {.callout-note} The health cost of incentives is a *moderated* effect, not a main-effect caveat. Reporting only the average performance gain from steeper incentives, as much of the older literature does, overstates the net benefit for the segment of the sales force least able to bear the stress. ::: ## Sales from Rank {#sec-sales-from-rank} Many of the most visible signals of commercial success are **ordinal**, not cardinal. Amazon publishes a sales rank for every book; Apple's App Store publishes ranked lists rather than download counts; the music, film, and publishing industries all live by charts. A rank is informative—rank 1 outsells rank 100—but it discards the magnitudes a firm actually needs: how *many* more units does rank 1 move than rank 100? Recovering demand magnitudes from rank is the central inference problem of this section. The difficulty is that the map from demand to rank is many-to-one and unknown. Two products can swap ranks after a small change in either one's sales, and the same rank can correspond to wildly different unit volumes in a thick versus a thin market. The literature solves this in three stages of increasing ambition, summarized in @tbl-rank-approaches: experimentally perturb rank and read off the demand response; supplement rank with auxiliary demand data; or impose a parametric demand–rank law and estimate it from rank data alone. | Study | Setting | Demand data required | Core idea | |---|---|---|---| | @chevalier2003measuring | Amazon books | Known/very low for chosen titles | Buy units of low-selling books; watch rank move; trace the rank–demand map | | @brynjolfsson2003consumer | Amazon books | Publisher demand data | Calibrate the rank–demand relationship directly | | @garg2013inferring | Apple App Store | None | Impose a Pareto law; identify it from paid and grossing ranks | | @he2020sales | Amazon (general) | None | Generalize @chevalier2003measuring beyond books | : Approaches to inferring demand from sales rank {#tbl-rank-approaches} ### The Experimental Approach The cleanest identification comes from intervention. @chevalier2003measuring run a field experiment on Amazon: they select books whose demand is either known or known to be very small, purchase large quantities relative to that baseline demand, and observe how each title's sales rank responds to the induced demand shock. Because the experimenter controls the size of the shock, the otherwise unobservable mapping between a change in units and a change in rank is revealed. Repeating this across the rank distribution traces out the rank–demand curve. The method's strength—a controlled demand shock—is also its limitation. It is practical only for **low-selling** titles, where a feasible experimental purchase is large relative to organic demand. At the head of the distribution, the purchase required to move rank by a perceptible amount is prohibitive, so the high-volume region of the curve cannot be identified experimentally. The generalization of this revealed-demand logic to Amazon products beyond books is developed in @he2020sales. ### The Auxiliary-Data Approach When the experimenter cannot perturb demand, the next-best instrument is external demand data. @brynjolfsson2003consumer obtain demand figures from a book publisher and pair them with observed ranks, which pins down the rank–demand relationship by direct calibration rather than by experiment. This dispenses with the need to intervene but substitutes a different scarce resource—proprietary unit-sales data—that most analysts cannot obtain. ### The Structural Approach: A Pareto Rank–Demand Law The most general method dispenses with both intervention and demand data, recovering magnitudes from rank alone by imposing structure on the demand distribution. @garg2013inferring develop this approach on Apple's App Store, which is an unusually favorable laboratory because it publishes three distinct ranked lists that, jointly, over-identify the model: 1. **Top-free apps** — ranked by download volume among zero-price apps. 2. **Top-paid apps** — ranked by download volume among positive-price apps. 3. **Top-grossing apps** — ranked by *revenue*, i.e., price times downloads. The key modeling assumption is that downloads follow a **Pareto** (power-law) distribution in rank, an empirical regularity in best-seller and long-tail markets [@garg2013inferring]. For the top-paid list, let $d_{r_p}$ denote downloads at paid rank $r_p$. The Pareto law states $$ d_{r_p} = b_p\, r_p^{-a_p}, \qquad 1 \le r_p \le 200, $$ {#eq-pareto-paid} where $a_p > 0$ is the **shape** parameter (the steepness of the long tail; a larger $a_p$ means demand falls off faster with rank) and $b_p > 0$ is a **scale** factor that depends on total market size for the platform (iPhone or iPad). The truncation at 200 reflects that the published list is finite. Taking logs of @eq-pareto-paid linearizes it, $\log d_{r_p} = \log b_p - a_p \log r_p$, so a single list with download data would yield $(a_p, b_p)$ from an ordinary least squares (OLS) regression of log-downloads on log-rank. The problem is that download magnitudes are not published; only ranks are. The grossing list supplies the missing leverage. #### Identification from the grossing list Assume the same app obeys a Pareto law in the grossing (revenue) list, with its own shape $a_g$ and scale $b_g$. For an app at grossing rank $r_g$ selling at price $p$, revenue equals price times the downloads it earns at its paid rank: $$ p\, d_{r_p} = b_g\, r_g^{-a_g}. $$ {#eq-pareto-grossing} Substituting the paid-list law @eq-pareto-paid for $d_{r_p}$ and taking logs gives, after rearranging to put grossing rank on the left, $$ \log r_g = \frac{1}{a_g}\log\!\left(\frac{b_g}{b_p}\right) + \frac{a_p}{a_g}\log r_p - \frac{1}{a_g}\log p . $$ {#eq-rank-mapping} @eq-rank-mapping is linear in observables. It maps an app's paid rank $r_p$ and price $p$ into its grossing rank $r_g$, and every quantity on the right except the structural parameters is in the data. It is therefore estimable as the truncated OLS regression $$ \log r_g = \beta_0 + \beta_1 \log r_p + \beta_2 \log p + \varepsilon, $$ {#eq-rank-ols} where the regression coefficients are nonlinear functions of the structural parameters. Matching coefficients between @eq-rank-mapping and @eq-rank-ols recovers the shapes directly: $$ a_g = -\frac{1}{\beta_2}, \qquad a_p = -\frac{\beta_1}{\beta_2}, \qquad \frac{b_g}{b_p} = \exp\!\left(-\frac{\beta_1}{\beta_2}\right). $$ {#eq-structural-recovery} The regression identifies the two shape parameters and the *ratio* of scales, but not the scales themselves, because rank data are invariant to a common rescaling of all download volumes. To pin down the levels, @garg2013inferring add one aggregate moment. Summing the paid-list law over all ranked apps in a day equates the model-implied total to observed aggregate downloads $D_t$: $$ D_t = \sum_{r_p=1}^{N} d_{r_p} = b_p \sum_{r_p=1}^{N} r_p^{-a_p}. $$ {#eq-aggregate-downloads} Because $a_p$ is already known from @eq-structural-recovery, the sum on the right is a computable constant, so @eq-aggregate-downloads solves for the scale levels: $$ b_p = \frac{\sum_{r_p=1}^{N} d_{r_p}}{\sum_{r_p=1}^{N} r_p^{-a_p}}, \qquad b_g = \exp\!\left(-\frac{\beta_0}{\beta_1}\right) \cdot \frac{\sum_{r_p=1}^{N} d_{r_p}}{\sum_{r_p=1}^{N} r_p^{-a_p}}. $$ {#eq-scale-recovery} With $(a_p, b_p)$ in hand, @eq-pareto-paid returns a download magnitude for every paid rank, completing the recovery of cardinal demand from ordinal lists. #### What breaks identification The estimator rests on assumptions that are explicit and falsifiable, and each is a potential failure point. - **Revenue comes only from upfront price.** The grossing equation @eq-pareto-grossing treats revenue as price times downloads, ignoring in-app purchases. @garg2013inferring argue this is reasonable for *paid* apps, which earn most of their money at the point of sale, while in-app monetization is concentrated in *free* apps, which the grossing analysis excludes [@garg2013inferring, p. 1256]. Where paid apps monetize heavily inside the app, the price term in @eq-rank-ols is misspecified and the recovered shapes are biased. - **Rank and price are cross-sectionally independent.** Estimation treats each app-day observation as independent even when an app appears across multiple days, ignoring the correlation that would arise from app-level unobservables. Failing this, the OLS standard errors understate sampling uncertainty. - **A single Pareto law fits the whole list.** A mixture of populations (e.g., games versus utilities) with different tail behavior would violate the single-shape assumption, and the linearized regression would average over heterogeneous slopes. @garg2013inferring estimate the model on roughly 200 paid apps, 200 grossing apps, and their prices over April–May 2011, drawing on Apple's public lists and third-party trackers of the period.[^datasources] The pipeline from the three published lists to recovered demand is summarized in @fig-rank-pipeline. [^datasources]: The original data were assembled from Apple's lists and contemporaneous trackers including Appshopper (shut down in 2021) and AppAnnie (now data.ai), with later coverage from providers such as Mobilewalla. The specific vendors are incidental to the method; any source of ranked lists plus a single aggregate-download moment suffices. ```{mermaid} %%| label: fig-rank-pipeline %%| fig-cap: "Recovering cardinal demand from ordinal App Store lists. Ranked lists and prices identify the Pareto shapes and the scale ratio via regression; one aggregate-download moment pins down the scale levels; the paid-list law then returns downloads at every rank." flowchart TD A[Top-paid ranks r_p] --> D[Regress log r_g on log r_p and log p] B[Top-grossing ranks r_g] --> D C[Prices p] --> D D --> E["Shapes a_p, a_g and scale ratio b_g / b_p"] F[Aggregate downloads D_t] --> G[Recover scale levels b_p, b_g] E --> G G --> H["Pareto law d = b_p r_p^(-a_p): downloads at every rank"] ``` #### A reproducible illustration The following simulation generates app-level ranks and prices from a known data-generating process, then recovers the structural parameters through @eq-rank-ols and @eq-structural-recovery. Because the truth is known, the example doubles as a check that the estimator is unbiased when its assumptions hold. ```{r rank-demand-sim, message=FALSE, warning=FALSE} set.seed(12) # True structural parameters a_p_true <- 0.80 # paid-list shape a_g_true <- 0.95 # grossing-list shape b_p_true <- 5e5 # paid-list scale b_g_true <- 2e6 # grossing-list scale N <- 200 r_p <- 1:N # paid ranks price <- round(runif(N, 0.99, 9.99), 2) # app prices # Downloads from the paid-list Pareto law (eq-pareto-paid) downloads <- b_p_true * r_p^(-a_p_true) # Grossing rank implied by the structural mapping (eq-rank-mapping), # with mild noise standing in for measurement error log_rg <- (1 / a_g_true) * log(b_g_true / b_p_true) + (a_p_true / a_g_true) * log(r_p) - (1 / a_g_true) * log(price) + rnorm(N, 0, 0.05) r_g <- exp(log_rg) # Estimate the truncated OLS regression (eq-rank-ols) fit <- lm(log(r_g) ~ log(r_p) + log(price)) b <- coef(fit) # Recover structural parameters (eq-structural-recovery) a_g_hat <- -1 / b[["log(price)"]] a_p_hat <- -b[["log(r_p)"]] / b[["log(price)"]] b_ratio_hat <- exp(-b[["log(r_p)"]] / b[["log(price)"]]) # Recover scale levels from the aggregate-download moment (eq-scale-recovery) D_t <- sum(downloads) b_p_hat <- D_t / sum(r_p^(-a_p_hat)) data.frame( parameter = c("a_p", "a_g", "b_g/b_p", "b_p"), truth = c(a_p_true, a_g_true, b_g_true / b_p_true, b_p_true), estimate = c(a_p_hat, a_g_hat, b_ratio_hat, b_p_hat) ) ``` The recovered shapes and scale track their true values, illustrating that the ordinal lists, plus one cardinal anchor, suffice to reconstruct the full demand schedule. ## The Salesperson as an Asset {#sec-salesperson-asset} The second measurement problem shifts from the product to the person. A sales force is a portfolio of human assets, and two questions dominate its management: who leaves, and what is each person worth going forward. Both resist naive measurement—turnover is contagious in ways that confound individual attribution, and a salesperson's value is forward-looking while the convenient metrics are backward-looking. ### Turnover: Own and Peer Effects {#sec-turnover} Salesperson turnover is expensive: it destroys accumulated account relationships and product knowledge and imposes replacement costs. Most prior work studied the *consequences* of voluntary turnover; @sunder2017salespeople instead model its *antecedents*, and in particular separate two channels that the data tend to confound. The first channel is the salesperson's **own** standing. Drawing on identity theory, a salesperson's role identity is reinforced or threatened by personal performance, so individual achievement shapes the propensity to stay. The second channel is **peer** influence. Drawing on social identity theory, a salesperson's attachment is shaped by the group, so the behavior of peers—above all, **peer turnover**—moves the individual's own exit decision. The empirical contribution is to estimate both channels jointly on a panel of 6,727 salespeople observed over two years, and the central finding is that **peer effects dominate own effects**: a colleague's departure is a stronger predictor of a salesperson's exit than that salesperson's own performance. ::: {.callout-note} ## Identification: distinguishing contagion from common shocks The headline that "peers drive turnover" is a causal claim, and peer effects are notoriously hard to identify. The **reflection problem** (a peer's outcome reflects the same group-level shocks that drive ego's outcome) and **homophily** (similar people self-select into the same teams) both generate peer correlations with no underlying contagion. Reading a peer-turnover coefficient as a causal contagion effect requires that team membership and the timing of peer exits be plausibly exogenous to ego's latent propensity to leave—conditioning on common shocks, not merely correlating outcomes. ::: A reduced-form hazard specification makes the two channels concrete. Let the hazard that salesperson $i$ on team $j$ exits in period $t$ be $$ h_{ijt} = h_0(t)\, \exp\!\big(\gamma\, \text{Perf}_{ijt} + \delta\, \text{PeerTurnover}_{jt} + \boldsymbol{\theta}^{\top}\mathbf{x}_{ijt}\big), $$ {#eq-turnover-hazard} where $h_0(t)$ is a baseline hazard, $\text{Perf}_{ijt}$ captures own performance (the identity channel), $\text{PeerTurnover}_{jt}$ is recent turnover among $i$'s peers (the social-identity channel), and $\mathbf{x}_{ijt}$ collects controls. The @sunder2017salespeople finding is that the estimated peer coefficient $\hat\delta$ is large relative to the own-performance coefficient $\hat\gamma$. ### Valuing a Salesperson's Future Contribution {#sec-salesperson-value} Traditional sales-force evaluation is **retrospective**: it ranks salespeople on realized volume, the metric that is easiest to observe but least informative about what the firm will earn from each person next year. As marketing has shifted toward a customer-centric, lifetime-value orientation, the natural analogue for the sales force is a **forward-looking, profit-based** valuation of each salesperson—an internal parallel to customer lifetime value. @kumar2014measuring propose exactly such a metric and embed it in a **latent class** model that recognizes the sales force is not homogeneous. The intuition for latent classes is that salespeople fall into a small number of unobserved **segments** that respond differently to managerial levers, so a single average response masks divergent effects. Formally, with $C$ latent segments, the expected future value of salesperson $i$ is the mixture $$ \widehat{\text{Value}}_i = \sum_{c=1}^{C} \pi_{ic}\, \mathbb{E}\!\left[V_i \mid \text{segment } c\right], $$ {#eq-salesperson-value} where $\pi_{ic}$ is the posterior probability that $i$ belongs to segment $c$ and $\mathbb{E}[V_i \mid \text{segment } c]$ is the discounted future profit contribution conditional on that segment's response parameters. Both the segment memberships $\pi_{ic}$ and the segment-specific response parameters are estimated jointly, typically by maximum likelihood via the expectation–maximization (EM) algorithm. The substantive payoff is a precise statement of when "one size fits all" fails. @kumar2014measuring find that segments respond **differently** to **training** and to **incentives**, so a uniform program is inefficient: the same training budget yields different returns across segments, and the ranking of training versus incentives can even reverse depending on the **time horizon**—an intervention that looks inferior in the short run may dominate over a longer one. The forward-looking metric thus reframes sales-force management from rewarding *past* volume to allocating development resources toward the salespeople and interventions with the highest *future* return. @fig-salesperson-value contrasts the retrospective and forward-looking views of sales-force evaluation. ```{mermaid} %%| label: fig-salesperson-value %%| fig-cap: "From retrospective to forward-looking sales-force evaluation. Realized volume looks backward; a latent-class future-value metric segments the sales force and allocates training and incentives to the highest forward return." flowchart LR A[Realized sales volume] --> B[Retrospective ranking] C[Salesperson behavior and responses] --> D[Latent-class segmentation] D --> E[Segment-specific future value] E --> F[Allocate training and incentives by horizon] B -. backward-looking .-> G((Evaluation)) F -. forward-looking .-> G ``` #### A reproducible illustration of latent-class value The following example simulates two latent segments of salespeople with different responses to training, fits a two-component mixture by EM, and recovers the segment-specific effects. It is a deliberately minimal stand-in for the richer specification in @kumar2014measuring, intended to make the mixture logic of @eq-salesperson-value concrete. ```{r latent-class-sim, message=FALSE, warning=FALSE} set.seed(34) n <- 600 # Two latent segments with different training -> future-value slopes seg <- rbinom(n, 1, 0.4) # segment indicator (unobserved in practice) train <- runif(n, 0, 10) # training hours slope <- ifelse(seg == 1, 1.8, 0.3) # high vs. low responders value <- 20 + slope * train + rnorm(n, 0, 4) dat <- data.frame(value, train) # Fit a 2-component mixture of regressions by EM (base R) em_mixreg <- function(y, x, K = 2, iters = 100) { n <- length(y) pi_k <- rep(1 / K, K) beta0 <- quantile(y, c(0.3, 0.7)); beta1 <- c(0.3, 1.5); sig <- rep(sd(y), K) for (it in seq_len(iters)) { # E-step: responsibilities dens <- sapply(1:K, function(k) pi_k[k] * dnorm(y, beta0[k] + beta1[k] * x, sig[k])) r <- dens / rowSums(dens) # M-step: weighted regressions for (k in 1:K) { w <- r[, k] fk <- lm(y ~ x, weights = w) beta0[k] <- coef(fk)[1]; beta1[k] <- coef(fk)[2] sig[k] <- sqrt(sum(w * residuals(fk)^2) / sum(w)) pi_k[k] <- mean(w) } } list(pi = pi_k, slope = beta1, intercept = beta0) } out <- em_mixreg(dat$value, dat$train, K = 2) data.frame( segment = c(1, 2), mix_weight = round(out$pi, 3), training_slope = round(out$slope, 3) ) ``` The estimator separates the high-responding segment (training slope near 1.8) from the low-responding one (near 0.3), reproducing the qualitative lesson of @kumar2014measuring: returns to a managerial lever are segment-specific, and the forward-looking value in @eq-salesperson-value averages over those segments weighted by membership. ## Key Takeaways - Variable compensation lifts sales but carries a **health cost**—stress, exhaustion, absenteeism—that is buffered by individual ability and social resources, so the profit-maximizing incentive slope is lower and more differentiated than the standard agency model implies [@habel2021]. - **Sales rank is ordinal**; recovering cardinal demand requires either an experimental demand shock [@chevalier2003measuring; @he2020sales], auxiliary demand data [@brynjolfsson2003consumer], or a parametric demand law identified from multiple ranked lists [@garg2013inferring]. - The Pareto rank–demand model (@eq-pareto-paid–@eq-scale-recovery) identifies tail **shapes** and a **scale ratio** from rank regressions, but needs one aggregate-download moment to fix scale **levels**; its identification breaks if revenue is not upfront, if cross-sectional independence fails, or if a single power law does not fit the list. - Salesperson **turnover is contagious**: peer turnover predicts individual exit more strongly than own performance, but reading this as causal contagion demands care with the reflection problem and homophily [@sunder2017salespeople]. - A **forward-looking, latent-class** valuation of the sales force (@eq-salesperson-value) shows that returns to training and incentives are segment- and horizon-specific, so uniform development programs are inefficient [@kumar2014measuring].