# =============================================================================
# generate_merc_images.R
# Charts for: "Mercenaries Will Ruin You: Machiavelli on Outsourced Core
#              Capability" (inphronesys.com, May 21, 2026)
# =============================================================================
# Three pedagogical / stylised models illustrating Machiavelli's argument in
# The Prince, chs. 12-14 that mercenary forces (here: pure-consultant or
# heavy-consultant operating models for CORE capability work) fail because
# incentives reverse under pressure. None of these are estimated from a
# proprietary dataset. They are transparent toy models with stated inputs.
#
# CITED INPUTS (real benchmarks, not invented):
#   - German consulting day rate, 2025: average invoiced EUR 1,300/day; partner
#     / executive tier EUR 1,600/day; analyst tier EUR 700/day. We use
#     EUR 1,400/day as a "senior tier-2" midpoint between the average and the
#     partner band. Verified URLs (page-fetched 2026-05-20):
#       BDU "Studie Honorare im Consulting 2025"  https://www.bdu.de/news/studie-honorare-im-consulting-2025-tagessaetze-leicht-ruecklaeufig/
#         (primary; quotes: "Der durchschnittlich fakturierte Tagessatz
#          betraegt 1.300 Euro in 2025"; "der Tagessatz eines
#          Geschaeftsfuehrers oder Partners im Durchschnitt bei 1.600 Euro";
#          "der eines Analysten bei 700 Euro".)
#       CONSULTING.de coverage of the same BDU study  https://www.consulting.de/artikel/ruecklaeufige-tagessaetze-im-consulting/
#         (corroborating, German trade press).
#   - Fully-loaded employer cost factor ~ 1.20-1.30 of gross salary for pure
#     Lohnnebenkosten; 1.50-1.65 once workplace, equipment, admin overhead are
#     included.
#       Sources:
#         Personio "Lohnnebenkosten"  https://www.personio.de/hr-lexikon/lohnnebenkosten/
#         Steuertipps Arbeitgeber-Brutto-Netto-Rechner  https://www.steuertipps.de/service/rechner/brutto-netto-gehaltsrechner-arbeitgeber
#       Senior fully-loaded EUR 120k/yr = EUR ~75k gross x ~1.60.
#       Junior fully-loaded EUR  70k/yr = EUR ~45k gross x ~1.55.
#
# PEDAGOGICAL INPUTS (illustrative, stated openly in the article):
#   - Capability stock growth rate, asymptote, atrophy fraction.
#   - Effort-vs-stress sigmoid parameters.
#   - One-time recruiting+onboarding spend.
# =============================================================================

suppressPackageStartupMessages({
  library(ggplot2)
  library(dplyr)
  library(tidyr)
  library(scales)
})

source("Scripts/theme_inphronesys.R")

img_dir <- "Images"
if (!dir.exists(img_dir)) dir.create(img_dir, recursive = TRUE)

# =============================================================================
# CHART 1 -- merc_tco_crossover.png
# 60-month cumulative TCO for three staffing modes
# =============================================================================

# --- Assumptions (cited above) -----------------------------------------------
day_rate        <- 1400          # EUR / billable consultant day
billable_days   <- 200           # billable consultant days per year
sen_loaded      <- 120000        # EUR / yr senior internal fully loaded
jun_loaded      <-  70000        # EUR / yr junior internal fully loaded
recruit_full    <-  30000        # one-time recruiting + onboarding (insourced)
recruit_hybrid  <-  15000        # one-time recruiting (hybrid - junior only)

# --- Monthly cash flow -------------------------------------------------------
months <- 0:60

consultant_per_mo <- day_rate * billable_days / 12        # ~ 23,333
hybrid_per_mo     <- consultant_per_mo + jun_loaded / 12  # ~ 29,167
insourced_per_mo  <- (sen_loaded + jun_loaded) / 12       # ~ 15,833

tco <- tibble(
  month = months,
  Consultant = consultant_per_mo * month,
  Hybrid     = recruit_hybrid + hybrid_per_mo * month,
  Insourced  = recruit_full   + insourced_per_mo * month
)

# --- Find crossover months (analytic) ----------------------------------------
# Insourced beats Consultant when:
#   recruit_full + insourced_per_mo * m  <  consultant_per_mo * m
#   m > recruit_full / (consultant_per_mo - insourced_per_mo)
cx_cons <- recruit_full / (consultant_per_mo - insourced_per_mo)
# Insourced beats Hybrid:
cx_hyb  <- (recruit_full - recruit_hybrid) / (hybrid_per_mo - insourced_per_mo)
cat(sprintf("Crossover insourced<consultant : month %.2f\n", cx_cons))
cat(sprintf("Crossover insourced<hybrid     : month %.2f\n", cx_hyb))

tco_long <- tco %>%
  pivot_longer(-month, names_to = "Mode", values_to = "EUR") %>%
  mutate(Mode = factor(Mode, levels = c("Hybrid", "Consultant", "Insourced")))

mode_colors <- c(
  "Insourced"  = iph_colors$blue,
  "Consultant" = iph_colors$red,
  "Hybrid"     = iph_colors$grey
)

# 5-yr endpoints for annotation
end5 <- tco_long %>% filter(month == 60)
cat("5-year cumulative TCO:\n")
print(end5)

p1 <- ggplot(tco_long, aes(x = month, y = EUR, color = Mode)) +
  geom_line(linewidth = 1.2) +
  geom_vline(xintercept = cx_cons, linetype = "dotted",
             color = iph_colors$red, linewidth = 0.6) +
  # NOTE: at the exact crossover month (cx_cons = 4.0) insourced and consultant
  # are equal; insourced is strictly cheaper only from the NEXT whole month
  # onward. Use floor(cx_cons) + 1, not ceiling(), to avoid labelling the
  # boundary month itself.
  annotate("text",
           x = cx_cons + 0.5, y = 1.55e6,
           label = sprintf("Insourced cheaper than\npure consultant from month %.0f",
                           floor(cx_cons) + 1),
           hjust = 0, vjust = 1, size = 3.4,
           color = iph_colors$red, family = "Inter") +
  # endpoint labels
  geom_point(data = end5, aes(x = month, y = EUR), size = 2.4) +
  geom_text(data = end5,
            aes(x = month + 0.8, y = EUR,
                label = paste0("EUR ", format(round(EUR / 1000), big.mark = ","), "k")),
            hjust = 0, vjust = 0.5, size = 3.4,
            family = "Inter", show.legend = FALSE) +
  scale_color_manual(values = mode_colors) +
  scale_y_continuous(
    labels = label_number(prefix = "EUR ", scale = 1e-3, suffix = "k", big.mark = ","),
    breaks = seq(0, 2e6, by = 250000),
    limits = c(0, 2.1e6),
    expand = expansion(mult = c(0, 0))
  ) +
  scale_x_continuous(breaks = seq(0, 60, by = 12),
                     limits = c(0, 70),
                     expand = expansion(mult = c(0, 0))) +
  labs(
    title = "Total cost of ownership: who is actually cheaper over 5 years?",
    subtitle = "Cumulative EUR spend for one core-capability FTE-equivalent. DACH benchmarks, 2024-2026.",
    x = "Month",
    y = NULL,
    color = NULL,
    caption = "Inputs: day rate EUR 1,400 (200 billable days/yr); senior fully-loaded EUR 120k/yr; junior EUR 70k/yr; insourced one-time recruit+onboard EUR 30k. Sources cited in script header."
  ) +
  theme_inphronesys(grid = "y") +
  theme(legend.position = "top",
        plot.caption = element_text(size = 9, color = iph_colors$grey,
                                     hjust = 0, margin = margin(t = 10)))

ggsave(file.path(img_dir, "merc_tco_crossover.png"), p1,
       width = 8, height = 5, dpi = 100, bg = "white")
cat("Saved: https://inphronesys.com/wp-content/uploads/2026/05/merc_tco_crossover-2.png\n")


# =============================================================================
# CHART 2 -- merc_capability_stock.png
# Capability stock under three operating models
# =============================================================================
#
# Pedagogical capability index. Asymptote = 80. Logistic-like saturating curve.
#   C(t) = K * (1 - exp(-k * t))
# k chosen so initial slope ~ 2 index-points / month for an insourced team
# (K*k = slope at t=0 -> k = 2/80 = 0.025).
#
# Consultant scenario:
#   - During engagement (months 0-18) the consultant provides an EXTERNAL stock
#     of 65 points on top of a tiny internal build of 0.3 pts/month (the
#     internal team does not have to own decisions).
#   - At month 18 the consultant exits and the external stock vanishes.
#   - Internal capability resumes building from a low base. The team has been
#     habituated to NOT owning the work, so the rebuild starts from the small
#     internal-only baseline.

months_cap <- 0:60
K   <- 80
k_r <- 0.025
engagement_end <- 18

internal_pure <- K * (1 - exp(-k_r * months_cap))                 # smooth

# Consultant scenario - internal-only stock
#   slow build during engagement, normal build after
internal_only_under_consultant <- numeric(length(months_cap))
slow_rate <- 0.3
for (i in seq_along(months_cap)) {
  t <- months_cap[i]
  if (t <= engagement_end) {
    internal_only_under_consultant[i] <- slow_rate * t
  } else {
    # Build from the level at month 18 using the same saturating curve, by
    # finding the effective time offset that matches starting level.
    start_lvl <- slow_rate * engagement_end
    delta_t   <- -log(1 - start_lvl / K) / k_r
    internal_only_under_consultant[i] <- K * (1 - exp(-k_r * (t - engagement_end + delta_t)))
  }
}

# Total capability under consultant (external boost only during engagement)
external_boost <- 65
total_under_consultant <- internal_only_under_consultant +
  ifelse(months_cap <= engagement_end, external_boost, 0)

cap_df <- tibble(
  month = months_cap,
  `Pure-insourced (you own the build)`     = internal_pure,
  `Total under consultant (incl. external)` = total_under_consultant,
  `Internal stock under consultant`         = internal_only_under_consultant
) %>%
  pivot_longer(-month, names_to = "Scenario", values_to = "Capability") %>%
  mutate(Scenario = factor(Scenario, levels = c(
    "Pure-insourced (you own the build)",
    "Total under consultant (incl. external)",
    "Internal stock under consultant"
  )))

cap_colors <- c(
  "Pure-insourced (you own the build)"      = iph_colors$blue,
  "Total under consultant (incl. external)" = iph_colors$grey,
  "Internal stock under consultant"         = iph_colors$red
)

cap_ltype <- c(
  "Pure-insourced (you own the build)"      = "solid",
  "Total under consultant (incl. external)" = "solid",
  "Internal stock under consultant"         = "dashed"
)

# Reporting numbers
report_pts <- cap_df %>%
  filter(month %in% c(0, 17, 18, 19, 60)) %>%
  arrange(Scenario, month)
cat("\nCapability stock checkpoints:\n")
print(report_pts)

cliff_drop <- total_under_consultant[months_cap == 18] -
              total_under_consultant[months_cap == 19]
cat(sprintf("Cliff drop month 18 -> 19 (consultant exit): %.1f index points\n",
            cliff_drop))

p2 <- ggplot(cap_df, aes(x = month, y = Capability,
                          color = Scenario, linetype = Scenario)) +
  geom_line(linewidth = 1.2) +
  geom_vline(xintercept = engagement_end, linetype = "dotted",
             color = iph_colors$red, linewidth = 0.6) +
  annotate("rect", xmin = engagement_end - 0.05, xmax = engagement_end + 0.05,
           ymin = 0, ymax = 80, alpha = 0) +
  annotate("text", x = engagement_end - 0.4,
           y = 78, label = "Consultant exits",
           hjust = 1, vjust = 1, size = 3.4,
           color = iph_colors$red, family = "Inter") +
  annotate("segment",
           x = engagement_end + 0.3, xend = engagement_end + 0.3,
           y = total_under_consultant[months_cap == 18],
           yend = total_under_consultant[months_cap == 19],
           arrow = arrow(length = unit(0.18, "cm"), type = "closed"),
           color = iph_colors$red, linewidth = 0.7) +
  annotate("text", x = engagement_end + 1.2,
           y = (total_under_consultant[months_cap == 18] +
                total_under_consultant[months_cap == 19]) / 2,
           label = sprintf("the mercenary cliff:\nlose %.0f index points overnight", cliff_drop),
           hjust = 0, vjust = 0.5, size = 3.4,
           color = iph_colors$red, family = "Inter") +
  scale_color_manual(values = cap_colors) +
  scale_linetype_manual(values = cap_ltype) +
  scale_y_continuous(limits = c(0, 90),
                     breaks = seq(0, 80, by = 20),
                     expand = expansion(mult = c(0, 0))) +
  scale_x_continuous(breaks = seq(0, 60, by = 12),
                     expand = expansion(mult = c(0, 0.02))) +
  labs(
    title = "Where does the capability actually live?",
    subtitle = "Pedagogical model: pure-insourced compounding vs consultant-led capability that walks out the door at month 18.",
    x = "Month",
    y = "Capability index (0-80 asymptote)",
    color = NULL, linetype = NULL,
    caption = "Stylised saturating-growth model. Pure-insourced: dC/dt at t=0 = 2 pts/mo, asymptote 80. Consultant engagement adds 65 external points; internal team builds at 0.3 pts/mo while consultant owns the work."
  ) +
  theme_inphronesys(grid = "y") +
  theme(legend.position = "top",
        legend.text = element_text(size = 9),
        plot.caption = element_text(size = 9, color = iph_colors$grey,
                                     hjust = 0, margin = margin(t = 10)))

ggsave(file.path(img_dir, "merc_capability_stock.png"), p2,
       width = 8, height = 5, dpi = 100, bg = "white")
cat("Saved: https://inphronesys.com/wp-content/uploads/2026/05/merc_capability_stock-2.png\n")


# =============================================================================
# CHART 3 -- merc_effort_under_stress.png  (wide / short)
# Stylised game-theoretic effort intensity vs project stress level
# =============================================================================
#
# Cartoon model -- NOT estimated. Stress runs 0 (routine) .. 10 (full crisis).
# Effort intensity in [0, 1].
#
# Functional forms (logistic):
#   sigmoid(x, k, x0) = 1 / (1 + exp(-k * (x - x0)))
#
# Fixed-fee consultant : effort = 0.65 - 0.35 * sigmoid(s, k=1.0, x0=5)
#   (rational risk-minimisation as the project goes sideways; they don't get
#    paid more for blood)
# Time & materials consultant : effort = 0.40 + 0.18 * sigmoid(s, k=0.8, x0=6)
#   (some upside from billing more hours, but capped low; still bounded by
#    "next client matters more than this one")
# Internal with retention/equity stake : effort = 0.50 + 0.45 * sigmoid(s, k=1.0, x0=5)
#   (reputation, bonus, career upside hinge on outcome; effort rises with
#    stress)
# =============================================================================

sigmoid <- function(x, k, x0) 1 / (1 + exp(-k * (x - x0)))

stress <- seq(0, 10, by = 0.05)

eff_df <- tibble(
  stress = stress,
  `Fixed-fee consultant`            = 0.65 - 0.35 * sigmoid(stress, k = 1.0, x0 = 5),
  `Time-&-materials consultant`     = 0.40 + 0.18 * sigmoid(stress, k = 0.8, x0 = 6),
  `Employee with reputation/equity` = 0.50 + 0.45 * sigmoid(stress, k = 1.0, x0 = 5)
) %>%
  pivot_longer(-stress, names_to = "Actor", values_to = "Effort") %>%
  mutate(Actor = factor(Actor, levels = c(
    "Employee with reputation/equity",
    "Time-&-materials consultant",
    "Fixed-fee consultant"
  )))

actor_colors <- c(
  "Employee with reputation/equity" = iph_colors$blue,
  "Time-&-materials consultant"     = iph_colors$grey,
  "Fixed-fee consultant"            = iph_colors$red
)

# Endpoints for reporting
endpoints <- eff_df %>%
  filter(stress %in% c(0, 5, 10)) %>%
  arrange(Actor, stress)
cat("\nEffort intensity at stress = 0, 5, 10:\n")
print(endpoints)

label_pts <- eff_df %>%
  filter(stress == 10)

p3 <- ggplot(eff_df, aes(x = stress, y = Effort, color = Actor)) +
  geom_line(linewidth = 1.3) +
  geom_point(data = label_pts, size = 2.4) +
  geom_text(data = label_pts,
            aes(x = stress + 0.15, label = sprintf("%.2f", Effort)),
            hjust = 0, vjust = 0.5, size = 3.4,
            family = "Inter", show.legend = FALSE) +
  annotate("text", x = 0.2, y = 1.02,
           label = "Routine", hjust = 0, vjust = 1,
           color = iph_colors$grey, size = 3.2, family = "Inter") +
  annotate("text", x = 9.8, y = 1.02,
           label = "Crisis", hjust = 1, vjust = 1,
           color = iph_colors$red, size = 3.2, family = "Inter") +
  scale_color_manual(values = actor_colors) +
  scale_x_continuous(breaks = 0:10, limits = c(0, 11),
                     expand = expansion(mult = c(0.01, 0))) +
  scale_y_continuous(limits = c(0, 1.05),
                     breaks = seq(0, 1, by = 0.2),
                     labels = percent_format(accuracy = 1)) +
  labs(
    title = "Whose effort goes UP when the project catches fire?",
    subtitle = "Stylised effort-intensity model. Stress on the x-axis is project pressure, not hours worked.",
    x = "Project stress level (0 = routine, 10 = crisis)",
    y = "Rational effort intensity",
    color = NULL,
    caption = "Game-theoretic cartoon, not estimated parameters. Functional form: logistic sigmoid. Point: fixed-fee mercenaries de-risk under stress; employees with skin in the game lean in."
  ) +
  theme_inphronesys(grid = "y") +
  theme(legend.position = "top",
        plot.caption = element_text(size = 9, color = iph_colors$grey,
                                     hjust = 0, margin = margin(t = 10)))

ggsave(file.path(img_dir, "merc_effort_under_stress.png"), p3,
       width = 8, height = 4, dpi = 100, bg = "white")
cat("Saved: https://inphronesys.com/wp-content/uploads/2026/05/merc_effort_under_stress-2.png\n")


# =============================================================================
# DATASET SUMMARY (printed -- Alpha/Charlie copy these EXACT numbers)
# =============================================================================
cat("\n=============================================================\n")
cat("FINAL DATASET SUMMARY (Bravo-Zero-R -> Alpha-Zero-Blog/Charlie-Zero)\n")
cat("=============================================================\n")
cat("ASSUMPTIONS\n")
cat(sprintf("  day_rate              = EUR %s/day\n", format(day_rate, big.mark=",")))
cat(sprintf("  billable_days/yr      = %d\n", billable_days))
cat(sprintf("  senior fully loaded   = EUR %s/yr\n", format(sen_loaded, big.mark=",")))
cat(sprintf("  junior fully loaded   = EUR %s/yr\n", format(jun_loaded, big.mark=",")))
cat(sprintf("  recruit_full          = EUR %s one-time\n", format(recruit_full, big.mark=",")))
cat(sprintf("  recruit_hybrid        = EUR %s one-time\n", format(recruit_hybrid, big.mark=",")))
cat(sprintf("  engagement_end        = month %d\n", engagement_end))
cat(sprintf("  capability asymptote  = %d index pts\n", K))
cat(sprintf("  insourced growth rate = dC/dt at t=0 = %.2f pts/mo\n", K * k_r))
cat("\nCHART 1 -- TCO\n")
cat(sprintf("  60-mo TCO consultant : EUR %s\n",
            format(tco$Consultant[tco$month==60], big.mark=",")))
cat(sprintf("  60-mo TCO hybrid     : EUR %s\n",
            format(tco$Hybrid[tco$month==60], big.mark=",")))
cat(sprintf("  60-mo TCO insourced  : EUR %s\n",
            format(tco$Insourced[tco$month==60], big.mark=",")))
cat(sprintf("  crossover consultant : month %.2f\n", cx_cons))
cat(sprintf("  crossover hybrid     : month %.2f\n", cx_hyb))
cat(sprintf("  savings insourced vs consultant @ 60mo : EUR %s (%.1f%%)\n",
            format(tco$Consultant[tco$month==60] - tco$Insourced[tco$month==60],
                   big.mark=","),
            100 * (tco$Consultant[tco$month==60] -
                   tco$Insourced[tco$month==60]) /
                  tco$Consultant[tco$month==60]))
cat(sprintf("  savings insourced vs hybrid     @ 60mo : EUR %s (%.1f%%)\n",
            format(tco$Hybrid[tco$month==60] - tco$Insourced[tco$month==60],
                   big.mark=","),
            100 * (tco$Hybrid[tco$month==60] -
                   tco$Insourced[tco$month==60]) /
                  tco$Hybrid[tco$month==60]))
cat("\nCHART 2 -- CAPABILITY\n")
cat(sprintf("  pure-insourced @ mo60         : %.1f\n",
            internal_pure[months_cap == 60]))
cat(sprintf("  total under consultant @ mo17 : %.1f\n",
            total_under_consultant[months_cap == 17]))
cat(sprintf("  total under consultant @ mo18 : %.1f (last month with consultant)\n",
            total_under_consultant[months_cap == 18]))
cat(sprintf("  total under consultant @ mo19 : %.1f (mercenary cliff)\n",
            total_under_consultant[months_cap == 19]))
cat(sprintf("  internal stock @ mo60 (post-consultant rebuild) : %.1f\n",
            internal_only_under_consultant[months_cap == 60]))
cat(sprintf("  capability gap pure vs post-consultant @ mo60   : %.1f pts\n",
            internal_pure[months_cap == 60] -
              internal_only_under_consultant[months_cap == 60]))
cat("\nCHART 3 -- EFFORT vs STRESS\n")
ep_wide <- endpoints %>% pivot_wider(names_from = stress, values_from = Effort,
                                      names_prefix = "s")
print(ep_wide)
cat("=============================================================\n")