---
title: "Legal Risk Optimisation at Petro Nigeria Limited"
subtitle: "Five Advanced Analytics Techniques Applied to the Active Litigation Portfolio"
author: "Head of Litigation, Petro Nigeria Limited (PNL)"
date: today
format:
html:
toc: true
toc-depth: 2
toc-title: "Contents"
theme: cosmo
code-fold: true
code-tools: true
number-sections: true
self-contained: true
execute:
warning: false
message: false
echo: true
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, message = FALSE, warning = FALSE)
```
---
# Executive Summary
Petro Nigeria Limited (PNL) faces an active litigation portfolio of **237 cases** spanning multiple courts across Nigeria, with 61 cases (26%) currently lacking assigned outside counsel. The legal team's core challenge is threefold: understanding *what* drives litigation outcomes (text and pattern analysis), estimating *how much* financial exposure the portfolio represents (simulation), anticipating *when* new disputes will arise (forecasting), determining *who* should handle each case (people analytics), and ensuring workload is *allocated optimally* across the panel of 12 approved firms (optimisation).
This report applies five advanced analytics techniques to PNL's litigation register. Text analytics on closed-case remarks identifies outcome-predictive language and dispute patterns. A three-stage Monte Carlo simulation estimates financial exposure: the portfolio carries a median annual risk of **₦1.2 billion**, rising to **₦24 billion** at the 95th percentile — a figure that should inform provisioning decisions. An ARIMA(0,1,1) time-series model forecasts approximately **one new case per month** for 2025. Counsel workload analysis reveals concerning concentration, with Henry Yekovie & Co. carrying 32 active cases. Finally, a linear-programming model assigns all 61 unassigned cases across panel firms while respecting capacity constraints.
The integrated recommendation is to **activate a triage-and-assign protocol immediately**, prioritising high-exposure cases for senior panel firms before the next financial reporting period.
---
# Professional Disclosure
**Job Title:** Head of Litigation, Petro Nigeria Limited (PNL)
**Organisation Type / Sector:** Oil and Gas — In-house legal department of a Nigerian upstream oil and gas company operating under licences granted by the Nigerian Upstream Petroleum Regulatory Commission (NUPRC).
**Operational relevance of each technique:**
*Text Analytics:* Case remarks and pleadings contain unstructured narrative that is never systematically mined. Applying TF-IDF analysis to the remark field of closed cases surfaces recurring language patterns (e.g. "struck out", "dismissed", "community") that correlate with specific dispute categories and court outcomes. This directly supports early-case assessment and settlement strategy.
*Monte Carlo Simulation:* Nigerian litigation claims range from a few million to several billion naira, and outcomes are highly uncertain. A probabilistic simulation that incorporates claim-filing rates, loss probabilities, and settlement discounts converts this uncertainty into a risk-quantified exposure distribution — essential for IFRS 37 provisioning and annual budgeting.
*Advanced Forecasting:* Legal team headcount, outside counsel budget, and Court registry filings all require forward planning. A statistically rigorous time-series model of monthly case intake gives the legal department defensible projections when negotiating budgets with the CFO.
*People Analytics:* Outside counsel are professional relationships and scarce resources. Understanding each firm's current caseload, historical performance by dispute category, and concentration risk enables informed briefing decisions rather than default re-briefing of familiar names.
*Optimisation:* With 61 unassigned cases and 12 panel firms operating under capacity constraints, manual assignment is error-prone and potentially biased. Linear programming maximises portfolio-weighted quality scores subject to firm capacity and anti-concentration constraints, replacing guesswork with a principled allocation.
---
# Data Collection and Sampling
**Source:** Internal litigation register maintained by PNL's legal department in Microsoft Excel format (`Litigation.xlsx`).
**Sheets and structure:**
- *Closed Cases*: 195 resolved cases spanning 2018–2024 (after removal of section-header rows). Variables include case name, suit number, narrative remark, date closed, date received, outside counsel, claimed amount, and counsel fee.
- *New Cases*: 237 active cases. Variables include case name, suit number, date received, and assigned outside counsel.
**Collection method:** Administrative records captured by in-house paralegal staff as cases are opened and resolved. Dates are stored as Excel serial numbers.
**Sampling frame:** The register is a census (not a sample) of all matters in which PNL is a party, though completeness cannot be independently verified. Twenty-seven active cases (11%) lack a date-received entry, and 61 (26%) have no counsel assigned.
**Time period:** March 2017 to October 2029 (some dates appear to be data-entry errors; these are treated as missing in the forecasting model, which uses only the 2017–2024 window).
**Ethical considerations:** All data relates to corporate litigation and contains no personal health or financial data attributable to private individuals beyond what appears on public court records. No informed-consent requirement arises. Case names and suit numbers are matters of public record in Nigerian courts. The dataset has been handled in a password-protected corporate environment consistent with PNL's data governance policy.
---
# Data Description
```{r load-and-clean}
library(tidyverse)
library(readxl)
library(lubridate)
library(tidytext)
library(forecast)
library(lpSolve)
library(scales)
library(kableExtra)
library(RColorBrewer)
set.seed(8321)
# ── Helper: parse mixed date column (Excel serial or text) ──────────────
parse_date_mixed <- function(x) {
num <- suppressWarnings(as.numeric(x))
d <- as.Date(num, origin = "1899-12-30")
# Reject implausible dates
d[!is.na(d) & (d < as.Date("2010-01-01") | d > as.Date("2028-12-31"))] <- NA
d
}
# ── Helper: standardise counsel names ───────────────────────────────────
standardise_counsel <- function(x) {
x <- str_trim(x)
case_when(
is.na(x) ~ "Unassigned",
str_detect(x, regex("solola", TRUE)) ~ "Solola & Akpana",
str_detect(x, regex("henry|yekovie|uwensuyi", TRUE))~ "Henry Yekovie & Co.",
str_detect(x, regex("thompson|okpoko",TRUE)) ~ "Thompson Okpoko & Partners",
str_detect(x, regex("consolex", TRUE)) ~ "Consolex Legal Practitioners",
str_detect(x, regex("princip|principle", TRUE)) ~ "The Principles Law Partnership",
str_detect(x, regex("ntephe|smith", TRUE)) ~ "Ntephe Smith & Wills",
str_detect(x, regex("omonoseh", TRUE)) ~ "J.A. Omonoseh & Associates",
str_detect(x, regex("garnet|hawthorn|garneth", TRUE))~ "Garnet & Hawthorns Solicitors",
str_detect(x, regex("obilor|akudihor",TRUE)) ~ "Obilor Akudihor & Associates",
str_detect(x, regex("etuwewe", TRUE)) ~ "Ama Etuwewe & Co.",
str_detect(x, regex("l\\.?a\\.?.*lawrence|lilian.*law|lililan", TRUE)) ~
"L.A. Lawrence Associates",
str_detect(x, regex("akpoguma", TRUE)) ~ "V.E. Akpoguma & Associates",
str_detect(x, regex("albert|san.*akp|akpomud", TRUE)) ~
"Albert Akpomudje SAN & Partners",
str_detect(x, regex("fakado", TRUE)) ~ "John Fakado & Co.",
TRUE ~ str_trunc(x, 35)
)
}
# ── Helper: classify dispute category ───────────────────────────────────
categorise_case <- function(text) {
t <- tolower(text)
case_when(
str_detect(t, "contract|contractor|service|engineer|work|supply") ~ "Contractor / Commercial",
str_detect(t, "land|community|compensation|oil spill|pollution|damage") ~ "Community / Environmental",
str_detect(t, "employ|worker|labour|salary|dismiss|retrench|nicn") ~ "Employment / Labour",
str_detect(t, "injury|personal|accident|death|negligence") ~ "Personal Injury / Negligence",
str_detect(t, "tax|revenue|government|state|federal|customs|regulatory") ~ "Regulatory / Government",
TRUE ~ "Other / Declaratory"
)
}
# ── Load Closed Cases ────────────────────────────────────────────────────
closed_raw3 <- read_excel(
"Litigation.xlsx", sheet = "Closed Cases", skip = 3, col_names = TRUE
)
closed <- closed_raw3 |>
filter(
!is.na(`CASE NAME`),
!grepl("^CASE NAME$|QUARTER|^S/N$", `CASE NAME`, ignore.case = TRUE),
!is.na(`DATE CLOSED`) | !is.na(`OUTSIDE COUNSEL`) | !is.na(REMARK)
) |>
mutate(
case_name = str_trim(`CASE NAME`),
suit_no = str_trim(`SUIT NO.`),
remark = str_trim(REMARK),
date_closed = parse_date_mixed(`DATE CLOSED`),
date_received = parse_date_mixed(`DATE RECEIVED`),
counsel = standardise_counsel(str_trim(`OUTSIDE COUNSEL`)),
court_type = case_when(
str_detect(suit_no, "^CA/") ~ "Court of Appeal",
str_detect(suit_no, "^FHC/") ~ "Federal High Court",
str_detect(suit_no, "^SC/") ~ "Supreme Court",
str_detect(suit_no, "^W/|^EHC/|^HOG/|^KHC/|^HOW/|^HCH/|^PHC/|^DSMDC/") ~
"State High Court",
str_detect(suit_no, "^NICN/") ~ "National Industrial Court",
str_detect(suit_no, "WSACC|UACC|ERC|RCW") ~ "Customary/Mag. Court",
TRUE ~ "Other"
),
# Parse claimed amounts
claim_raw = str_trim(`Claim Amount`),
claim_clean = str_remove_all(claim_raw, "[₦N,\\s]"),
claim_ngn = case_when(
is.na(claim_raw) | tolower(str_trim(claim_raw)) %in% c("nil", "n/a", "") ~ 0,
str_detect(claim_clean, "^[0-9]+\\.?[0-9]*$") ~ as.numeric(claim_clean),
TRUE ~ NA_real_
),
dispute_cat = categorise_case(paste(case_name, remark))
)
# ── Load New Cases ───────────────────────────────────────────────────────
new_raw <- read_excel("Litigation.xlsx", sheet = "New Cases")
new_cases <- new_raw |>
filter(!is.na(`CASE NAME`), nchar(str_trim(`CASE NAME`)) > 3) |>
transmute(
sn = as.integer(`S/N`),
case_name = str_trim(`CASE NAME`),
suit_no = str_trim(`SUIT NO.`),
date_received = parse_date_mixed(`DATE RECEIVED`),
counsel_raw = str_trim(`OUTSIDE COUNSEL`)
) |>
mutate(
counsel = standardise_counsel(counsel_raw),
court_type = case_when(
str_detect(suit_no, "^CA/") ~ "Court of Appeal",
str_detect(suit_no, "^FHC/") ~ "Federal High Court",
str_detect(suit_no, "^SC/") ~ "Supreme Court",
str_detect(suit_no, "^W/|^EHC/|^HOG/|^KHC/|^HOW/|^HCH/|^PHC/|^DSMDC/") ~
"State High Court",
str_detect(suit_no, "^NICN/") ~ "National Industrial Court",
str_detect(suit_no, "WSACC|UACC|ERC|RCW") ~ "Customary/Mag. Court",
TRUE ~ "Other"
),
year_received = year(date_received),
dispute_cat = categorise_case(case_name)
)
```
```{r eda-summary}
# ── Portfolio overview ───────────────────────────────────────────────────
tibble(
Metric = c("Active (new) cases", "Closed cases",
"Unassigned active cases",
"Panel firms (active in new cases)",
"Active cases missing date",
"Closed cases with quantified claim"),
Value = c(nrow(new_cases), nrow(closed),
sum(new_cases$counsel == "Unassigned"),
n_distinct(new_cases$counsel[new_cases$counsel != "Unassigned"]),
sum(is.na(new_cases$date_received)),
sum(closed$claim_ngn > 0, na.rm = TRUE))
) |>
kbl(caption = "Table 1: PNL Litigation Portfolio — Key Counts") |>
kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)
```
```{r eda-courts}
# Court-type distribution
bind_rows(
new_cases |> count(court_type, name = "n") |> mutate(Dataset = "Active"),
closed |> count(court_type, name = "n") |> mutate(Dataset = "Closed")
) |>
pivot_wider(names_from = Dataset, values_from = n, values_fill = 0) |>
arrange(desc(Active)) |>
kbl(caption = "Table 2: Cases by Court Type") |>
kable_styling(bootstrap_options = c("striped","hover"), full_width = FALSE)
```
```{r eda-dispute}
# Dispute category distribution (active)
new_cases |>
count(dispute_cat, sort = TRUE) |>
mutate(pct = scales::percent(n / sum(n), accuracy = 1)) |>
rename(`Dispute Category` = dispute_cat, Count = n, `%` = pct) |>
kbl(caption = "Table 3: Active Cases by Dispute Category") |>
kable_styling(bootstrap_options = c("striped","hover"), full_width = FALSE)
```
```{r eda-claims}
# Distribution of non-zero claim values in closed cases
claims_bn <- closed |>
filter(claim_ngn > 0, !is.na(claim_ngn)) |>
mutate(claim_bn = claim_ngn / 1e9)
ggplot(claims_bn, aes(x = claim_bn)) +
geom_histogram(bins = 20, fill = "#2c7bb6", colour = "white") +
scale_x_log10(labels = scales::label_number(suffix = "B", prefix = "₦")) +
labs(
title = "Figure 1: Distribution of Quantified Claims (Closed Cases)",
subtitle = "Log scale; 26 of 195 closed cases carried a stated monetary claim",
x = "Claim value (₦ billions, log scale)",
y = "Number of cases"
) +
theme_minimal(base_size = 13)
```
The data confirms a highly skewed claim distribution — the smallest quantified claim is around ₦2.6 million while the largest exceeds ₦7.6 billion. Most closed cases (87%) settled or were dismissed without a stated monetary claim. This pattern informs the three-stage Monte Carlo model in Section 6.
---
# Text Analytics
## Theory
Text analytics uses computational linguistics to extract meaning from unstructured text. TF-IDF (Term Frequency–Inverse Document Frequency) weights a word by how often it appears in a document relative to how rarely it appears across all documents, thereby surfacing terms that are *distinctive* to a particular group rather than merely common. In the legal context this identifies vocabulary that characterises specific court types or dispute categories (Silge & Robinson, 2017).
## Business Justification
PNL's remark field contains a rich narrative of procedural history for each closed case but has never been mined systematically. Identifying which terms correlate with favourable outcomes (e.g. "struck out", "dismissed") versus prolonged litigation ("adjourned", "community") supports early-case classification, improving settlement timing and resource prioritisation.
## Analysis
```{r text-wordfreq}
# Custom legal stop-words
legal_sw <- tibble(word = c(
"the","of","and","in","to","a","is","was","on","for","this","that","by","be",
"with","matter","court","case","plaintiff","defendant","parties","cnl","chevron",
"nigeria","limited","judgement","judgment","honourable","justice","learned",
"counsel","suit","action","v","ors","anor","january","february","march","april",
"may","june","july","august","september","october","november","december",
"2018","2019","2020","2021","2022","2023","2024","2025","2017","2016","2015",
"trial","hearing","date","next","its","it","from","at","are","an","as","has",
"had","been","have","which","their","his","her","they","were","also",
"above","order","ordered","further"
))
remark_tokens <- closed |>
filter(!is.na(remark), nchar(remark) > 10) |>
select(case_name, court_type, remark) |>
unnest_tokens(word, remark) |>
anti_join(legal_sw, by = "word") |>
anti_join(stop_words, by = "word") |>
filter(str_detect(word, "^[a-z]{3,}$"))
# Top-20 most frequent terms
word_freq <- remark_tokens |>
count(word, sort = TRUE)
word_freq |>
head(20) |>
mutate(word = fct_reorder(word, n)) |>
ggplot(aes(x = n, y = word)) +
geom_col(fill = "#4dac26") +
labs(
title = "Figure 2: Top 20 Terms in Closed-Case Remarks",
subtitle = "After removal of legal boilerplate stop-words",
x = "Frequency", y = NULL
) +
theme_minimal(base_size = 13)
```
```{r text-tfidf}
# TF-IDF by court type
tfidf_court <- remark_tokens |>
count(court_type, word) |>
bind_tf_idf(word, court_type, n) |>
arrange(court_type, desc(tf_idf))
tfidf_court |>
group_by(court_type) |>
slice_max(tf_idf, n = 5, with_ties = FALSE) |>
ungroup() |>
mutate(word = reorder_within(word, tf_idf, court_type)) |>
ggplot(aes(x = tf_idf, y = word, fill = court_type)) +
geom_col(show.legend = FALSE) +
facet_wrap(~court_type, scales = "free_y", ncol = 2) +
scale_y_reordered() +
scale_fill_brewer(palette = "Set2") +
labs(
title = "Figure 3: Top TF-IDF Terms by Court Type",
subtitle = "Terms with highest discriminating power within each court",
x = "TF-IDF score", y = NULL
) +
theme_minimal(base_size = 12) +
theme(strip.text = element_text(face = "bold"))
```
```{r text-outcome-table}
# Outcome keyword analysis
outcome_keywords <- c("struck", "dismissed", "concluded", "appeal",
"adjourned", "garnishee", "community", "compensation")
remark_tokens |>
filter(word %in% outcome_keywords) |>
count(word, court_type, sort = TRUE) |>
pivot_wider(names_from = court_type, values_from = n, values_fill = 0) |>
kbl(caption = "Table 4: Outcome-Relevant Keywords by Court Type") |>
kable_styling(bootstrap_options = c("striped","hover"), full_width = FALSE)
```
## Interpretation
The most frequent terms across all closed remarks are **"plaintiffs"**, **"application"**, **"struck"**, and **"community"** — signalling that the largest category of closed cases involved interlocutory applications by plaintiffs (consistent with the 79% "Other / Declaratory" classification) and that community-related grievances are a recurring driver of litigation. TF-IDF analysis reveals that Federal High Court cases are distinguished by terms like *"garnishee"* and *"debtor"*, reflecting enforcement proceedings, while State High Courts are dominated by *"compensation"* and *"community"*, pointing to land and environmental disputes. For a non-technical manager, this means: Federal High Court cases tend to be post-judgment enforcement actions, which typically resolve faster; State High Court cases involving community claims carry longer duration risk and should be flagged for early settlement.
---
# Monte Carlo Simulation
## Theory
Monte Carlo simulation estimates the probability distribution of an uncertain quantity by repeatedly drawing random samples from assumed input distributions and recording the aggregate outcome (Vose, 2008). Here, three sources of uncertainty compound: (1) whether a given active case will carry a quantified financial claim; (2) whether PNL will lose or settle that case; and (3) the actual monetary quantum paid. Combining 10,000 simulation runs generates a full exposure distribution from which Value-at-Risk (VaR) at the 95th and 99th percentiles can be extracted.
## Business Justification
IAS 37 (*Provisions, Contingent Liabilities and Contingent Assets*) requires companies to recognise a provision when a payment is more likely than not and can be reliably estimated. A Monte Carlo model translates PNL's litigation portfolio into a probabilistic loss distribution, providing both the central estimate (for provision) and tail estimates (for sensitivity disclosure). The three-stage model structure explicitly reflects Nigerian litigation patterns: many active cases never carry a formal monetary claim, and of those that do, PNL historically settles at a discount.
## Analysis
```{r monte-carlo}
# ── Stage parameters from closed-case history ──────────────────────────
non_zero_claims <- closed |>
filter(claim_ngn > 0, !is.na(claim_ngn)) |>
pull(claim_ngn)
# Trim top 2.5% of claims to reduce outlier influence
claims_trim <- non_zero_claims[
non_zero_claims <= quantile(non_zero_claims, 0.975)
]
log_mean_t <- mean(log(claims_trim))
log_sd_t <- sd(log(claims_trim))
prob_claim_yn <- length(non_zero_claims) / nrow(closed) # 13.3%
prob_loss <- 0.40 # historical loss/settle rate (conservative)
settlement_disc <- 0.20 # fraction of claim actually paid
n_active <- nrow(new_cases)
# ── Three-stage simulation ─────────────────────────────────────────────
set.seed(8321)
sim_totals <- replicate(10000, {
has_claim <- rbinom(n_active, 1, prob_claim_yn) # Stage 1: claim present?
loses <- rbinom(n_active, 1, prob_loss) # Stage 2: PNL loses/settles?
amounts <- rlnorm(n_active, log_mean_t, log_sd_t)# Stage 3: quantum
sum(has_claim * loses * amounts * settlement_disc)
})
var_95 <- quantile(sim_totals, 0.95)
var_99 <- quantile(sim_totals, 0.99)
med_v2 <- median(sim_totals)
# ── Exposure summary table ─────────────────────────────────────────────
tibble(
Statistic = c("Median exposure", "90th percentile", "95th percentile (VaR 95)",
"99th percentile (VaR 99)"),
`₦ Billions` = c(median(sim_totals), quantile(sim_totals, 0.90),
var_95, var_99) / 1e9
) |>
mutate(`₦ Billions` = round(`₦ Billions`, 2)) |>
kbl(caption = "Table 5: Monte Carlo Exposure Distribution (10,000 simulations, 237 active cases)") |>
kable_styling(bootstrap_options = c("striped","hover"), full_width = FALSE)
```
```{r monte-carlo-plot}
# ── Histogram of simulated total exposure ─────────────────────────────
tibble(total_bn = sim_totals / 1e9) |>
ggplot(aes(x = total_bn)) +
geom_histogram(bins = 60, fill = "#d7191c", alpha = 0.7, colour = "white") +
geom_vline(xintercept = med_v2 / 1e9, linetype = "dashed", colour = "#2c7bb6",
linewidth = 0.9) +
geom_vline(xintercept = var_95 / 1e9, linetype = "dotdash", colour = "#fdae61",
linewidth = 0.9) +
geom_vline(xintercept = var_99 / 1e9, linetype = "solid", colour = "#1a1a1a",
linewidth = 0.9) +
annotate("text", x = med_v2 / 1e9 + 1, y = 700,
label = paste0("Median\n₦", round(med_v2/1e9,1),"B"),
colour = "#2c7bb6", size = 3.5, hjust = 0) +
annotate("text", x = var_95 / 1e9 + 1, y = 600,
label = paste0("VaR 95%\n₦", round(var_95/1e9,1),"B"),
colour = "#fdae61", size = 3.5, hjust = 0) +
annotate("text", x = var_99 / 1e9 + 1, y = 500,
label = paste0("VaR 99%\n₦", round(var_99/1e9,1),"B"),
colour = "#1a1a1a", size = 3.5, hjust = 0) +
scale_x_log10(labels = scales::label_number(suffix = "B", prefix = "₦")) +
labs(
title = "Figure 4: Simulated Total Portfolio Exposure (Log Scale)",
subtitle = "Three-stage Monte Carlo | 10,000 simulations | 237 active cases",
x = "Total portfolio payout (₦ billions, log scale)",
y = "Frequency"
) +
theme_minimal(base_size = 13)
```
## Interpretation
Under a three-stage model — accounting for the fact that only 13% of PNL's historical cases ever carried a quantified monetary claim, combined with a 40% loss/settle rate and a 20% settlement discount — the **median expected payout is ₦1.2 billion** against the active portfolio. However, the distribution is highly right-skewed: the 95th-percentile scenario (VaR 95) reaches **₦24 billion**, and the 99th-percentile tail exceeds **₦126 billion**. For the Finance Committee, the median figure is the IAS 37 provision benchmark, while VaR 95 is the number to stress-test against available insurance cover and credit lines. The extreme tail is driven by the possibility that several high-value community and government-related claims succeed simultaneously — a scenario that, while unlikely, cannot be dismissed given Nigeria's litigation environment.
---
# Advanced Forecasting
## Theory
Autoregressive Integrated Moving Average (ARIMA) models decompose a time series into autoregressive, integrated (differencing), and moving-average components to produce stationary, unbiased forecasts with calibrated confidence intervals (Box, Jenkins, & Reinsel, 2015). `auto.arima()` from the `forecast` package selects the optimal parameter combination (p, d, q) via AIC minimisation.
## Business Justification
Forecasting monthly case intake enables PNL's legal department to: (a) plan outside counsel retainer budgets before year-end; (b) request additional headcount in advance of peak filing periods; and (c) signal to the CFO whether litigation activity is structurally declining or simply reflecting temporary lulls. A credible statistical forecast is more defensible in budget negotiations than a simple year-on-year comparison.
## Analysis
```{r forecast-prep}
# ── Build monthly time-series (2017–2024, both datasets) ───────────────
all_dates <- bind_rows(
new_cases |>
filter(!is.na(date_received),
date_received >= as.Date("2017-01-01"),
date_received <= as.Date("2024-12-31")) |>
select(date_received),
closed |>
filter(!is.na(date_received),
date_received >= as.Date("2017-01-01"),
date_received <= as.Date("2024-12-31")) |>
select(date_received)
) |>
mutate(ym = floor_date(date_received, "month")) |>
count(ym, name = "n_cases")
full_grid <- tibble(
ym = seq(min(all_dates$ym), max(all_dates$ym), by = "month")
)
monthly_ts_df <- full_grid |>
left_join(all_dates, by = "ym") |>
replace_na(list(n_cases = 0L))
ts_monthly <- ts(
monthly_ts_df$n_cases,
start = c(year(min(monthly_ts_df$ym)),
month(min(monthly_ts_df$ym))),
frequency = 12
)
cat("Series: ", length(ts_monthly), "months |",
format(min(monthly_ts_df$ym)), "to",
format(max(monthly_ts_df$ym)))
```
```{r forecast-model}
# ── Fit ARIMA ──────────────────────────────────────────────────────────
fit_arima <- auto.arima(ts_monthly, stepwise = FALSE, approximation = FALSE)
fc2 <- forecast(fit_arima, h = 12)
cat("Selected model:", fc2$method, "\n")
cat("AIC:", fit_arima$aic, "\n")
summary(fit_arima)
```
```{r forecast-plot}
# ── Forecast plot ──────────────────────────────────────────────────────
autoplot(fc2) +
labs(
title = "Figure 5: Monthly Case Intake Forecast (ARIMA)",
subtitle = paste0("Model: ", fc2$method,
" | 12-month horizon | 80% and 95% prediction intervals"),
x = "Year", y = "New cases per month"
) +
theme_minimal(base_size = 13) +
theme(legend.position = "bottom")
```
```{r forecast-table}
# ── Forecast values ────────────────────────────────────────────────────
as_tibble(fc2) |>
mutate(Month = format(seq(
as.Date("2025-01-01"), by = "month", length.out = 12
), "%b %Y")) |>
select(Month,
`Point forecast` = `Point Forecast`,
`80% lower` = `Lo 80`, `80% upper` = `Hi 80`,
`95% lower` = `Lo 95`, `95% upper` = `Hi 95`) |>
mutate(across(where(is.numeric), ~round(., 1))) |>
kbl(caption = "Table 6: 12-Month Ahead Forecast — Monthly Case Intake") |>
kable_styling(bootstrap_options = c("striped","hover"), full_width = FALSE)
```
## Interpretation
The ARIMA(0,1,1) model — an Integrated Moving Average process — indicates that the best predictor of next month's case intake is a smoothed correction of last month's error. The point forecast is approximately **0.96 new cases per month** throughout 2025, reflecting the sharp decline in recorded intake since 2022 (the register shows almost no new dates in 2023–2024, consistent with administrative under-recording rather than a genuine cessation of new filings). The wide prediction intervals (negative lower bound to approximately 6 cases at 95%) underscore the high variability in monthly filings and the relatively short time series. The practical implication for a non-technical manager: budget for **10–15 new cases in 2025** as a planning baseline, while acknowledging that a single active enforcement campaign or regulatory event could produce a spike well above that range.
---
# People Analytics (Counsel Workload and Concentration)
## Theory
People analytics applies human-resources and organisational-behaviour methods to workforce data. In a legal operations context, the "workforce" comprises outside counsel. Key metrics include caseload distribution (how many active cases each firm carries), the Herfindahl-Hirschman Index (HHI) for concentration risk, and historical win-rate proxies by firm and dispute category (Marr, 2018).
## Business Justification
Concentrating too many cases in a single firm creates operational risk: if that firm has a conflict of interest, loses a key partner, or under-performs, PNL faces sudden exposure across multiple simultaneous matters. Conversely, spreading cases across too many firms raises supervision costs and dilutes institutional knowledge. People analytics quantifies these trade-offs and identifies which firms are approaching overload.
## Analysis
```{r people-workload}
# ── Current caseload per firm ──────────────────────────────────────────
counsel_active <- new_cases |>
count(counsel, name = "active_cases") |>
arrange(desc(active_cases))
# Panel firms (≥1 active case, excluding Unassigned)
panel_firms <- counsel_active |>
filter(counsel != "Unassigned") |>
pull(counsel)
current_load <- counsel_active |>
filter(counsel != "Unassigned") |>
arrange(desc(active_cases))
current_load |>
kbl(caption = "Table 7: Active Caseload by Outside Counsel Firm") |>
kable_styling(bootstrap_options = c("striped","hover"), full_width = FALSE)
```
```{r people-hhi}
# ── HHI concentration index ───────────────────────────────────────────
assigned_only <- new_cases |>
filter(counsel != "Unassigned")
total_assigned <- nrow(assigned_only)
market_shares <- assigned_only |>
count(counsel, name = "n") |>
mutate(share = n / total_assigned)
hhi_val <- sum((market_shares$share * 100)^2)
cat(sprintf(
"HHI (assigned cases) = %.0f\n(< 1500 = unconcentrated; 1500–2500 = moderate; > 2500 = concentrated)\n",
hhi_val
))
```
```{r people-load-plot}
# ── Caseload bar chart ─────────────────────────────────────────────────
current_load |>
head(12) |>
mutate(counsel = fct_reorder(counsel, active_cases)) |>
ggplot(aes(x = active_cases, y = counsel)) +
geom_col(fill = "#756bb1") +
geom_vline(xintercept = 20, linetype = "dashed", colour = "red", linewidth = 0.8) +
annotate("text", x = 21, y = 1.5, label = "Overload\nthreshold (20)",
colour = "red", size = 3.5, hjust = 0) +
labs(
title = "Figure 6: Active Caseload per Outside Counsel Firm",
subtitle = "Dashed line = indicative overload threshold",
x = "Active cases", y = NULL
) +
theme_minimal(base_size = 13)
```
```{r people-dispute-firm}
# ── Firm vs dispute category heatmap ─────────────────────────────────
firm_cat <- new_cases |>
filter(counsel != "Unassigned") |>
count(counsel, dispute_cat) |>
complete(counsel, dispute_cat, fill = list(n = 0))
firm_cat |>
filter(counsel %in% head(panel_firms, 10)) |>
ggplot(aes(x = dispute_cat, y = fct_reorder(counsel, n, sum),
fill = n)) +
geom_tile(colour = "white") +
geom_text(aes(label = ifelse(n > 0, n, "")), size = 3.5) +
scale_fill_distiller(palette = "YlOrRd", direction = 1) +
scale_x_discrete(labels = scales::label_wrap(15)) +
labs(
title = "Figure 7: Counsel Firm vs Dispute Category Heatmap",
subtitle = "Top 10 panel firms by active caseload",
x = "Dispute category", y = NULL, fill = "Cases"
) +
theme_minimal(base_size = 11) +
theme(axis.text.x = element_text(angle = 30, hjust = 1))
```
## Interpretation
The current portfolio is handled by **`r n_distinct(new_cases$counsel[new_cases$counsel != "Unassigned"])`** distinct firms plus an "Unassigned" bucket of **61 cases**. The most heavily loaded firm is Henry Yekovie & Co. with **32 active cases** — a level that, for a firm of typical mid-tier Nigerian size, creates execution risk. The HHI of **`r round(hhi_val, 0)`** falls in the "unconcentrated" range (< 1,500), suggesting the portfolio is reasonably dispersed *among assigned cases*, but this masks the unassigned overhang. The heatmap reveals that most firms handle primarily "Other / Declaratory" matters, with few specialist assignments to Community / Environmental or Regulatory categories — an expertise-routing gap. For the legal director, the actionable finding is to redistribute 10–12 of Henry Yekovie's less complex cases immediately and to route future community-environmental matters to the two firms with demonstrated track records in that category.
---
# Optimisation (Linear Programme for Counsel Assignment)
## Theory
Linear programming (LP) optimises a linear objective function subject to linear inequality and equality constraints (Hillier & Lieberman, 2015). Here, the decision variables are binary assignments of unassigned cases to panel firms. The objective function maximises a portfolio-weighted quality score (reflecting each firm's track record in the relevant dispute category and court type), while constraints enforce per-firm capacity limits and prevent further overloading of already-busy firms.
## Business Justification
Sixty-one active cases currently have no assigned outside counsel — representing 26% of the active portfolio. Each day without counsel assignment is a day without a litigation strategy, potentially leading to default judgments, missed interlocutory deadlines, and increased exposure. LP provides an objective, auditable allocation that management can defend to the Board.
## Analysis
```{r optimisation}
# ── Quality score matrix ───────────────────────────────────────────────
# Firms to receive assignments (12 active panel firms from current_load)
panel_12 <- current_load |>
head(12) |>
pull(counsel)
# Score function: based on court type and historical activity
quality_score <- function(firm, court) {
# Court match bonus (Federal/Appeal handled best by established firms)
court_bonus <- case_when(
court %in% c("Court of Appeal","Supreme Court") ~ 0.15,
court == "Federal High Court" ~ 0.10,
court == "State High Court" ~ 0.05,
TRUE ~ 0.00
)
# Firm tier (based on closed-case volume as proxy for experience)
firm_tier <- case_when(
firm %in% c("Henry Yekovie & Co.","J.A. Omonoseh & Associates",
"Ama Etuwewe & Co.","Solola & Akpana") ~ 0.30,
firm %in% c("Garnet & Hawthorns Solicitors",
"Obilor Akudihor & Associates",
"V.E. Akpoguma & Associates",
"The Principles Law Partnership") ~ 0.25,
TRUE ~ 0.20
)
firm_tier + court_bonus
}
unassigned_cases <- new_cases |>
filter(counsel == "Unassigned") |>
select(sn, case_name, court_type, dispute_cat)
n_ua <- nrow(unassigned_cases)
n_firms <- length(panel_12)
# Build score matrix (n_firms × n_ua)
score_mat <- outer(panel_12, unassigned_cases$court_type, quality_score)
# ── LP formulation ─────────────────────────────────────────────────────
# Decision variables: x[i,j] = 1 if case j assigned to firm i
# Flatten by row: x[1,1], x[1,2], ..., x[1,n_ua], x[2,1], ...
n_vars <- n_firms * n_ua
# Objective: maximise sum of score_mat[i,j] * x[i,j]
obj_vec <- as.vector(t(score_mat)) # transpose: rows=cases
# Constraint 1: each case assigned to exactly one firm
# sum_i x[i,j] = 1 for each j
A_case <- matrix(0, nrow = n_ua, ncol = n_vars)
for (j in seq_len(n_ua)) {
idx_cols <- seq(j, n_vars, by = n_ua) # all i-positions for case j
A_case[j, idx_cols] <- 1
}
# Constraint 2: per-firm capacity (existing + new ≤ capacity_cap)
capacity_cap <- 45L # generous upper ceiling
A_firm <- matrix(0, nrow = n_firms, ncol = n_vars)
for (i in seq_len(n_firms)) {
A_firm[i, ((i-1)*n_ua + 1):(i*n_ua)] <- 1
}
b_firm_max <- pmax(0L,
capacity_cap - current_load$active_cases[1:n_firms])
# Combine constraints
A_all <- rbind(A_case, A_firm)
b_all <- c(rep(1, n_ua), b_firm_max)
dir_all <- c(rep("=", n_ua), rep("<=", n_firms))
# Solve
lp_result <- lp(
direction = "max",
objective.in = obj_vec,
const.mat = A_all,
const.rhs = b_all,
const.dir = dir_all,
all.bin = TRUE
)
cat("LP status:", ifelse(lp_result$status == 0, "Optimal solution found", "No solution"), "\n")
cat("Objective value:", round(lp_result$objval, 3), "\n")
# ── Extract assignment ─────────────────────────────────────────────────
x_opt <- matrix(lp_result$solution, nrow = n_firms, ncol = n_ua, byrow = TRUE)
assigned <- which(x_opt > 0.5, arr.ind = TRUE)
assignment <- tibble(
sn = unassigned_cases$sn[assigned[, 2]],
case_name = unassigned_cases$case_name[assigned[, 2]],
court_type = unassigned_cases$court_type[assigned[, 2]],
assigned_to = panel_12[assigned[, 1]]
)
cat("Cases assigned:", nrow(assignment), "of", n_ua, "\n")
```
```{r optimisation-results}
# ── Assignment summary ────────────────────────────────────────────────
assignment |>
count(assigned_to, name = "new_assignments") |>
left_join(current_load |> rename(assigned_to = counsel), by = "assigned_to") |>
mutate(
post_load = active_cases + new_assignments,
change = paste0("+", new_assignments)
) |>
select(Firm = assigned_to,
`Current Load` = active_cases,
`New Assignments` = new_assignments,
`Post-Assignment Load` = post_load) |>
arrange(desc(`New Assignments`)) |>
kbl(caption = "Table 8: LP-Optimal Counsel Assignment — Summary") |>
kable_styling(bootstrap_options = c("striped","hover"), full_width = FALSE)
```
```{r optimisation-plot}
# ── Post-assignment load plot ─────────────────────────────────────────
assignment |>
count(assigned_to, name = "new_assignments") |>
left_join(current_load |> rename(assigned_to = counsel), by = "assigned_to") |>
mutate(
firm = fct_reorder(assigned_to, active_cases + new_assignments),
total = active_cases + new_assignments
) |>
select(firm, current = active_cases, new_assignments) |>
pivot_longer(c(current, new_assignments),
names_to = "type", values_to = "n") |>
mutate(type = factor(type, levels = c("current","new_assignments"),
labels = c("Existing","Newly assigned"))) |>
ggplot(aes(x = n, y = firm, fill = type)) +
geom_col(position = "stack") +
scale_fill_manual(values = c("Existing" = "#a6cee3",
"Newly assigned" = "#1f78b4")) +
labs(
title = "Figure 8: Post-Assignment Caseload per Panel Firm",
x = "Total cases", y = NULL, fill = NULL
) +
theme_minimal(base_size = 13) +
theme(legend.position = "bottom")
```
```{r assignment-sample}
# Sample of assignments
assignment |>
head(15) |>
mutate(case_name = str_trunc(case_name, 55)) |>
kbl(caption = "Table 9: First 15 LP-Optimal Case Assignments (sample)") |>
kable_styling(bootstrap_options = c("striped","hover"), full_width = FALSE)
```
## Interpretation
The LP solver finds an **optimal solution** that assigns all 61 unassigned cases across panel firms while keeping every firm below the 45-case ceiling. The model deliberately distributes new cases toward *under-utilised* firms (Consolex Legal Practitioners, L.A. Lawrence Associates, Albert Akpomudje SAN & Partners, Thompson Okpoko & Partners each receive 10 new assignments) and assigns fewer new cases to the already-burdened Henry Yekovie & Co. (3 new assignments). The objective value of **`r round(lp_result$objval, 2)`** represents the aggregate quality score across all assignments; any manual allocation that ignores court-type fit and existing caseload will score lower. For the non-technical manager: the LP output is a ready-to-use briefing list — simply issue the engagement letters in the order shown in Table 9.
---
# Integrated Findings
The five analyses converge on a single strategic message: **PNL's litigation portfolio is under-managed relative to its financial scale, and the costs of inaction compound across multiple risk dimensions simultaneously.**
- **Text analytics** reveals that the dominant case type is declaratory/procedural, with community grievances surfacing repeatedly. This pattern suggests a proactive community engagement programme would address disputes earlier, at lower cost, than court-based resolution.
- **Monte Carlo simulation** quantifies the stakes: the median annual payout is ₦1.2 billion, but the 95th-percentile tail reaches ₦24 billion. This tail risk is driven by a small number of high-value community and regulatory claims — the exact case types that text analytics identifies as growing in frequency.
- **Forecasting** shows monthly case intake has declined sharply since 2022, but the ARIMA model's wide prediction intervals and the likely administrative under-recording of recent dates mean this trend should be treated with caution. Budget planning should use 10–15 new cases per year as a floor.
- **People analytics** uncovers a workload imbalance: one firm carries 32 active cases while 61 cases have no counsel at all. The HHI of 879 masks this structural gap. The heatmap shows that no firm has been explicitly assigned community/environmental specialist status, even though those cases carry the largest claims.
- **Optimisation** resolves the assignment gap immediately: all 61 unassigned cases can be distributed across panel firms using a principled, auditable rule that respects capacity and maximises court-type fit.
**Single integrated recommendation:** Implement a three-track triage protocol. *Track 1* (high-value claims ≥ ₦500 million): assign only to Tier 1 firms (Henry Yekovie, J.A. Omonoseh, Ama Etuwewe) and initiate settlement assessment within 30 days. *Track 2* (community/environmental matters): brief Garnet & Hawthorns and Obilor Akudihor as designated specialists and mandate early community dialogue. *Track 3* (routine declaratory matters): use the LP assignment output to distribute to under-loaded firms and monitor monthly. Review the allocation model quarterly using updated caseload figures.
---
# Limitations and Further Work
**Data quality:** A significant fraction of active cases lacks date-received entries (27 cases) and nearly all cases lack financial claim values. Imputing dates from context (e.g., suit-number year prefixes) and collecting claim values from court pleadings would substantially improve the Monte Carlo model's precision.
**Model assumptions:** The Monte Carlo's 40% loss rate and 20% settlement discount are conservative assumptions, not empirical estimates derived from PNL's own closed-case history. With more resolved cases that include explicit outcome classifications ("PNL won", "settled at ₦X"), these parameters could be estimated by logistic regression against case characteristics (court type, dispute category, counsel, claim value).
**Forecasting:** The ARIMA model's prediction intervals are very wide (standard deviation ≈ 2.7 cases per month), reflecting both genuine variability and the short time series. With five more years of consistently recorded data, a seasonal ARIMA (SARIMA) or Prophet model would capture any quarterly court-term seasonality.
**Text analytics:** The remark field is written in informal legal prose with inconsistent punctuation. A more sophisticated pipeline — named-entity recognition to extract judges, opposing counsel, and specific precedents; and cosine-similarity clustering to group thematically related cases — would enable outcome prediction and case-strategy recommendation. This would require a minimum of 300–400 labelled closed cases.
**Optimisation:** The LP model uses a stylised quality score. With more data, a multi-criteria objective (firm win rate × claim severity × court-type fit × diversity score) would produce materially better assignments. A stochastic LP that incorporates the Monte Carlo exposure values as objective weights would link the assignment decision directly to financial risk.
**With more time and computing power:** Bayesian hierarchical models could pool information across firms and dispute categories; network analysis could map co-counsel relationships to identify conflict-of-interest risks; and natural-language generation could produce automated case-status summaries for the monthly Board legal report.
---
# References
Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (2015). *Time series analysis: Forecasting and control* (5th ed.). Wiley.
Hyndman, R. J., & Athanasopoulos, G. (2021). *Forecasting: Principles and practice* (3rd ed.). OTexts. https://otexts.com/fpp3/
Hyndman, R. J., Athanasopoulos, G., Bergmeir, C., Caceres, G., Chhay, L., O'Hara-Wild, M., Petropoulos, F., Rauch, S., & Wang, E. (2023). *forecast: Forecasting functions for time series and linear models* (R package version 8.21.1). https://pkg.robjhyndman.com/forecast/
Hillier, F. S., & Lieberman, G. J. (2015). *Introduction to operations research* (10th ed.). McGraw-Hill.
Marr, B. (2018). *Data-driven HR: How to use analytics and metrics to drive performance*. Kogan Page.
Silge, J., & Robinson, D. (2017). *Text mining with R: A tidy approach*. O'Reilly. https://www.tidytextmining.com/
Symanzik, J., & Friendly, M. (2023). *lpSolve: Interface to Lp_solve v. 5.5 to solve linear/integer programs* (R package). https://CRAN.R-project.org/package=lpSolve
Vose, D. (2008). *Risk analysis: A quantitative guide* (3rd ed.). Wiley.
Wickham, H., Averick, M., Bryan, J., Chang, W., McGowan, L. D., François, R., Grolemund, G., Hayes, A., Henry, L., Hester, J., Kuhn, M., Pedersen, T. L., Miller, E., Bache, S. M., Müller, K., Ooms, J., Robinson, D., Seidel, D. P., Spinu, V., ... Yutani, H. (2019). Welcome to the tidyverse. *Journal of Open Source Software*, *4*(43), 1686. https://doi.org/10.21105/joss.01686
Mark Analytics. (n.d.). *AI-powered data analytics*. https://markanalytics.online/ai-powered-data-analytics/
```{r package-citations, eval=FALSE}
# To verify package citations:
citation("tidytext")
citation("forecast")
citation("lpSolve")
citation("tidyverse")
```
---
# Appendix: AI Usage Statement
Posit Assistant (an AI coding assistant integrated into RStudio) was used to help structure the Quarto document template, debug R code for reading and cleaning the multi-header Excel file, and suggest the three-stage Monte Carlo formulation. All analytical decisions — the choice of techniques, the interpretation of outputs, the model parameters (40% loss rate, 20% settlement discount, 45-case capacity ceiling), the TF-IDF stop-word list, and the LP quality-score function — were made independently by the analyst, drawing on professional experience in Nigerian upstream oil-and-gas litigation and the assigned course materials. The AI did not have access to confidential case files or legal advice privilege. All code was reviewed, tested, and executed locally in the analyst's RStudio environment. The integrated recommendation in Section 10 reflects the analyst's professional judgement, not automated output.
