What is cost per ticket, and how do you measure it in Metabase?

Joins a finance costs table to monthly ticket counts.

-- Fully-loaded monthly cost per ticket: support costs ÷ tickets handled.
-- support_costs holds one row per month per cost line (salaries, tooling,
-- overhead allocations) from finance's export.
WITH monthly_costs AS (
  SELECT
    date_trunc('month', c.cost_month)  AS month,
    SUM(c.amount)                      AS support_cost
  FROM support_costs c
  GROUP BY 1
),
monthly_tickets AS (
  SELECT
    date_trunc('month', t.solved_at)   AS month,
    COUNT(*)                           AS tickets_handled
  FROM tickets t
  WHERE t.solved_at IS NOT NULL
  GROUP BY 1
)
SELECT
  c.month,
  c.support_cost,
  t.tickets_handled,
  ROUND(c.support_cost / NULLIF(t.tickets_handled, 0), 2) AS cost_per_ticket
FROM monthly_costs c
JOIN monthly_tickets t USING (month)
ORDER BY c.month;

Allocates each month's cost by handle-time share, then divides by that channel's tickets.

-- Cost per ticket by channel, allocating each month's cost by the share
-- of agent handle time that channel consumed.
WITH monthly_costs AS (
  SELECT
    date_trunc('month', c.cost_month) AS month,
    SUM(c.amount)                     AS support_cost
  FROM support_costs c
  GROUP BY 1
),
channel_effort AS (
  SELECT
    date_trunc('month', t.solved_at) AS month,
    t.channel,
    COUNT(*)                         AS tickets,
    SUM(t.handle_minutes)            AS handle_minutes
  FROM tickets t
  WHERE t.solved_at IS NOT NULL
  GROUP BY 1, 2
)
SELECT
  e.month,
  e.channel,
  e.tickets,
  ROUND(
    c.support_cost
    * e.handle_minutes
    / NULLIF(SUM(e.handle_minutes) OVER (PARTITION BY e.month), 0)
    / NULLIF(e.tickets, 0), 2
  ) AS cost_per_ticket
FROM channel_effort e
JOIN monthly_costs c ON c.month = e.month
ORDER BY e.month, cost_per_ticket DESC;