---
id: ev
title: Damage as a distribution, not a mean
status: open
dependsOn: [protocol]
exitCriterion: >
  Fire allocation is chosen on P(threshold), and the calculator is tested against
  hand-computed cases.
---

# ev

At a to-hit of 11 a PPC has an expected 0.83 damage and an actual outcome of
"nothing, 92% of the time". Overkill decisions need the distribution; the mean
says a Locust needs two PPCs when it needs many more. (The figure was written
here against a to-hit of 10, which 2d6 reaches one time in six, not one in
twelve.)

The calculator lives in `crates/sds-core/src/ev.rs`. Nothing calls it yet.

- [x] Per-shot PMF over integer damage: `1 - P(hit)` at zero, the rest across the
      cluster table for the rack size, times per-missile damage
- [x] Convolve shots for an allocation; memoise on
      `(rack, per-missile damage, to-hit, cluster modifier)`
- [x] Query it for mean, p50, p90, `P(>=20)` (the piloting-roll cliff)
- [x] Carry expected packet count alongside, for punch-versus-sandblast
- [x] `P(kill)` and `P(breach)`, against the location the damage reaches rather
      than the target's total. `at_least(threshold)` is still the whole of the
      arithmetic; what was missing was not the threshold but the distribution to
      apply it to. `EvCache::location_allocation` carries the per-location
      compound distribution, and `hitloc` supplies the shares. See
      `plan/features.md` for the size of the error this removed
- [ ] Feed AMS into the cluster modifier. The key has the field and the roll
      applies it; nothing on the wire says a target mounts AMS
- [ ] Force-level greedy allocation against the concave value curve. Waits on
      force-level assignment machinery, which does not exist yet. Greedy on a
      submodular objective is within 1-1/e; any search over subsets is exponential
- [ ] **Declare high-concentration weapons first.** Now measurable: `p_breach`
      says whether a location is expected to open, which is the thing a later
      cluster weapon would be firing through. Declaration order is
      resolution order in MegaMek and nothing sorts it, so a PPC can open a
      location for the cluster weapons behind it. Free, once there is an
      allocation to order