# High-PR dynamics — why the paper numbers stop working Built from twelve real fleets across five battles in the 90M–270M PR range (SKM, Teerak, Viigii, BigChickenSmallEgg, NotDrLatBC, DestroyerOfEmpires, Teaspoon). The headline: **at high PR, a ship's own statline has almost no bearing on whether it survives.** What decides it is which enemy stack it lands opposite. Every per-ship metric in these files — `dmg/1kPR`, `EHP/1kPR`, `dpt` — is measuring something with near-zero explanatory power at this level. --- ## 1. The measurement 100 paired stacks, correlation against casualty %: | Predictor | r | |---|---| | Own EHP per 1k PR | **0.076** | | Own damage per 1k PR | **−0.056** | | Slot number (1 = biggest) | 0.012 | | **log(my stack PR ÷ paired stack PR)** | **−0.560** | And the gradient is clean and monotonic: | Position in the pairing | n | Mean casualties | |---|---|---| | Outgunned >10× | 12 | **100%** | | Outgunned 2–10× | 18 | 94% | | Within 2× | 40 | 58% | | Outgun 2–10× | 18 | 40% | | Outgun >10× | 12 | **17%** | A stack's own quality is noise. The PR of whatever it is matched against is everything. > Pairings here are reconstructed from wave-1 positional order. Wave 2 re-stacks > the survivors and unpaired stacks flank at random, so the true relationship is > stronger than −0.560 — the residual is partly my reconstruction losing the > wave-2 shuffle. --- ## 2. Battles are ten duels, not attrition Across 120 stacks: | Casualties | Stacks | | |---|---|---| | 0–2% (untouched) | 23 | `############` | | 2–20% | 10 | `#####` | | 20–50% | 17 | `#########` | | 50–80% | 6 | `###` | | 80–98% | 1 | `#` | | 98–100% (wiped) | 63 | `################################` | **72% of stacks end at one extreme or the other. Only 19% take a partial loss between 20% and 80%.** Damage does not spread across a fleet. Each slot is a near-independent duel whose loser is usually annihilated. "My fleet has X effective HP" is not a quantity the engine ever computes. ### Worked example — SKM vs Teerak, 263M vs 268M PR (0.98 ratio) | Slot | Attacker | Stack PR | Lost | Defender | Stack PR | Lost | |---|---|---|---|---|---|---| | 1 | Nirvana | 88.2M | 58% | M.Chlor | 111.6M | 60% | | 2 | Angel | 88.1M | 20% | C.Gemini | 70.5M | **100%** | | 3 | Tiger | 50.9M | **0%** | Nirvana | 43.2M | **100%** | | 4 | M.Epidote | 5.1M | **100%** | Strafez Queen | 26.1M | **100%** | | 5 | F.Broadsword | 5.1M | **100%** | C.Aries | 16.7M | **100%** | | 6 | T.Maru | 5.1M | **100%** | Pyth | 22.5k *(1 ship)* | **100%** | | 7 | V.Borrelly | 5.0M | **0%** | C.Cancer | 1 ship | **100%** | | 8 | Strafez King | 5.0M | **0%** | F.Spear | 1 ship | **100%** | | 9 | E.Aurora | 5.0M | **0%** | T.Fenrir | 1 ship | **100%** | | 10 | Strafez Queen | 5.0M | **0%** | Tiger | 1 ship | **100%** | Slots 6–10 are the whole lesson. SKM's bottom five stacks are **all sized to 5.0–5.1M PR** — deliberately identical. Four of them took zero casualties. One, T.Maru, was wiped completely. Nothing about T.Maru caused that. Its wave-1 opponent was a **single Pyth**, which cannot scratch 99,065 corvettes. T.Maru died in wave 2: once Teerak's dummies were gone, M.Chlor (26,978 surviving units × 500 energy ≈ 13.5M damage in one shot, against a ~10.9M stack hull pool) flanked a randomly chosen SKM stack and happened to pick T.Maru. **Five identical stacks; the RNG deleted one.** That is not a stat problem and no amount of ship tuning changes it. --- ## 3. What high-PR players actually do All twelve fleets share three properties. ### Ten stacks, always Every single fleet fields exactly **10** — the `maxstack` cap. At this level the cap is not a ceiling you approach, it is a constraint you build against. Slot count is the scarce resource ([Combat-Mechanics.md](Combat-Mechanics.md) §1). ### Stack PR is engineered, not incidental | Fleet | Top/bottom stack PR ratio | Top stack as share of fleet | |---|---|---| | DestroyerOfEmpires (vs NDLB) | **1×** | 11% | | DestroyerOfEmpires (vs Teaspoon) | **1×** | 11% | | NotDrLatBC (vs SKM) | 4× | 16% | | Teaspoon | 6× | 13% | | SKM (vs Teerak) | 18× | 34% | | BigChickenSmallEgg | 424× | 25% | | Teerak | >10,000× | 42% | DestroyerOfEmpires flattens every stack to within a factor of one — all ten between 9.8M and 12.0M. That denies the opponent any favourable pairing: there is no small stack to farm and no huge stack to gang. Against NotDrLatBC the result was a perfectly clean cut — **10/10 stacks at an extreme**, six wiped and four untouched. Others tier deliberately: SKM runs three heavyweights (88M / 88M / 51M) and then **seven stacks all at 5.0–5.1M**, controlling exactly which slot each lands in. ### Dummies fill the tail Teerak fields **five one-ship stacks** (Pyth, C.Cancer, F.Spear, T.Fenrir, Tiger); NotDrLatBC fields three (E.Pulsar, F.Sword, F.Broadsword). Others use Strafez Fodder blocks. All of it exists to occupy slots. Note what the dummies achieved for Teerak: slots 6–10 all died, and in exchange **SKM's slots 7, 8, 9 and 10 took zero casualties**. The dummies traded nothing for nothing. Their real function is denying the opponent free flanks and controlling where the real stacks land. --- ## 4. Why the paper numbers fail here Three separate reasons, each sufficient on its own. 1. **Pairing dominates.** A ship with excellent damage per PR that lands opposite a 20×-larger stack contributes one shot and dies. A mediocre hull opposite a one-ship dummy survives untouched. r = −0.560 for pairing versus r ≈ 0.07 for own stats. 2. **Outcomes are bimodal.** Metrics like EHP per PR describe graceful degradation. Nothing degrades gracefully — 72% of stacks are at 0% or 100%. 3. **Wave 2 is random.** Once stacks die, `_restack` drops them and unpaired stacks pick targets with `rng.choice(alive)`. Among several identically-sized stacks, which one dies is chance. None of this makes the per-ship analysis wrong — it makes it **narrowly scoped**. Ship stats decide who wins a given pairing, and they still govern low-PR play where fleets are not engineered. They do not decide who wins a high-PR battle. --- ## 5. Consequences for balance work - **Per-ship stat changes have limited reach at the top.** Nothing in [../Ship-Balance-Changes.md](../Ship-Balance-Changes.md) would meaningfully alter any battle on this page. That is an argument for the conclusion already reached there — that the roster does not need broad tuning — but for a different reason than the one recorded. - **The real high-PR levers are structural**: the 10-stack cap, flank target selection, and whether stack ordering should be visible or manipulable. - **Random compositions understate engineered play.** Every simulation in these files samples 6 random hulls at equal PR share. Real high-PR fleets are 10 deliberately-sized stacks. The simulated race tables measure roster depth, not what good players do with it. - **A "1×-flattened" fleet is a real strategy** and nothing in the analysis models it. Worth simulating directly. --- ## 5a. How much is chance? Measured Re-running the same real fleets 200 times through the reference engine (the only RNG is flank target choice): | Battle | PR ratio | Wins / 200 | Attacker PR lost: best → median → worst | **Swing** | |---|---|---|---|---| | SKM vs Teerak | 0.98 | 200 (100%) | 72.2M → 72.4M → 75.7M | 3.5M (1.3%) | | **NotDrLatBC vs DoE** | 1.48 | **91 (46%)** | 50.9M → 68.5M → 87.1M | **36.2M (23%)** | | Teaspoon vs DoE | 0.76 | 200 (100%) | 41.9M → 54.8M → 64.9M | 23.0M (15%) | **NotDrLatBC vs DoE is a coin flip.** Identical fleets, identical PR, and the outcome swings on which stacks the RNG picks — 36.2M PR, 23% of the attacking fleet, between the lucky and unlucky end. The variance is not uniform, and the cause is instructive: - **Teerak's five one-ship dummies died instantly**, leaving almost no live targets to choose between. Few targets, little RNG — swing 1.3%. - **DoE's ten PR-flattened stacks all survived into the choice**, giving the flank RNG a wide menu every time. Many targets, high RNG — swing 23%. **Flattening a fleet increases variance.** It denies the opponent a favourable pairing, but it also hands the dice more to decide. A dummy-heavy tail does the reverse: it is more deterministic, because the tail evaporates before choices matter. That is a genuine strategic trade neither my metrics nor the race tables model, and it is measurable: point estimates are the wrong output for a high-PR matchup. `eye-of-sauron` defaults to 1,000 iterations for exactly this reason. --- ## 6. Open questions 1. **Is stack order visible to the opponent before committing?** The entire positioning game depends on the answer, and it is not addressed anywhere in these files. 2. **Does flattening beat tiering?** Unresolved on win rate — DestroyerOfEmpires flattens and lost both battles shown, but both against larger fleets. What §5a *does* establish is that flattening raises variance sharply, so the question is partly "how much risk is the flattening player buying?". 3. ~~How much does wave-2 RNG actually swing outcomes?~~ **Answered — §5a.** Up to 23% of the attacking fleet, and one sampled battle is a 46% coin flip. 4. **Does the 5.0M-stack convention reflect a known breakpoint?** SKM's seven identical stacks look like a learned heuristic rather than a coincidence.