Queen-death heatmap — method and figures

Inputs, transformations, and outputs. Each figure’s caption states only what was computed.

Contents

• 1. Data
• 2. Cross-map figures
• 3. Night-map figures
• 4. Wall-respecting diffusion

1 · Data

For each game in the quality-filtered set we walk the playerKill events and keep (killer_x, killer_y, killer_pid, killed_pid, killed_category) plus the game’s map index, quality rank, and gold_on_left flag. Positions are mirrored to a canonical gold-on-left frame; y is flipped from Cartesian (game) to pixel coordinates so it matches the screenshot.

Every quality-filtered game is included — 182,447 games in total (49,147 day, 50,943 night, 47,427 dusk, 34,891 twilight), 6,096,016 kill events, 650,988 of them queen deaths. Where applicable, both sides of a map are mirror-folded onto the gold half via x' = min(x, 1920 - x), doubling effective sample density in the visible area.

2 · Cross-map figures

Wall-respecting diffusion (σ=24 px; algorithm in §4) run on each map independently with a per-map empirical mask. Densities are divided by the number of games sampled in that map so peaks are comparable across maps.

Peak density: maximum cell value of the per-game density. Concentration ratio: peak divided by the mean over playable cells in that map.

3 · Night-map figures

3.1 · Density

3.2 · Local D/K deviation

For each cell, two diffusion-smoothed densities: D = density of queen-deaths (rows where killed_cat == "Queen"; 180,136 events); K = density of kills by queens (rows where killer_pid ∈ {1, 2}; 701,574 events). Plot log₁₀(D/K) minus the global value log₁₀(ΣD / ΣK). Cells with low combined signal (D+K below the 20th percentile of the playable region) are masked out.

3.3 · Death by killer type

Queen-death rows partitioned by killer: killer_pid ∈ {1, 2} → killer is the enemy queen; killer_pid ≥ 3 → killer is a worker, which must be a winged soldier to have killed the queen. In the full night dataset, 53.7% are by enemy queen (96,739 events) and 46.3% by enemy soldier (83,397 events).

The two densities recombined as a balance map: log₁₀(Dₛₒₗₙᵢₑₐ / Dₑᴴᴴᴱₑₙ) minus its global value log₁₀(ΣDₛₒₗ / ΣDₑᴴᴴᴱₑₙ) = −0.06:

4 · Wall-respecting diffusion

Kill positions are smoothed on a 2 px-per-cell grid using discrete Jacobi diffusion, with the playable region acting as a no-flux domain so density never crosses solid map geometry.

1. Histogram. Build the per-cell kill count H by 2D-binning the event positions on the grid.
2. Playable mask. Smooth the histogram of all kills (not just queen deaths) with a small Gaussian (σ=2 cells) and threshold to obtain a binary mask M. Cells where some kill ever landed count as playable; the rest are walls. No manual segmentation.
3. Initialise. f ← H · M; mass on wall cells is zeroed.
4. Iterate. For each cell c ∈ M, f(c) ← (1 - α) f(c) + α · meann ∈ N(c) ∩ M f(n) with α=0.2 over the four orthogonal neighbours. Wall cells stay at zero; their absence from the neighbour set is the no-flux boundary condition.
5. Stop. After T iterations the variance per axis is approximately α·T cells², so we run T = round(σ²/α) iterations to hit a target bandwidth. With cell size = 2 px and target σ = 24 px, that’s T = round(12²/0.2) = 720 iterations.

The result is rendered as an alpha-modulated overlay on the map screenshot: alpha = 0.92 · progress^0.55 where progress = norm(density) clipped to [0,1] and forced to zero on cells with no density, so low-density cells let the map sprite show through and high-density cells render opaque.