Comparative histograms

After a solution passes validation, the game computes several independent metrics that trade off against each other and shows the player's value on each as a marker on a histogram of all players' (or friends') values for that puzzle. State owned: per-puzzle score distributions aggregated on a server, plus the player's best per metric. Update rule: on completion, simulate the solution, compute metrics, upload them, and fetch the current distributions. The metrics come from a design-evaluation mechanic; this mechanic owns only the population comparison. Canonical forms are Zachtronics games: SpaceChem ranks instructions, cycles, and reactors, and Zach Barth designed its global histograms so players could check a solution without being overwhelmed by the top players a leaderboard lists; Opus Magnum compares cost, cycles, and area; TIS-100, Shenzhen I/O, Infinifactory, and Exapunks use the same pattern.

Instead of a rank, the player sees where they sit in a crowd on each axis. A solution that is slow but cheap still feels good, and a visible tail of better scores invites returning to a solved puzzle to shave cycles. Comparison is social but low in intimidation.

• number of metrics and how strongly they trade off against each other
• global distribution versus friends-only comparison
• bin width and handling of outliers or exploit scores
• per-metric personal bests versus recognition of Pareto-optimal combinations
• whether any reward is attached to good scores (Zachtronics deliberately attaches none)

• Metrics that do not trade off collapse into one dominant solution, and the histograms show a single spike.
• Exploit or bugged solutions create impossible scores that distort the left tail.
• Late puzzles are attempted only by skilled survivors, so average players appear below median on every metric.
• Independent per-metric bars ignore balanced solutions; Opus Magnum players invented an unofficial sum metric to score them.

• Players replay solved puzzles to move their marker, extending content life without new content.
• Communities build external record trackers for Pareto frontiers that the in-game histograms do not show.
• Friend comparison produces asynchronous rivalry without direct competition.

• Can distributions seeded by automated solvers before launch give useful comparison targets without discouraging human players?
• Does showing a Pareto frontier instead of per-metric histograms change which tradeoffs players explore?