IA idea · Games & puzzles
How many attempts until the rare item? Drop rates and pity systems
Research question
For a game with a published drop rate p, how many attempts are needed on average and in the unluckiest 10% of cases, and how does a “pity” guarantee after N attempts change the expected cost?
Adapt it: change the place, the data or the comparison until the question is yours.
Why it makes a good exploration
Many games publish drop rates; few players understand what they imply. The geometric distribution answers “how many tries?” and pity systems give a modified distribution worth analysing — with clear consumer implications.
The mathematics you'll need
- Geometric distribution: mean, variance, percentiles
- Cumulative probability and logarithms
- Truncated distributions with a pity rule
- Expected cost
Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.
Where the data comes from
Use a game's published drop rates; optionally record your own attempts.
- Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.
Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.
A possible outline
- Explain the geometric model and independence.
- Compute mean, median and 90th percentile.
- Add a pity rule and recompute.
- Compare expected cost with and without pity.
- Reflect on regulation and player psychology.
Pitfalls that cost marks
- Assuming the published rate without checking your data.
- Confusing mean and median.
- Ignoring independence assumptions.
Showing personal engagement
- Use a game you play.
- Test the published rate with your own records.
- Discuss whether loot boxes are gambling.
See Criterion C: personal engagement for what examiners look for.
Taking it further
Model a soft pity system where the probability rises after each failure.