Bias and Variance in Darts
Variance and bias are fundamental concepts in statistics. This interactive application demonstrates how the concepts apply in a dartboard setting, both over single games and over many games.
- Bias is the distance and direction of a player's aim point from the bullseye. A biased but consistent player hits the same wrong spot every time.
- Variance is how much each throw scatters around that aim point. An unbiased but inconsistent player aims at the bullseye yet hits everywhere around it.
One game is 10 throws per player, and each game is won by the player with the higher total. Scoring depends only on where the dart lands relative to the center: 50 points in the bull, then 25, 15, 10, and 5 in the outer bands; a dart off the board scores nothing.
How to use the tool:
- Input: configure the bias and variance of the two players.
- Actions: throw darts, either a single dart, the remaining darts of the current game, or 1,000 games in one go.
- Output: see where every dart lands on the board, and the summary statistics for each player.
The application works best on desktop.
The application
Input
Actions
Output
Figure 1: Dartboard
Table 1: Player statistics
| Player | Darts | Points | Games won | Est. bias (mm) | Est. σ (mm) |
|---|
The estimated bias and spread summarize all throws so far. Each round of 10 darts is won by the player with the higher total.
Questions for consideration
| # | Question | What to look for | Suggested values |
|---|---|---|---|
| 1 | Is a player with low bias but very high variance more likely to win in the long term? | Try 1 game, then 1,000. Compare short-run luck against the long-run "Games won" tally. | |
| 2 | Can you detect a small bias, or does variance hide it? | Compare the estimated bias after 10 darts; then simulate 1,000 games and compare again. |