Finding the Best Dog Treat with Statistics
Key takeaways
- Bebop, my 83lb, 33 inch tall, Greyhound, loves three things: running fast, following me around the house, and treats.
- Fortunately for Bebop’s palate, the Bradley-Terry model gives us a way to figure out a “strength” of treat from pairwise comparisons.
- Equivalently, if we write each strength as an exponential score,
Bebop, my 83lb, 33 inch tall, Greyhound, loves three things: running fast, following me around the house, and treats. Whether it’s a chew treat, pizza out of a child’s hand who strayed too far from a party, or a small tray of cat food, he has a nose for what he likes and the athleticism to give him a fair shot at getting it. I’ve watched him eat for years, so it was upsetting to realize I don’t know what his favorite snack is, and can’t easily ask him.
Fortunately for Bebop’s palate, the Bradley-Terry model gives us a way to figure out a “strength” of treat from pairwise comparisons. The model assigns each competitor (or treat) (i) a positive strength score pi. Given two competitors i and j, the probability that i beats j is:
Equivalently, if we write each strength as an exponential score,