Lift Ratio

The lift ratio tells us how many times more / less Goods A and B occur together than we'd expect, assuming independence.

A lift ratio can equal...

• Lift Ratio = 1.00 ➡️ The goods are purchased together as much as we'd expect, assuming independence.
• Lift Ratio > 1.00 ➡️ The goods are purchased together more than expected, assuming independence.
• Lift Ratio < 1.00 ➡️ The goods are purchased together less than expected, assuming independence.

It's a "level-up" from Support and Confidence, as it incorporates assumed independence of the goods.

Scenario: Your online drop-shipping store has 100 transactions. Out of all transactions, 50 of them include a hoodie and 15 of them include a hat. Of the hoodie transactions, 10 of them include a hat. Find the lift ratio for "Hoodie ➡ Hat".

Lift Ratio(A ➡ B) = Confidence(A ➡ B) / Benchmark Confidence(B)

Confidence(Hoodie ➡ Hat) = Transactions with Hoodie & Hat / Transactions with Hoodie
Confidence(Hoodie ➡ Hat) = 10 / 50
Confidence(Hoodie ➡ Hat) = 0.20

Benchmark Confidence(Hat) = Transactions with Hat / All Transactions
Benchmark Confidence(Hat) = 15 / 100
Benchmark Confidence(Hat) = 0.15

Lift Ratio(Hoodie ➡ Hat) = 0.20 / 0.15
Lift Ratio(Hoodie ➡ Hat) = 1.33

Answer: Given a hoodie is in the basket, a hat being purchased as well is 1.33 times more likely than if purchasing a hat was independent of purchasing a hoodie.

In other words... hats being purchased with hoodie orders is occurring 1.33 times more than we would've assumed (given the two goods are independent)!

If the Lift Ratio is above 1.00, it suggests there is an association.

The higher it is, the stronger the association!

Scenario: You run an online drop-shipping store and find a lift ratio for "Hoodie ➡ Hat" of 1.33. Is there an association between hoodies and hats?

Answer: Since our lift ratio for "Hoodie ➡ Hat" of 1.33 is above 1.00, this suggests that hats occur in hoodie transactions 1.33 times more than they would if they were independent. In other words... there's an association!

If the Lift Ratio is below 1.00, it suggests there is NOT an association.

The lower it is, the weaker the association!

Scenario: You run an online drop-shipping store and find a lift ratio for "Hoodie ➡ Hat" of 0.45. Is there an association between hoodies and hats?

Answer: Since our lift ratio for "Hoodie ➡ Hat" of 0.45 is below 1.00, this suggests that hats occur in hoodie transactions 0.45 times less than they would if they were independent. In other words... there's a lack of association!