Does Vex cheerless reduction effect pay Deflect costs?

Yes, Vex, Cheerless can reduce the cost of Deflect.

According to RiftJudge FAQ #10609, #10442, and #8596, this interaction works because of the order of cost calculation established in Rule 356.4:

1. Deflect is a mandatory additional cost (Rule 809.1.d) that is added to the spell's total cost during the cost-finalization process.
2. Vex, Cheerless applies a discount to the total cost of the spell.
3. Because the Deflect cost is included in the total cost before discounts are applied, Vex, Cheerless's discount effectively offsets the Deflect cost.

Key Considerations:

• Order of Operations: Per Rule 356.4, you determine the base cost, add mandatory costs (like Deflect), and then apply discounts (like Vex, Cheerless).
• Minimum Energy: Vex's "minimum 1 Energy" restriction applies only to the spell's base cost, not the total cost including additional costs. Consequently, Vex, Cheerless can reduce the final cost (including Deflect) below what would otherwise be the minimum for that spell.
• Mandatory vs. Optional: This only works because Deflect is a mandatory additional cost. If you were dealing with an optional additional cost, the interaction would depend on the specific card's rules (as seen with Ezreal in FAQ #9237).