When I did the math, as long as you’re confident you can hit tier 20 where you’re awarded 300 gems, then you break even.
Valor Pass = $10 for 300 gems + 1 EHT to start = at least 560 gems in value
Tier 3 awards ETT = 160 gems at least
Tier 4 awards 100 gems
Tier 7 awards EHT = 260 gems at least
Tier 8 awards WE flask = 100 gems
Tier 15 awards 100 Atlantis coins = 280 gems at least
Tier 17 awards Raid flask = 100 gems
Tier 19 awards 10 challenge coins = 260 gems at least
Tier 20 awards 300 gems
Total: 2120 gems in value if you purchase the Valor pass. Using the most favorable valuation of half a cent per gem (from the Atlantis gem deals), that still comes out to $10.60 in value, which has already surpassed the $10 you paid for the Valor pass.
Not to mention this calculation uses the most favorable gem values for each level (e.g. using the discounted gem value for 10 pulls or 30 Atlantis pulls and applying that to a single pull, which is pricier), and also values the gems based on the most favorable deal possible. Plus all the extra food/iron bundles, loot tickets, trainer heroes, and 15 barbarian emblems you get along the way to tier 20 is certainly worth something too (I just can’t put a gem value on them).
tl;dr As long as you’re confident you can hit tier 20, the Valor pass will already have paid for itself.