In my estimation, a player should get around 6-7 horns in average per day (without gemming for additional chance to get Gold/Iron/Wooden key reward).
So if a season lasts for 56 days (8 weeks) then in average a player should only get around 336-392 horns.
Assuming the player can also enter 2 PvP tourneys (open & restricted) consistently each week (for 8 weeks), the player will get additional 6 x 2 x 8 = 96 horns.
(It’s safe to assume that an average player will be unable to enter elite tourney consistently for 8 weeks in a row and the most realistic target at the moment for average player is to obtain 5 weapons with different colors)
In total a player should get around 432-488 horns per season.
Since one battle pass tier requires 30 horns, then a player should be able to reach tier 14-16 of the battle pass for free.
Using these assumptions, if you want to purchase a Battle Pass, you’ll need to spend:
500 crowns = USD 10 for purchasing the battle pass itself.
150 gems (each tier can be bought with 150 gems) x 14-16 remaining tiers = 2100-2400 gems.
(In my personal opinion, it’s cheaper if you just gemming the remaining tiers, rather than gemming the daily bounties)
My reasoning: If you buy a battle pass, most likely you’ve purchased the VIP pass too - since VIP pass is the more rewarding one between the two so I don’t think you’ll be so desperate to get extra keys from Daily Bounties anyway.
However bear in mind too that when you complete a Battle Pass up to tier 30, you’ll get 6 x (200+50) gems reward along the road so you’ll get 1500 gems back.
So basically if you purchase a Battle Pass with my assumptions above, in net you’ll need to spend:
10 USD for the Premium Battle Pass
600-900 gems net for reaching tier 30. (less than 10 USD if you need crowns to get the gems)
It’s just my own calculation on the Battle Pass thingy.
I know that the actual number will vary by a lot between players.
I don’t count the gems from PVP score & rank rewards too.
It’s expensive in my opinion since the only valuable item that cannot be obtained easily elsewhere at the moment is the legendary flux and rare flux (to some extent) - maybe they will drop from chests but I haven’t got one myself)
Most likely later, events in game will give us more horns so that we don’t need to use gems to get to tier 30 so that at least we can get the free side of the battle pass rewards for free - though they are actually quite awful.