People sharing some slightly wrong/incomplete numbers here so I just want to correct them for anyone reading…
Shrine average gems = 225
We get roughly 16 a year = ~3600 gems
Gems per month from free play = 408
Therefore free gems per year = 3600 + 408 * 12 = ~8500 gems
There’s also the anniversary each year which gives us an extra generous login and bigger fortune shrine, plus typically January has a special PvP season with bonus gems. That probably makes the grand total something like 9000 gems.
Full breakdown of gems from free play (per month):
112 from PvP [60 + (67-20) + ~5]
25 from PvP daily gem
11 from Biweekly [5 / 14 * 30.5]
17 from SCB [4 / 7 * 30.5]
61 from Daily missions [2 * 30.5]
13 from Standard login bonus [12 / 28 * 30.5]
6 from Cumulative login bonus [20 / 100 * 30.5]
44 from Featured monster login bonus [10 / 7 * 30.5] - these seem to be regular now
64 from Limited-time events [4 * 16] - varies each month so a simplification here, balancion’s is 10 gems and comes regularly while others are 16-20, ST 33 and UC 55-60.
30 from MBQ [~1.5 * legendary MBQ]
25 from Event achievements [SCB+biweekly+crown+moalith+limited events]
I don’t think I missed anything, but let me know if I did! Obviously this is assuming you complete everything.