I’m not sure how you came up with that conclusion but that’s incorrect and Dante00 is correct. Although numbers still need adjusting.
The non-ancient item on its own needs compensate (13 x 750% + 100%) / (12 x 750% + 375% + 100%) = 3.96% worth of damage. Remember that lot of damage modfiers are multiplicative. So if the non-ancient item gives more than 3.96% additional damage, it is better option than using ancient.
Using non-ancient item does not mean net loss of 371% of damage. The net loss is 3.96%.