Need combined average over multiple years using Vlookup or averageif?

[samst]

My Data basically looks like the table below...

I'm trying to figure out a formula that will look up the letter in Sheet 2 find the corresponding letter in Sheet 1 and then determine the average of the 2017 and 2018 corresponding month.

For example
For the letter A the formula should return the value 75.1 and for the letter B the value should be 959.5



Sheet 1
2017 2018
1/9/2017 1/16/2017 1/23/2017 1/30/2017 2/6/2017 1/2/2018 1/9/2018 1/16/2018 1/23/2018 1/30/2018
A 12 161 33 53 68 42 98 123 81 73
B 117 1108 1140 1145 1048 1192 957 896 1121 1389
C 12 73 71 61 87 82 89 86 80 71
D 12 138 99 59 72 93 87 119 95 104
E 3 6 4 4 5 23 44 85 15
F 736 6030 3248 3203 3748 2646 3630 3019 3147 1909
G 216 1523 995 690 784 472 612 633 835 415

Sheet 2

A Jan Need combined average of Jan 2017 and 2018
B Jan Need combined average of Jan 2017 and 2018
C Feb Need combined average of Feb 2017 and 2018
D Feb Need combined average of Feb 2017 and 2018
E Feb Need combined average of Feb 2017 and 2018
F Feb Need combined average of Feb 2017 and 2018
G Feb Need combined average of Feb 2017 and 2018