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4441 8 HCP

The average 8 HCL hands should not invite game. A few excellent 8 HCL hands can invite game. If you are in imp and vulerable some situation should always invite game. Also remember in general your chance of making a NT game is about 20% less then any game in this type of hands. If there is no chance for a major game you are better off not invite game.  The more chance you have in a major game the more likely you should invite game. I'll let you decide what to do by just present you with the following data.

16+ HCL NT opening hand (normal hand which accepts game)

8 HCL no 5 card suit (8 HCP) A good hand can invite. (or imp scoring vul ) goto 4441 link for more detail

North south cannot make any contract = 0.05% East West cannot make any contract = 48.61%
North south make partial contract = 50.74% East West make partial contract = 50.42%
North south make any game = 48.55% East West make any game = 0.95%
North south make any small slam = 0.66% East West make any small slam = 0.02%
North south make any grand slam = 0.00% East West make any grand slam = 0.00%

8 HCL 5 card suit (7 HCP) not that good

North south cannot make any contract = 0.12% East West cannot make any contract = 30.76%
North south make partial contract = 58.33% East West make partial contract = 65.55%
North south make any game = 40.47% East West make any game = 3.63%
North south make any small slam = 0.97% East West make any small slam = 0.06%
North south make any grand slam = 0.10% East West make any grand slam = 0.00%

8 HCL 6 card suit (6 HCP) not that good

North south cannot make any contract = 0.11% East West cannot make any contract = 13.09%
North south make partial contract = 55.94% East West make partial contract = 78.76%
North south make any game = 41.50% East West make any game = 7.99%
North south make any small slam = 2.22% East West make any small slam = 0.16%
North south make any grand slam = 0.23% East West make any grand slam = 0.00%