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Thus, there's a mix-match of reasons why Tommies turned out to be this way:
- Mills Bombs being completely useless on the live version of the unit (and even if you made them cheap, they would never be researched (moving accuracy)
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- Tommies being completely helpless when fighting anything other than infantry (moving accuracy)
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- Bren guns being too RNG with the occasional 12 second reload time, making an AI-mostly squad completely unreliable (Bren reload time normalization)
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I am not sure if Tommie's moving accuracy has the affects you describe since as far as I know Piats, bren and grenades require unit to be stationary to fire.
In addition since brens do not fire on the move they will probably not reload out of cover unless ordered to stop and shoot out of cover.