Can a wildshaped druid deal static attack damage?

Question

If, for example, I wildshape into a boar, can I use Tusk to reliably deal 4 damage, rather than rolling 1d6 + 1 damage?

Is this one of the effects of:

Your game Statistics [being] replaced by the Statistics of the beast

Answer 1

Taking the average damage instead of rolling is an option presented to the DM in the Monster Manual.

We see in the introduction to the Monster Manual:

You have the option of taking average damage or rolling the damage; for this reason, both the average damage and the die expression are presented.

The Monster Manual is explicitly written to be a DM-facing source:

The Monster Manual is one of three books that form the foundation of the Dungeons & Dragons game, the other two being the Player’s Handbook and the Dungeon Master’s Guide. The Monster Manual, like the Dungeon Master’s Guide, is a book for DMs. Use it to populate your D&D adventures with pesky goblins, stinky troglodytes, savage orcs, mighty dragons, and a veritable horde of creepy crawlies.

So the option for taking the average is for DMs. As a player, you use the rules from the Player's Handbook when making your attacks, even when Wild Shaped into a beast:

On a hit, you roll damage, unless the particular attack has rules that specify otherwise.

The Boar's tusk attack does not have rules the specify otherwise. The Monster Manual has an optional rule that the DM may generally apply to all, some, or none of the attacks they make with NPCs, but there is not specific rule in the particular attack that allow you to do anything other than roll the damage dice.