Specifically, in cell H2, you want to create a drop-down list of all the nations listed in column B, and in cells I2 and J2, display the player names and average score, respectively, according to ...

For this reason, I'll check "First Column" and uncheck "Header Row" in the Table Design tab. Likewise, if you have a header row and no header columns, make sure Word is aware of this at this stage.