Display number of posts in category for current year

I’ve spent a couple of hours trying to figure out how to do this but I’m really struggling so I hope someone can help me on here. I basically want to display (in the sidebar on every page) the number of posts in a particular category for the current year (categoery ID is 13, name is Call Outs). I found this bit of code:

<div>
Call outs this year:
  <?php
    $category = get_the_category();
    echo $category[0]->category_count;
  ?>
</div>

I assumed that if I changed the [0] to 13 then it would display the number of posts in that category, but that’s not the case. Can anyone help? It seems like such a simple thing but it’s doing my head in!