MongoDB Aggregation - return default value for documents that don't match query - mongodb

Question

I'm having trouble figuring out the right aggregation pipe operations to return the results I need.
I have a collection similar to the following :-
{
"_id" : "writer1",
"Name" : "writer1",
"Website" : "website1",
"Reviews" : [
{
"Film" : {
"Name" : "Jurassic Park",
"Genre" : "Action"
},
"Score" : 4
},
{
"Technology" : {
"Name" : "Mad Max",
"Genre" : "Action"
},
"Score" : 5
}
]
}
{
"_id" : "writer2",
"Name" : "writer2",
"Website" : "website1",
"Reviews" : [
{
"Technology" : {
"Name" : "Mad Max",
"Genre" : "Action"
},
"Score" : 5
}
]
}
And this is my aggregation so far : -
db.writers.aggregate([
{ "$unwind" : "$Reviews" },
{ "$match" : { "Reviews.Film.Name" : "Jurassic Park" } },
{ "$group" : { "_id" : "$Website" , "score" : { "$avg" : "$Reviews.Score" },
writers :{ $push: { name:"$Name", score:"$Reviews.Score" } }
}}
])
This returns only writers who have a review of the matching film and also only websites that have at least 1 writer who has reviewed the film,
however, I need to return all websites containing a list of their all writers, with a score of 0 if they haven't written a review for the specified film.
so, I am currently getting : -
{ "_id" : "website1", "score" : 4, "writers" : [ { "name" : "writer1", "score" : 4 } ] }
When I actually need : -
{ "_id" : "website1", "score" : 2, "writers" : [ { "name" : "writer1", "score" : 4 },{ "name" :"writer2", "score" : 0 } ] }
Can anyone point me in the right direction?
Cheers