[{"_id":1,"submissions":[1,2,3,4]},{"_id":2,"submissions":[1,2,3,4,5,6,7,8]},{"_id":3,"submissions":[1,2,3,7,8,9]}]

db.collection.aggregate([{$addFields:{totalSubmissions:{$size:"$submissions"}}},{$sort:{totalSubmissions:-1}},{$limit:1}])