5v5 matches
number of heroes in the pool = K
dimension of the embedding = E
 - encode a hero as a one-hot of heroes = 1-of-K
 - learn a (K, E) matrix to go from hero -> vector (+ bias)
   (notice that it can do set-of-heroes -> vector too)
 - learn a logistic regression from both the embeddings of team1 and team2 to predict the winner by backprop through the embedding.
 - do stats and t-SNE plots of embeddings of single heroes or combinations (teams) of heroes
 - ...
 - PROFIT!!!
 - /!\ may not work /!\

in Torch(~like):

K = 42 -- number of heroes
E = 50
emb = nn.SparseLinear(K,E)
model = nn.Sequential():add(nn.ParallelTable():add(emb):add(emb)):add(nn.JoinTable(1)):add(nn.Linear(2*E,1)):add(nn.Sigmoid())
criterion = nn.BCECriterion()

for game in games() do
  team1, team2, result = game.get_teams() -- team1 and team2 are both 5-of-K vectors, result is 0 or 1 (first or second team)
  -- be sure to randomize team1/team2 as radiants/dire sides, otherwise it'll learn the side bias too ;-)
  error = criterion:forward(model:forward({team1, team2}))
  grad = criterion:backward(model.output, result)
  model:zeroGradParameters()
  model:backward({team1, team2}, grad)
  model:updateParameters(learning_rate)
end