I have a dataframe dfof football matches and corresponding mean scoring rates for each team. The first 2 columns are Home and Away teams, the 3rd and 4th columns are mean scoring rates for Home and Away teams respectively. For example:

       Home      Away HomeRate AwayRate
1   Arsenal   Bristol      1.3      1.3
2   Chelsea Newcastle      2.4      2.3
3 Liverpool     Leeds      3.3      1.7
4    Bolton    Fulham      2.1      2.5

I want to generate 3 new columns, “HomeWin”, “Draw”, “AwayWin” giving Poisson probabilities of home win, draw, away win respectively for each match and add these columns to my dataframe. I assume events are independent.

I can do this manually for each individual match separately. But I don’t know how to do this all at once for the whole table.
Take for instance 2nd row (Chelsea vs Newcastle). I can create a probability matrix consisting of probabilities for each respective scoreline between Chelsea and Newcastle (0-0, 0-1 0-2, etc):

H <- c(dpois(0:20, df[2,3]), ppois(20, df[2,3], lower.tail=FALSE))
A <- c(dpois(0:20, df[2,4]), ppois(20, df[2,3], lower.tail=FALSE))
ProbMatrix = outer(H, A)

In the above block, df[2,3] is Chelsea mean score rate, df[2,4] is Newcastle mean score rate and I am assuming max number of possible goals scored for each side is 20 (hence I am using dpois(0:20) and ppois(20) in the above, to get the total sum of probabilities as close to 1 as possible.

Then I can simply sum over various elements of the matrix above to generate Home, Away and Draw win probabilities:

Prob_Home_Win = sum(ProbMatrix[lower.tri(ProbMatrix)])
Prob_Away_Win = sum(ProbMatrix[upper.tri(ProbMatrix)])
Prob_Draw = sum(diag(ProbMatrix))

But how can I generate efficiently the whole HomeWin, AwayWin and Draw columns yielding the probabilities for each match in df ?