# Elo ranking for attack and defence seperately

I want to create a simple statistical model for the bowler versus batsman contest in a game of cricket (it's similar to pitcher versus batter in baseball). Let's say the simple the model is this:

One bowler bowls one ball to one batsman. There are 3 possible outcomes:

• The batsman is out and scores 0 runs
• The batsman is not out and scores 0 runs
• The batsman is not out and scores 1 or more runs

My goal is to is calculate the likelihood of each outcome based on exactly who the batsman is and who the bowler is. To do this I have a very large data set of balls bowled from real cricket matches.

In another question a helpful comment suggested Elo rankings for the players would be a good approach to achieve this. I initially planned to score the three possible outcomes in a similar way to how win/draws/losses are scored by Elo rankings in Chess. However, I then thought that perhaps instead of thinking of a single event with three outcomes it might be better to think of it as two events each with two outcomes:

Event 1

• The batsman is out
• The batsman is not out

Event 2

• The batsman scores 0 runs
• The batsman scores 1 or more runs

Then I might calculate 2 separate Elo rankings for each player - one based on the contest between the bowler and batsman to get the batsmen out, and another based on the contest between the bowler to limit the scoring of runs and the batsman to score as many runs as possible.

My question is whether I will be able to achieve my goal using this approach? Or is there some better way?

Intuitively, based on my knowledge of cricket, it does seems to make sense to have two ratings rather than one. This is because players are not simply considered to be weak or strong but are also categorized by how they approach the game. Considering batsmen for example:

• Some are easy to get out and also score runs at a low rate (they just aren't very good)
• Some are aggressive and score runs at a high rate but as they take a lot of risks they get out quickly
• Some are defensive and score runs at a low rate but because they don't take risks they are difficult to get out
• Some are difficult to get out but are also able to score runs quickly (only the best players can do this)