Rating Cricketers: Thoughts On A Simple Model

One way to rate cricketers is to measure them on their contribution to winning, or not losing, a match. A team’s chance of winning a match can be modelled as a function of the following factors:

- how many runs the team scores
- how many runs the other team scores
- how many wickets the team loses
- how many wickets the other team loses

And because of the time constraint on a cricket match, whether it is a Test or first-class match to be completed in a given number of days or a match with limited overs, these factors matter as well:

- how quickly the team scores runs
- how quickly the other team scores runs

According to this view, a cricketer’s contribution to the result of the match will depend on their contribution to each of these factors. In terms of bowling, a cricketer’s contribution will depend upon:

- how many wickets the cricketer takes
- how quickly the cricketer takes wickets (i.e. the cricketer’s bowling strike rate)
- how many runs the cricketer concedes from their bowling
- how quickly runs are scored from the cricketer’s bowling (i.e. the cricketer’s economy rate)

What would need to be done to measure the cricketer’s contribution in terms of bowling is to determine how each of these factors affects the team’s chance of winning. For example, each wicket a team takes could increase its chance of winning by, say, 0.5 per cent. A bowler who took 10 wickets in a match would therefore have increased their team’s chance of winning by 5 per cent. As another example, each run a team concedes may decrease its chance of winning by, say, 0.05 per cent. A bowler who concedes 100 runs in a match then would therefore have decreased their team’s chance of winning by 5 per cent.

In terms of batting, a cricketer’s contribution to the result of the match will depend upon:

- how many runs the cricketer scores
- how quickly the cricketer scores runs (i.e. the cricketer’s batting strike rate)
- whether the cricketer loses their wicket
- how long the cricketer can stay in before losing their wicket

And similarly to bowling, what would need to be done to measure the cricketer’s contribution in terms of batting is to determine how each of these factors affects the team’s chance of winning. For example, each run a team makes could increase its chance of winning by, say, 0.05 per cent. A batsman who makes 100 runs in a match would therefore have increased their team’s chance of winning by 5 per cent.

It would be interesting to estimate how important each of these factors is to the result of a cricket match, and how we might reassess the contribution of cricketers in light of them. One concern with this simple model is how to capture the contribution of fieldsmen. All thoughts and comments welcome.