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I know the run rate is calculated by dividing the number of runs scored by number of overs.

How do I calculate the run rate midway through an over? If say a team scores 223 runs in 43.5 overs, what would the run rate be?

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Run rate is calculated for how many runs are scored in an over i.e. how many runs per six balls. So you just need to convert completed overs in balls. Then calculate the run rate with respect to six balls.

So in the above example completed balls is 43 X 6 = 258 + 5 balls. So total completed balls is 263. So now calculate with respect to six balls. So if 223 runs in 263 balls then how many runs in 6 balls? So 223 X 6 / 263 = 5.087 runs per over.

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