Relative Runs Explained

Relative Runs^© (as well as the associated stats below) offers a novel approach to expressing statistics in cricket. It seeks to capture a complicated issue simply. Namely, Relative Runs aims to provide a simple, transparent, numerical vehicle through which to express the value of a player’ contributions in a cricket match, be that a batter or bowler.

Whereas standard cricket statistics (e.g. runs, wickets, strike rate & economy) are absolute in nature, Relative Runs offers a way to capture the relative contribution of players.

This is something we do instinctively when we talk about cricket matches. We frame the performances of players within the story of the match to give them added depth and complexity, to convey value. Relative Runs provides a neat, numerical route to this same end.

So how does it work?

It’s pretty simple. Instead of runs being expressed as a raw score, the are expressed relative to a par score in the innings concerned. Take the total of an innings, minus extras, divide it by the number of batters that appeared in the innings and then you have the Par score. The Relative Runs (RR) are equal to a batter’s runs (their real score) minus the Par.

RR = runs-Par, where Par = (total-extras)/batters

Let’s take an example. Say in a T20 innings, a team scores 220, where 20 runs were extras, and eight batters appeared at the crease in the innings. The Par score for that innings would be: (220-20)/8 = 25.

This is to say, the average contribution of a batter was 25 runs. Let’s say one opener got a duck, his Relative Runs will be -25. The first drop, however, scored an impressive century. Imagine he scored 120. His RR is (+)95.

To put it another way, the opener was 25 runs under par, while the first drop was 95 runs over par. RR thus gives us a very clean way of notating the over- or under-performance of the batters. At it’s core, this is the job RR is doing – we are quantifying over- and under-performance in the game.

One logical consequence of RR are other stats that follow the same idea. A similar thing can be done for strike rate (SR): Create a par strike rate ((total-extras/balls faced)*100), minus it from a player’s SR and then you have their Relative Strike Rate (RSr).

The same logic applies to bowlers’ economy rates. Take the innings run rate, minus it from a bowlers economy and you have their Relative Economy (REc).

You might be wondering why I’ve chosen to derive RR (and the other stats) from just a single innings and not all innings across a match. This is simply because innings across a match can be very different – teams are facing different bowling attacks, at different times, on different states of pitch. The truest demonstration of relative contribution, I believe, is compared with teammates in the same innings.

What about wickets? Well, you could do the same thing to determine the relative amount of wickets a bowler takes in an innings. However, there is one key difference between wickets and runs-associated stats in cricket. Whereas any amount of runs can theoretically be scored in an innings, only 10 wickets can ever be taken by a bowling side in an innings.

Because of that absolute maximum, the relative contribution of a bowler in terms of wickets, is information we can glean just from glancing at a bowling analysis. If a bowler has taken three wickets, they have 30 per cent of the total possible wickets. If there were only three wickets taken in the innings, they have 100 per cent of them. This less nuanced than runs-related stats and virtually self-evident.

Why is this important or interesting?

Well, it might not be interesting to everyone but there is a persistent problem with the absolute nature of cricket stats. With the huge variance in conditions and scores in cricket, there is no in-built way to measure, for example, one century against another. Two tons, scored in vastly different conditions, against different bowling attacks, in two very different totals, are trivially very different in terms of their value to the team.

To score 100 when your team scores 600/4 is vastly different to scoring 100 when you’re bowled out for 200.

Of course, there is no substitute for the entire story of an innings. Relative Runs can’t substitute the total narrative but it does give us a numerical representation of the idea of a relative contribution.

How much did one batter/bowler contribute to an innings compared to their teammates? RR has an answer to that question. It’s not an exhaustive answer, but an answer that standard cricket stats cannot provide on face value.

Want to know a bit more about how Relative Runs can be applied to analyse performance? Well, then take a look at this article in which I used RR to review the 2023 Ashes series in England as well as India’s Test tour of West Indies in that same year.