Test partnerships – does it matter who bats with whom?

Does cricket lose something when we are dispelled of its myths? Some fictions are unhelpful, such as Michael Vaughan’s success without having thrived at county level. However, we like to believe in partnerships: every smile and punch of gloves boosting the batting of our heroes, spurring them on to greater heights.

Thus I write hesitantly – I am loathe to reduce cricket to a spreadsheet, even though I literally do that. Hopefully some unsolved X factors will remain after the stats revolution.

On to today’s topic. Last time we saw that right-left partnerships don’t influence white ball run rate. This post covers the currency of red ball cricket: averages. Does who you’re batting with impact your average?

Considering the period 2010 to today, seven pairs performed much better than expected based on the records of the individuals in that partnership. Two pairs performed worse. They are shown below, ordered by how surprising that out-performance is.

That’s nine outliers – seven good and two bad.

But what are the chances each outlier was just fluke? After all, Clarke & Ponting only had 20 partnerships in the 2010s. After this analysis of error bars on averages we have a way to answer that – by quantifying how likely it is that a specific average (eg. Jermaine Blackwood averaging 37 in England) is arrived at by chance, based on the sample size.

With 120 partnerships (min 20 innings) since 2010, we would expect six pairs to lie two standard deviations from expected average. Actually we have nine. On the face of it, that’s evidence that some duos do get a boost from batting together. However, two of the nine drop off the list with further scrutiny. Kayes and Iqbal happened to bat together more at home than away. Bell/Pietersen somehow had 19 of their 23 partnerships in the first innings. Adjust the calculations to reflect that, and we have seven outliers, whilst by chance we would expect to have six. In layman’s terms, if each duo batted together enough times, their partnership average would eventually reach their combined average.

Here’s the chart of all 120 players, plotting variance to expectation against frequency. Even with small sample sizes, most partnerships average within five runs of expectation.

Where does this leave us? Remembering that “absence of evidence is not evidence of absence“, the jury’s deliberations will continue, but they will now be leaning in favour of specific partnerships not making a significant impact on a player’s average. Cricket is a one on one sport, bowler against the batsman on strike.


PS. How did I arrive at the expected average for a partnership? Start with the mean of the post-2010 average of the two players in each partnership. Add 1.5 runs for any partnership that isn’t two openers, on the basis that one of the batsmen will start the partnership with their eye-in. Add 4.6% for the extras that would be scored in that innings. It’s a slightly different formula for when a senior batsman is with a tailender.

PPS. Why the cut-off in 2010? “No balls” dropped off then. Here’s the 50 year history of extras in Test cricket. Extras count towards partnership totals, so the maths gets more involved when extras vary significantly by year.

Do right-left pairings score faster in ODIs?

Let’s start with the superficial (Boo! Hiss!) – a right-left pair score 0.8 runs per hundred balls faster than a right-right duo.

ODI partnership summary – min 120 balls, top nine teams only, up to 18 June 2020.

But right-left pairings aren’t something exotic. They are the normal state of affairs. 48% of ODI runs are scored by this combination. No bowler should be phased by normality.

Jarrod Kimber, while concluding that “it’s complicated”, suggested the quicker left-right scoring is a combination of additional wides and ensuring unfavourable spin matchups for the fielding team.

But what about taking into account how quickly players usually score? Gayle, Munro, Morgan are quick scoring left handers, who will be involved in fast scoring partnerships.

I’ve taken each ODI pairing of the last five years and looked at how quickly they should score together – which is the mean of their strike rates. For instance, Sikhar Dhawan (98) and Rohit Sharma (96) would be expected to score 97 runs per hundred balls. Actually, they favoured setting a base, and scored at 86 per hundred balls. No right-left benefit there. However, the Dhawan-Sharma point is anecdotal – the real story is in the general case.

Two ways we can look at this – firstly, excess runs per hundred balls (ie. take all the right-left pairings, compare the runs they scored against expectation based on individual strike rates, and divide by the number of balls bowled). Right-left combinations are weaker than right-right pairs on this metric by 0.2 runs per hundred balls.

Next, because the first method is weighted towards players that batted together lots (Roy-Bairstow’s blitzes have a big impact), we take the raw average of each pairing. For example, Dhawan-Sharma’s impact score is 86 minus 97, being -11 runs per hundred balls. Taking the average for all right-left pairs, they come out 0.4 runs slower per hundred balls than right-right partnerships.

That’s 2-0 to the right-right pairings. Right-left combinations look slower than right-right pairings, once you adjust for who is batting.

But could it be impacted by time of the innings? For instance, do lots of right-left pairs open the batting, so score more slowly at that stage of the innings? Let’s repeat those same two calculations, but just for openers.

Darn it. We have three measures saying right-left pairings are of no benefit, against one saying that they are.

We need more data.

The good news – I’ve finally found a use for all those meaningless T20Is: to test right-left supremacy.

Running the same methodology for 2015-20, it’s nice to see some familiar faces. Dharwan and Sharma top the list, with 1,663 runs together. This time their collective strike rate of 141 is much closer to what we’d expect. And the general case:

Conclusion & Discussion: If anything your team will score faster with two right-handers batting together. Why should that be? One thought: with a left-right combination, the bowler must have a different approach for each batsman, and adopt the optimum lines and lengths for the player on strike. However, with two right handers that isn’t necessary. Is there a risk that a bowler tries to apply the same plan to two quite different right-handed players? I’ve no idea, but it kinda feels possible.


This has all been a bit dry, so let’s have some fun. Firstly, the Campbell-Hope award for the pairings who added up to more than the sum of their parts:

Min 300 runs. Top nine teams only.

And the same for slow scoring – where two batsmen either don’t gel or happen to have come together to consolidate not dominate:

Min 300 runs. Top nine teams only.

PS. That was supposed to be some harmless trivia. But Angelo had to spoil it. Did you see him in four of the twelve pairings? Another hypothesis to test: “Is Angelo Mathews better with some players than others”?

Further readingCricinfo analysis of ODI partnership averages. Concluded no advantage to left-right partnerships. Doesn’t cover strike rates though – so I may have done something original here.