In cricket, being left-handed comes with some peculiar advantages (and disadvantages). Bowlers, on the whole, tend to be right-arm bowlers and find it difficult to get lbws against left-handers if the ball isn't swinging. On the other hand, this same predominance of right-arm bowlers means that lefties invariably face a massive rough outside their off stump as a Test match progresses.
The desire for a left-right batting combination has produced many a change in batting orders. Commentators often argue that in ODI cricket, left-right combinations might find it easier to score quickly, as the bowler has to keep adjusting his line and length and bowl to different fields if the strike is rotated regularly. This increases the chance that the bowler may bowl a bad ball. To take a hypothetical case, should this extend to promoting JP Duminy ahead of Faf du Plessis to join Hashim Amla at the wicket? Is there any evidence to suggest that left-right stands are more prolific than others?
I looked at all ODI partnerships since 1979 in ODI games featuring only Test teams (excluding Bangladesh and Zimbabwe). I have considered the top seven batting positions only. For most of the 1980s and early '90s, one out of four batsmen in the top seven was a left-hander. Starting in the late '90s, this has increased to one in three.
Except for a short period in the late '90s, there has been no significant difference in the run-scoring abilities of left- and right-handers in ODI cricket. From the start of 1995 to the end of 2000, 70 left-handers batted in the top seven of an ODI innings in matches featuring only the top eight Test teams, and averaged 33.6. In these games, 199 right-handers averaged 29.3 batting in the top seven. You can imagine the names - Ganguly, Bevan, Kirsten, Jayasuriya, Lara, Gilchrist, Thorpe, Knight, Twose, Fleming - every team had a top left-hander, if not two, in those years.
Now that we have some idea of how left- and right-handers have performed over the years, let's see if the partnership record is a variance. In other words, if, despite the overall quality of left- and right-handers being more or less equal, left-right stands are more prolific, perhaps there is something to the idea that teams should try and play left-right combinations whenever possible, even if it means shuffling the batting order at short notice.
First, let's look at how frequently the three types of partnerships occur - two right-handers, two left-handers, and left-right pairs. In the 21st century, two right-handers have been as likely to bat together in an ODI as a left-right pair. This change from the 1980s, when right-hand pairs predominated, is understandable given the overall increase in number of left-handers in international teams.
Next, let's look at partnership averages. The evidence suggests that left-right partnerships have done better than right-right partnerships only during periods when left-handers have been better than right-handers overall (prominently so in the late 1990s). In the 21st century, two right-handers have batted together 5984 times in for the top six wickets in an ODI and produced 35.3 runs per stand. Two left-handers have batted together 1317 times and averaged 34.4 runs per stand. Left-right pairs have batted 6767 times and averaged 36.3. So left-right pairs have done two runs better than two left-handers, and one run better than two right-handers. During this time, 154 left-handers have averaged 32.8 in ODIs, the same as the 341 right-handers have. So perhaps there is some minor benefit to left-right pairs. If you look at median stands, the median left-right stand in the 21st century has been worth 23 runs. The median left-left and right-right stands have been worth 22 runs each.
Let's look at how teams have done against different opponents in the 21st century. The record in the table below does not, in my view, provide any clear evidence to suggest that left-right pairs have done better than right-right or left-left pairs. If anything, it suggests that weak bowling attacks have struggled against left-right pairs. New Zealand have not had a strong attack for much of the decade. Their current attack is perhaps their best since the days of Shane Bond. India have fared best when they haven't been faced with a left-hander. Pakistan on the other hand have dominated left-left pairs.
Finally, let's look at batting teams in the 21st century. In general, teams with strong left-handers have done well with at least one left-hander at the wicket. Australia have been the only side to have consistently dominant left-handers in their batting order in the last 15 years. India have had Yuvraj Singh, Gautam Gambhir, Shikhar Dhawan, Suresh Raina, and to a lesser extent, Sourav Ganguly.
The record does not suggest that there is any advantage to sending a left-hander in to join a right-hander (or vice versa), compared to sending a right-hander in to join a right-hander, or a left-hander to join a left-hander. Further, it shows that bowlers should be used to bowling against left-right pairs since such pairs are as common as right-hand pairs in contemporary international cricket. This raises an interesting point when one is comparing bowlers from the 1970s and early 1980s with bowlers from more recent times. The latter have had to be just as effective against good-quality left-handers as they have against good-quality right-handers.
Left-right pairs have no systematic advantage over other types of batting pairs in the ODI game. If the choice is between a left-hander and right-hander, the batsman in better form ought to be selected, regardless of how many other batsmen of that type are already present in the line-up. In Test matches, the story may perhaps be different.