Cook's fifty problem, England's left-armer problem

Alastair Cook, the erstwhile Honours-Board-Bothering machine, the one-time avaricious hoarder of three-figures scores, has scored only three hundreds in the 38 Tests he has played since the 2013 Ashes began. He has reached the half-century mark 23 times in 70 innings in those games; in the 40 Tests he played before that (from the tour to Bangladesh in 2010 to the end of the New Zealand micro-series earlier in the 2013 summer), he had made 22 fifties in 69 innings, but converted 15 of them into centuries (including six in a row from July 2012 to May 2013, the last five of which were in his early months as captain).

So, although he has continued to reach fifty almost once every three innings, his conversion rate has collapsed from the best in Test cricket to the worst. Of the 25 players to have made ten or more fifties in Tests since July 2013, Cook's conversion rate of 13% is the lowest - other than he, only Kaushal Silva (two out of 13) has converted less than a quarter of his fifties into hundreds. In the 2010-2013 period, Cook's 68% conversion was the best of the 40 players with at least ten scores of 50-plus. To give some context to his excellence at that time, the next seven batsmen in the conversion-rate list were Kallis, Dravid, Sangakkara, Clarke, Younis Khan, Chanderpaul and Amla.

To add further curiosity to the stats, conversion rates in all Test cricket have risen since July 2013 - excluding Cook, the rate has increased from 28.8% in the 2010-2013 period, to 33.4% since the start of the 2013 Ashes (and, for all other openers, from 27.5% to 35.1%). The England captain's conversion stats have been swimming upstream like a randy salmon.

Cook was similarly ineffective at converting fifties earlier in his career. After his stellar 2006 entry to the Test arena (five of his first nine fifties were converted into hundreds), in 70 innings between the New Year's Ashes Test in 2007 and that 2010 Bangladesh tour, he made 25 fifties, and converted only six, four of which were against the lowly ranked, ineffective West Indies.

Just as his fifty rate has remained relatively steady through these three wildly divergent conversion-rate periods in his career, so has his proportion of single-figure dismissals. In fact, his failing-to-trouble-the-tens-column rate was actually higher in his most successful phase. He was out in single figures 14 times in the 2007-2010 period; 19 times in his peak 2010-2013 phase; and 15 times from the 2013 Ashes to now.

Cook, it seems, is almost exactly as adept at beginning his innings as he ever was, but he has become (again) vastly less effective at prolonging it. His average since the 2013 Ashes began is a solid 41.5 - very solid for a player playing so few big innings. Many of his non-hundreds have been important innings.

However, this is a batsman who used to be one of the toughest to dismiss when set - in the 2010-2013 phase, once he had survived the first 15 overs, it took on average 161 balls to dismiss him, more than any other regular Test batsmen other than Chanderpaul (166 balls per dismissal from over 16 onwards), and his after-the-15th-over average of 81 was comfortably the highest of those who batted more than ten times in that part of Test innings. Since the 2013 Ashes, Cook's figures are down to an average of 49 (25th best of those with ten or more relevant innings), and a dismissal once every 116 balls (seventh best) - still impressive, still adhesive, still valuable to his team, but significantly declined.

Is there a reason for this? Perhaps bowlers have become more persistent in challenging his weaknesses. Perhaps the burden of captaincy has fractured the impregnable cocoon in which he used to bat once established, or a decade of Test-match opening has worn down his mental stamina. Perhaps the added pressure of being a prime lynchpin in a more fragile batting line-up has added strain to his batsmanship, and made opponents treasure and target his wicket even more. Perhaps Edward Snowden's disclosure in June 2013 of the covert surveillance programmes of the US government made Cook worry that his batting was being spied on by the CIA; perhaps Croatia's accession to the European Union on July 1, 2013 made the Essex man fret about the potential geopolitical implications of the rapid expansion of the EU in the aftermath of the collapse of the communist bloc. We may never know.

Cook is the most striking example, but England as a team have struggled to capitalise on their half-centuries. In the 2010-2013 period detailed above, England's 36% conversion rate was second only to South Africa (41%) of the nine regular Test-playing teams. Without Cook, at 30%, they would still have been third. In the 2013-2016 block, England are eighth in the conversion league, at 24%. With Cook's 3-out-of-23 figure removed, England's rate is 26%, still eighth in a table led narrowly by Pakistan (42.6%) from South Africa (42.1%).

Joe Root has made only one century from his past eight 50-plus scores, having turned eight of his previous 19 half-centuries into tons. Ian Bell, after his momentous, career-defining 2013 Ashes, converted only two of the 11 Test half-centuries he made subsequently into three figures. Recently the entire England team has struggled even to convert three-quarter centuries into centuries. Since the start of last summer's home international season, English batsmen have reached 75 in a total of 33 innings. They have converted only 12 of those into centuries (36%). All other Test teams collectively have converted 60% of their 75s into hundreds over the same period. Only West Indies (one out of six) are below 50% at converting 75s into tons. Australia have converted 77% (24 out of 31).

All in all, curious and unhelpful from an English perspective. Explanations on a postcard, please, addressed to The ECB, No.1 Cricket Street, Cricketsville, Cricketshire, England. Soon, preferably. By 11am on Friday morning, if you have the time.

Of those who have played a significant quantity of Test cricket, none of England's current batting line-up, nor any likely potential replacements, has a better record against left-arm seamers than right-arm seamers. Root averages 37.4 against left-arm pacers, 47.6 against right-arm pacers, Bairstow 28.3 to 48.5, Ballance 21.2 to 53.2, Moeen 26.7 to 32.8, Stokes 24.6 to 44.4. Furthermore, Bell's figures are 33.6 to 42.0, and Jos Buttler's 23.7 to 40.1.

Cook is the closest - 40.4 against left-arm pace, 42.5 against right-arm pace. Even so, he was dismissed by a decent but hardly devilish Rahat Ali delivery in the second innings at Lord's, having scored, in effect (after being aided by some rather Kamranakmalian catching) 25 for 3 against Mohammad Amir in the first, which does not suggest that England's leader is in tip-top flourishing-against-high-quality-left-arm-seamers form.

Since the beginning of the 2006 English summer, 20 England players have faced at least 30 overs of pace from both left-armers and right-armers. Only three average more against left-armers - Matt Prior (48.8 to 39.1), Adam Lyth (a not very good 23.2 to an even worse 17.3), and, intriguingly, the recently-departed-from-the-team Nick Compton (54.6 against left-arm seam, the best of the 20 England players involved in this stat; 19.3 against right-arm seam, second worst of any non-specialist bowler who has faced at least 500 balls of right-arm pace since 2006, ahead only of Lahiru Thirimanne [18.4]).

Part of the disparity must be due to the fact that England have played several recent Tests against some very good left-arm pacemen, and have faced some less-than-Marshallesque right-armers, but still those are numbers for Pakistan to pin on their bedroom ceilings at night to help them get to sleep. (I assume international cricketers pin statistics to their bedroom ceilings.) (I cannot imagine why they would not.) (I would, if I was an international cricketer.) (I do, and I am not an international cricketer.)

Stats, of course, are made to be broken. Or flatly ignored. Or tweaked, or reinterpreted, or counter-statted with another stat. Or used as legal evidence, quiz questions, or chat-up lines. England's batsmen will need to start declamping these two unwanted numerical albatrosses from around their statistical necks, or this series could become very problematic indeed.