England's ODI batting line-up has been on a tear in the last year. The 2015 World Cup was clearly a debacle at the time, as England lost to Bangladesh and failed to qualify for the quarter-finals, but in the longer term it seems to have done English cricket plenty of good, as it shook the team management to make changes that were long overdue. Out went batsmen like Ian Bell and Gary Ballance, who couldn't keep up with the tempo of the modern 50-over game. In their stead came fearless hitters like Jason Roy and Alex Hales - batsmen who could consistently hit boundaries and weren't afraid to attack from ball one. In the last year, the transformation of England's batting, from tentative, caged and defensive to fearless, free-spirited and aggressive, has been quite sensational. Here are some of their ODI batting achievements from the last 13 months:

A comparison of their numbers in the 15 months till the 2015 World Cup and the period since then shows incredible improvement in all batting parameters. The average is up 34%, the run rate 21%, matches per century has improved by 51%, and the balls per six by 39%. With such huge improvements in batting numbers, it's hardly surprising that their win-loss ratio has gone up from 0.565 to 1.33, an improvement of 136%.

Since April 2015, England are the only team whose batsmen have collectively scored at a strike rate of more than 100. They also have an excellent conversion rate of 15 hundreds, out of 45 fifty-plus scores. Their balls per boundary is the lowest among all teams too. In the period between January 2014 and March 2015, they fared quite poorly on all those parameters: their strike rate was seventh among the top nine teams, the average was below 30, while the batsmen struck a four or a six every 12.44 balls.

ODI batting stats for teams since Apr 2015 Team Average* Strike rate* 100s/50s Balls per 4/6 England 37.22 100.96 15/ 30 8.40 New Zealand 39.01 95.39 8/ 27 8.99 Australia 36.22 91.94 6/ 32 9.94 Sri Lanka 32.81 90.79 3/ 33 10.67 India 39.15 89.42 11/ 26 10.90 Bangladesh 35.3 88.51 5/ 15 8.89 Pakistan 34.14 87.54 5/ 31 10.71 South Africa 33.27 86.47 12/ 19 10.65 West Indies 22.73 80.21 3/ 6 10.45

ODI batting stats for teams between Jan 2014 and Mar 2015 Team Average* Strike rate* 100s/ 50s Balls per 4/6 New Zealand 37.12 95.87 15/ 36 8.57 South Africa 41.47 95.75 23/ 37 9.54 Australia 35.74 92.13 12/ 43 9.72 India 36.04 88.91 16/ 46 9.73 West Indies 29.95 88.85 10/ 28 9.17 Sri Lanka 31.47 85.91 22/ 51 10.26 England 27.60 83.10 11/ 35 12.44 Pakistan 26.93 81.99 6/ 36 11.45 Bangladesh 27.34 80.60 6/ 28 11.27

* Average and strike rate calculated on runs scored off the bat, excluding extras

England's batsmen have shown greater urgency throughout their innings over the last year, but the biggest difference has been in the middle overs. While the run rate has gone up by 18% in the first 15 and by 13% in the last ten, in the middle overs the increase has been almost 27%. Since that's also the largest chunk of an ODI innings, that difference in scoring rate has translated into a much larger total.

England's batting numbers in the middle overs have improved significantly over the last year ESPNcricinfo Ltd

During the years when the England team were clearly behind the leaders in the 50-over format, their batting in general, and especially the conservatism in the middle overs, was a huge factor for their poor results. Out of the top nine teams, their run rate of 4.98 in the middle overs was eighth, worse than all teams except Bangladesh.

In the last year, though, they have surged ahead of all other teams and are the only ones scoring at more than a run a ball. Their balls per boundary has dropped from 15.86 to 9.35, a huge improvement of 41%. Four of their batsmen have scored 350-plus runs at better than a run a ball in the middle overs: Eoin Morgan (683 runs at a strike rate of 103), Joe Root (538 runs at 103), Jos Buttler (366 runs at 108), and Alex Hales (358 runs at 102). Together, these four batsmen have scored 59% of England's total runs in the middle overs in the last year.

Teams in the middle overs (15.1 to 40.0) in ODIs Jan 2014 to Mar 2015 Apr 2015 onwards Team Average Run rate BpB* Average Run rate BpB* England 30.55 4.98 15.86 45.12 6.30 9.35 Bangladesh 33.15 4.89 14.09 45.96 5.70 9.50 Sri Lanka 37.83 5.31 11.56 38.06 5.55 12.41 New Zealand 40.47 5.55 10.54 40.49 5.52 11.42 Pakistan 31.47 5.03 13.37 37.18 5.44 11.98 West Indies 37.19 5.54 10.25 27.00 5.39 10.74 Australia 44.62 5.44 11.94 35.95 5.36 12.41 India 47.24 5.74 10.10 47.65 5.31 12.50 South Africa 51.10 6.03 10.85 44.14 5.28 13.01

* Balls per boundary (4 or 6)

Those four batsmen have also been among England's top run-getters overall during this period, along with Roy and Ben Stokes. Five of those six England batsmen have scored 600-plus runs at 40-plus averages and strike rates of more than 90, while Stokes has averaged 29 at a strike rate of 108. Those are the sort of numbers that England fans couldn't have dreamt of, from their top-order batsmen a few years ago. Hales has scored over 900 runs, while Morgan has almost as many despite a lean series in South Africa, thanks to an outstanding summer in 2015, when he scored 600 ODI runs in ten innings.

England have clearly found their ODI mojo in the last year; it remains to be seen, though, if they can keep it going till the 2019 World Cup.