Keep an eye out for one of the horses running in the Herbie Dyke Stakes at Te Rapa near Hamilton on Saturday. It is an eight-year-old gelding co-owned by England’s Kiwi head coach, Brendon McCullum, and named, rather aptly, Defibrillate.

There is little question that over the past nine months McCullum has helped jolt England’s previously flatlining Test team back to life, their run of nine wins from 10 since his arrival built on fast scoring with the bat and innovation in field, all in the image of their ultra-aggressive captain, Ben Stokes.

Related: ‘Now I feel like I belong’: Leach out to create better memories in New Zealand

Underneath this, coinciding with the end of the pandemic and the mentally sapping restrictions that all international cricketers endured, has been a heavy emphasis on off-field fun; England will have hit more cricket balls than golf balls before next Thursday’s day-night first Test against New Zealand in Mount Maunganui, but not by many.

However, their four days spent on the scenic courses of McCullum’s native South Island at the start of this tour, and the VIP trip to the Abu Dhabi Grand Prix before their 3-0 clean sweep in Pakistan last December, were not just about camaraderie and clearing minds before entering the cauldron of Test cricket. At a time when the global freelance Twenty20 circuit is offering riches that outstrip national contracts for the very best – 63 English cricketers having played in the various leagues this winter – McCullum is also hoping to make life in the Test set-up as desirable as possible.

“That is the thinking,” said McCullum on Thursday, before England’s stable of bowlers had a run out on the second and final day of their solitary warm-up match in Hamilton. “There’s so many options these days that you’ve got to make Test cricket enjoyable, not just on the field but off the field too.

“We want to try to get those guys to know that when they board the plane to head overseas, or jump into the car to head down to Lord’s, it is to join up with a team they know they’re going to have a great time with. The results will hopefully follow.

“You can’t guarantee that, but what you can do is put some money in the bank when it comes to experiences and relationships. For too long – I always felt when playing anyway – that everything was based around the cricket and sometimes you forgot to enjoy yourself. That’s the theory. We’ll see how it works out, but it’s worth a crack.”

This approach is a far cry from the pre-Ashes bootcamps under the former head coach Andy Flower. There was the brutal Bavaria trip before the 3-1 win in Australia in 2010-11 or the bizarre surveillance training weekend in Staffordshire four years later that left players grumbling about a waste of time and preceded the 5-0 whitewash.

The more relaxed Trevor Bayliss did introduce golf trips to Spain during his time as head coach from 2015 to 2019, but on a quid-pro-quo basis, with strategy meetings and fielding drills the trade-off. In contrast, not a single team talk took place when England were enjoying their relaxed start to this tour, with cricket off the menu entirely.

Another such break is understood to be in the pipeline in between the one-off Test against Ireland at Lord’s that starts on 1 June and the Ashes campaign that starts on 16 June. Australia’ are likely to be competing in the World Test Championship final at the Oval from 7 June.

Related: Rehan Ahmed’s rise continues with place in England white-ball squads

On this tour, McCullum claims the upshot has been that it’s the hardest they have worked once training did get under way. “We want an environment where you want to turn up to work, have a good time, be the best version of yourself, push the boundaries of what you’re capable of as a cricketer. That’s our focus,” he said.

England’s XI for the series opener against the Black Caps seems settled, even if Cyclone Gabrielle – forecast to strike further north at the start of next week – has the potential to disrupt their final preparations. The returning Broad appears likeliest to join Anderson and Ollie Robinson at Bay Oval, ahead of Matt Potts and Olly Stone. All five bowled three solid spells apiece on Thursday and shared the wickets as the NZ XI were bowled out for 310 in 82.1 overs.

A voluntary net session is slated for Friday. And Saturday? Back to the golf course for some, while others may join their head coach at the racetrack to see if Defibrillate – third favourite at the time of writing – prevails. Cricket-wise, they hold no concerns about being short of a gallop.