Which one of Andy Carroll’s gorgeously brutal hat-trick goals against Arsenal last weekend was your individual moment of the season so far? I know. It’s not an easy choice. Maybe the first one where he seems to be actually running in midair, gliding through the forest canopy above the Arsenal defence, before butting the ball into the net with such power David Ospina looks genuinely alarmed. Or the one where he chests and fumbles and scuffs and then, tiring of the whole thing, abruptly conjures up a kind of whirling roundhouse overhead-shin into the corner of the net.

Or maybe the header for the third, notable for the way Carroll seems to engulf Héctor Bellerín completely as they wait for the ball to drop, clattering down on top of him like a vast mahogany Victorian bookcase toppling off the wall. Ferenc Puskas was said to have a foot that was “like a hand”. Carroll has a head like a foot. Such power, skill, finesse … Never mind boots. They should make Andy Carroll replica heads. Complete with patented forehead throb technology. I’d buy half a dozen.

Andy Carroll inspires West Ham with hat-trick in 3-3 thriller with Arsenal Read more

At the end of which it was predictable that Carroll would be mooted, vaguely, as an outside shot for England’s squad for Euro 2016 this summer. The suggestion is Roy Hodgson may now consider “taking him to France”. Because this is what you do with Carroll. You don’t select him. You “take him”, you ship him out, like mobilising some particularly fearsome piece of weaponry, battering at the container walls as the ships leave Dover, peering out at the cowering villagers as the colony thunders south through Normandy.

It is, of course, unlikely this will happen. Carroll hasn’t been picked for a competitive game in three years. England have a mini-glut of worthy strikers ahead of him. Carroll’s hat-trick was thrilling but it adds up to 43% of his entire goal tally in the past year. Despite being employed at vast expense to do little other than score goals, he hasn’t done so with his right foot in almost three seasons.

Plus there is the basic mismatch between the measured, geometric rhythms of international football and the unrestrained physicality of a player who could probably demolish a stud wall with one of those frightening full-body lunge-tackles.

Carroll has not been booked yet playing for England. He has one red and two yellow cards in three years in the Premier League. But he does tend to push at the edges. Leicester City’s Jamie Vardy has committed 34 fouls this season in the league, Tottenham’s Harry Kane 38. Carroll, in a third of the time, is romping up behind on 29.

Albeit, this isn’t really the point for a player who wouldn’t spend much time on the pitch anyway, and whose threat is a highly specialised thing, to be reserved for a moment of crisis. To wave Carroll away as simply a physical presence is to miss the undeniable brilliance of his heading, the extreme levels of skill and timing involved. His real superpower is the way he picks the flight of the ball so early, focused completely on the physics of that parabola of collision, moving past defenders who always seem somehow to be standing still, like people in a disaster movie transfixed by some CGI tornado looming up in the middle distance, sending cows and cars spiralling up into the clouds above the fields. This may not be the most fashionable skill. But Carroll is surely as good at it as anyone anywhere .

So the idea is that Carroll would offer you “that option”. If plan A fails, well, just junk it all and adopt a completely different set of direct football tactics for about 10 minutes at the end. Peter Crouch used to offer England That Option. With little success at tournaments. Not surprising given Crouch’s height coincides with no obvious heading skills, and that he is instead a neat, clever footballer and excellent finisher, in effect the smallest extremely tall footballer in the world.

And really That Option is a chimera in itself. Don’t give in to it, Roy. Training one way, adopting a style, grooving a set of skills, building combinations: this is something to stick by, not to simply junk because of some throbbing vein in the temples. To make That Option work everything needs to change. Suddenly every pass, every movement is re-geared. That Option – which is always the same option, physical, long-ball instant football – is a bit like going to a business meeting with a medieval mace in your briefcase. Just in case. Just in case you need, you know, that option.

The best teams don’t do this. They have belief in a set of tactics, and reinforce or vary it from the bench. The last two World Cup finals were won with extra-time goals created not by hoofing it up to some great elbow-jabbing goal-zeppelin. But by playing with more of the same, more precision, more care, the winning goals scored by players who embody a consistency of method.

For all his talents Carroll is at odds with what England do have, a group of hard-running, athletic, technically decent young players. As well as an evolving Premier League style somewhere in between the structured pressing of Spurs and Liverpool and the counterattack of the league leaders Leicester that may just finally fit the personnel and the occasion.

Carroll, meanwhile should simply be enjoyed for what he is, a player it is hard not to respond to on some visceral, emotional level, who seems to speak to the old, buried folk ideal of English football as a kind of trial of strength, some swarming, steaming bladder-wrestle. He is, for now, the end of a line too. There aren’t any younger versions out there in the Premier League. The academies don’t produce these kind of players. Carroll is what we still have, a kind of heritage exhibit, last of the Mohicans, but also a player of huge skill and rather discredited craft.