So Neesham, who lost form and dropped so far out of sight that he was even omitted from the Otago team, has an opportunity against a Sri Lankan team of only ordinary powers; he has fought his way back to national consideration after shifting to Wellington and performing soundly in domestic cricket.
He and Anderson have been rivals for the all-rounder position for much of their careers. Anderson is ahead in short-form cricket, with Neesham seemingly more suited to tests.
In fact, if you examine the test, ODI and T20 records of both, they are remarkably even. Neesham is the more correct technician of a batsman, possessed of an easy grace in his shot making. Anderson is the devastating hitter who can turn a match.
Their test batting records are almost identical: 683 runs in 22 innings for Anderson, with one century and four 50s at an average of 32.52. Neesham has 709 runs in 22 innings, with two centuries and four 50s at an average of 33.76.
Their test bowling is similarly similar: 13 wickets from 23 spells at an average of 41.18 for Anderson; Neesham has 12 wickets from 21 spells at an average of 48.21.
In ODIs, both have a batting average of 27, with Anderson topping the run scoring (1100 runs - including that blistering century in 36 balls - compared with Neesham's 800). It must be pointed out that Neesham's time at the one-day batting crease included a painful experiment opening the batting - a trial that did him and the team no favours.
It's with the ball in ODIs that the two all-rounders' records diverge. Anderson has 60 wickets at an average of 25.03, an economy rate of 6.06 and a strike rate of 24.7. Neesham has 34 wickets at 38.02, an economy rate of 6.51 and a strike rate of 35.
That is where Neesham needs to impress against Sri Lanka. His medium-fast bowling tends to be more of the straight up-and-down variety, potentially plundered by a class batsman on the lash. If he can show a bit more movement in the air or off the pitch, it could greatly enhance his figures and prospects.
His omission from the ODI side (he last played in the 2017 Champions Trophy) was almost certainly occasioned more by his bowling than his batting after he proved expensive (and mostly wicketless) against the likes of Ireland and Bangladesh.
His batting is his real strength. Anderson can be hit-and-miss (no pun intended) in the middle order, while Neesham has a world mark of his own to underline his talent. He is one of the few to score consecutive hundreds in his first two tests.
The other seven, incidentally, are Mohammad Azharuddin (who had three consecutive centuries on debut for India), plus his compatriots Sourav Ganguly and Rohit Sharma, Bill Ponsford, Doug Walters and Greg Blewett of Australia, and Alvin Kallicharan of the West Indies.
Interestingly, all did it at home except Ganguly (both in England) and Neesham, whose second century was against the West Indies in Kingston.
You don't lose talent like that, and that is why his bowling in the series against Sri Lanka will be key. If that goes well, a more testing one-day series against India follows (though Anderson might also get a trot if fit).
A berth in the 15-man World Cup squad is a possibility but Neesham will have to emphasise his batting prowess - and, more importantly perhaps, back it up with the ball.