I have a good friend in Texas who shoots field target with his Air Arms springer. His skill has improved to placing at AFTA nationals. He has found Air Arms pellets to be best, but began sorting pellets for matches a couple of years ago. He sent this image last week, showing results of about 300 he sorted from a new tin of AA 8.4 grain, "4.51 mm" pellets. He does this while watching TV and the photo shows the results of more than one session, as he sorts into tins marked by gaged head size. He said that these last 300 he sorted : "10% were 4.48 mm, 65% were 4.49, and 25% were 4.50". You can see that very few are actually 4.51. Consider that the pellet is called 4.51 if it clears the 4.51 aperture, so they would be a bit smaller than that diameter. He did not find a single pellet that did not clear 4.50 mm aperture. My friend says that he can use 4.48 to 4.52 in his rifle, but that matching the size and shooting only one size at a given zero point will give him better patterns. My friend is an experience engineer who works in a field requiring mechanical precision, and he did not readily accept the premise that a Pelletgage was really needed. His controlled practice sessions convinced him.
That's my take, too. You may very well think that head size is not critical for your gun, but you would see much bigger patterns if you were shooting pellets with the range of 4.48-4.50 all mixed, for instance.
Air Arms sells their Diabolo Field pellets, 8.4 grain, in 4.50, 4.51, and 4.52 mm sizes. The two issues you MAY find is that a new tin is, say. 0.03 mm smaller than the last in. Or worse, you have a mixture of 4.48-4.51 mm in your tin. And a third issue is when you shoot that 4.46 mm pellet in a match and see the notorious "flyer" about an inch and a half off the aimpoint at 30 yards.
Now, you need to know FIRST if your gun is "pellet sensitive" and what size works best. Then you are left with the concern of being able to get that size, regardless of what you buy. And I have seen many reports like this one. Although I'm still a dedicated JSB shooter myself, I sort for 4.51 or 4.52 for my Marauder (with Lothar Walther barrel). I have found that the 10.3 grain JSB Exact are pretty good, but I check every tin, and for most matches, I sort for one size and zero my rifle on the range with that size. I DO see the occasional pellet that will be +/- 0.04 and am convinced accuracy is affected for my rifle.

Pellet manufacturers have lapses in their process controls, and this lack of control isn't predictable. Those who have gotten six good tins ahd have been shooting them for a whole season may think it is all silliness.
Good luck shooting!