You do realize Hammond only played 82 tests compared with Root's 159. When you take into account exactly half of Hammond's tests were against Australia, then as now the best team in the world, and that he averages 8 more than Root then your dismissal of him shows rather a lot of recency bias.
If you really want to get into the weeds of comparing players 100 years apart then you need to do it properly, and look at how the average for all batsmen in test cricket was 10 higher than it is today and stuff like that. Hammond played in the most batsmen friendly 20 year period in test history. So his average being 8 higher than Root's isn't actually something in his favour when Hammond's average of 58 was only 13 higher than the average of all players, and Roots is more like 25 higher.

Obviously Australia were the best team in the world back then, they were only 3 test teams when he made his England debut. It was a completely different sport. Hammond didn't have to juggle ODI's and T20 and swapping between them. He didn't have to go into test series with 0 warm up games because it's the 5th series of the year and there's no time.
When Hammond would pad up for his first test in Australa he'd have played 10 warm up matches and been in the country 2 months getting used to conditions. Root will have flown in 2 weeks before and he'll play 5 test matches on the spin and then play an ODI series and fly somewhere else he'll play with no prep. Hammond never even faced proper spin bowling, back in his day almost no one did it, and proper turning the ball with drift and spin didn't come about until the 50's, before that it was basically just bowling slowly enough that you could relaibly aim for the cracks in a pitch and only used defensively.
Anyway I honestly find all this stuff tedious which why I generally choose not to bother comparing. Different sports. Also how do you compare someone with a player you've never even seen play. Live or on video? I'm personally never going to be able to say player X from 100 years ago was better than Joe Root, who I've seen play incredible cricket live 20+ times and most of his innings on TV just because a scorebook said he had a slightly higher average.
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