Verity earned the respect of Bradman, generally regarded as the greatest batsman to have played cricket, and enjoyed bowling at him. Bradman described Verity as a great cricketer and wrote that throughout their respective careers, he "grew more and more to respect both as a gentleman and as a player." Robertson-Glasgow thought that Verity was "one of only three or four bowlers who came to the battle with Bradman on not unequal terms". During the 17 Tests in which they faced each other, Verity dismissed Bradman eight times, more than any other bowler. Robertson-Glasgow believed that, but for Verity, Bradman would have averaged over 150 in Tests instead of his actual batting average. In all first-class cricket, Verity dismissed Bradman 10 times in total, on two occasions twice in the same game. Only Clarrie Grimmett equalled 10 first-class dismissals of Bradman. However, Bradman once said: "I think I know all about Clarrie (Grimmett), but with Hedley I am never sure. You see, there's no breaking-point with him."