All have been stellar for their teams over the last few years, with the latest match-winning exploit coming from Herath, who took 13 wickets in the Test against Zimbabwe in Harare, which also propelled him to 350 Test wickets in 75 Tests, the second-fastest among spinners. That was his ninth Man-of-the-Match award in 51 Tests during this period; in his previous 24 Tests he had won only one.
In fact, the three Asian spinners have been easily the key bowlers for their teams during this period, while Lyon has done his bit as well, though he hasn't come to terms with Asian conditions yet. Ashwin has won seven awards in 39 matches, and Yasir two in 19 (though he has won three series awards in his short career so far).
In terms of overall numbers during this period, Ashwin, Herath and Yasir have been outstanding. They have all taken more than five wickets per Test and around 35% of their team's wickets, at averages in the mid-20s, with plenty of five-fors and strike rates of less than 60. Lyon's numbers are not as extraordinary, but his problem has been bowling in Asia. He averages 42.57 in the continent, and 31.09 everywhere else.
In terms of averages, Ashwin's 24.29 is the best among the four, but he has also bowled in extremely spin-friendly conditions in most of the home Tests. The same is largely true for Herath as well, but Yasir has had to toil on true pitches that don't offer as much assistance to spinners.
One way to normalise the effects of the pitch is to compare the bowler's numbers with those of other spinners who played in the same game. It may not always ensure a completely fair comparison - the numbers also depend on the quality of other spinners in the match - but it does indicate how the other spinners fared in the same conditions.
In the 39 Tests that Ashwin has played, he has averaged 24.29, while the other spinners have averaged 33.09 in those matches. (Ashwin has taken almost 35% of the spin wickets in those games.) The ratio of the averages indicate that Ashwin has been 1.36 times better than the other spinners. The corresponding ratio for Herath is 1.41, which shows Herath has been a bit better than Ashwin when compared to other spinners in the Tests they played. (Excluding the two Tests against Zimbabwe, Herath's ratio is 1.37.)
However, those ratios are lower than that of Yasir, who has been truly outstanding especially in the UAE, where conditions that haven't offered him - and other spinners - that much assistance. (Yasir also had a ten-wicket haul at Lord's earlier this year, though a couple of poor Tests thereafter meant his overall series average was 40.73.) In the 19 Tests Yasir has played, his average is 27.37, while other spinners have averaged 45.76 in the same conditions. That means Yasir has been 1.67 times better than the other spinners in these 19 Tests, which indicates a high level of skill and an ability to conquer conditions.
All three of these Asian spinners have exceptional ratios in home Tests (with the UAE counting as home Tests for Yasir). In India, Ashwin averages 20.37 while other spinners have averaged 30.69, giving Ashwin a ratio of 1.51. Herath has averaged 20.77 in 25 home Tests during this period, compared to 33.83 by other spinners in Sri Lanka, giving him a ratio of 1.73, while Yasir is again the best of the lot with a ratio of 1.77 - he averaged 25.34 in ten Tests in the UAE, compared to 44.90 by other spinners.
Yasir's overall numbers are also pretty balanced in terms of averages against right- and left-hand batsmen. He averages 28.42 against right-handers and 25.90 against the lefties. Ashwin's average is significantly better against left-handers, while 80% of Herath's wickets are of right-hand batsmen. Lyon does better against left-handers too, though he has a fairly high percentage of right-hand wickets.
Lyon has an opportunity to improve his Asia numbers when Australia tour India early next year, but the other three are obvious match-winners in favourable conditions. It isn't a surprise that they occupy three of the top six spots on the ICC's Test rankings.
S Rajesh is stats editor of ESPNcricinfo. Follow him on Twitter.