I’m not convinced. I took all spinners with 149 or more wickets since WWII, and found split their wickets into which Test it was in their careers, so I could find the overall average in debut Tests, second Tests, third Tests, etc.
To get rid of some noise I actually took a five-Test moving average, so the first data point in the graph below is the overall average in the spinners’ first to fifth Tests, the next the average in their second to sixth Tests, etc.
Also I weighted wickets by the average of the batsmen dismissed.
Note that there’s a bit of a selection effect going on. I’m only looking at spinners who were good enough to play enough Tests to take 149+ wickets. Towards the right-hand end of the graph this is also a factor — if you imagine it continuing further on out, you’d eventually just be plotting Warne, Murali, and Kumble. There are, for those interested, 24 bowlers going into Tests 1-36, then 23 in Test 37, 22 in Tests 38-43, 20 in Test 44, 19 in Tests 45 and 46, and 18 in Tests 47-49.
I don’t know how much I want to read into the graph, though I’m happy in saying that spinners improve after their first ten Tests or so. After that there may or may not be a trend — batsmen working them out? Certainly there’s no strong evidence that Panesar will improve significantly (he’s played 33 Tests), though of course it’s possible.
Here’s the corresponding graph for pacemen:
There are 46 bowlers going into all of those data points. There’s a downward trend — pacemen tend to get better with experience, at least for a few dozen Tests.
One thing to try in future is age rather than Test experience. The people who’ve done this sort of analysis in baseball say that age is a better thing to use than Major League experience. But of course baseball is not cricket, so I’m not sure what will come out of it.