A prosperous and successful plumber is an expert at plumbing. Someone who is a good source for accurate information on plumbing is an expert on plumbing. More generally, an expert at a topic is someone who has gained the most attention, praise, income, and so on via their association with the topic. But this may not be the best expert on that topic. He may have succeeded by not giving the most accurate information, but by telling people what they want or expect to hear, or by entertaining them.
We often rely on the heuristic of looking to an expert at a topic, when what we want is an expert on a topic.
Is this not a mistake our sports channels routinely make, hiring experts at cricket instead of experts on cricket? For example, I’d count the likes of Atul Wassan, Navjot Singh Sidhu and Chetan Sharma as experts at cricket, and Harsha Bhogle as an expert on cricket—and I think we all agree on who is a better commentator. Of course, there are some who are both experts at and on cricket, such as Richie Benaud and Sunil Gavaskar (when he’s switched on and is not on auto-pilot). But our broadcasters don’t care too much: they just want the experts at cricket because those people come into the television studio with the benefit of already being celebrities, and viewers crave familiarity. If they happen to also speak insightfully about the game, well, that’s a bonus.