Posted 17 June 2008 - 07:25 AM
Everyone -- critics and readers included -- who has or learns of a bad service experience at a restaurant gives in to the human instinct to generalize from it. But an accurate statistical model doesn't.
If we assume that every restaurant -- even a four-star restaurant -- has incidents of bad service (for the purposes of a mathematical model let's divide service instances into "good" and "bad," though reality is probably closer to a point system, say 1 to 10) then every restaurant has what we could call a "service failure rate." Let's say a busy restaurant with 150 seats has 50 tables (average table size in a lot of restaurants works out to 3 and change, I believe) and does 3 sittings at dinner and 1 at lunch. That's 200 tables served per day. Assuming a 6-day week and some holiday closings we're looking at maybe 300 days of service. So that's 60,000 tables served per year, or 5,000 per month.
Just to make this simple, let's define our "period" as a month. Out of those 5,000 tables served in a month, how many are likely to experience service failure? At a restaurant with a superb service team, the number could be pretty low, maybe just a couple of tables a day. Having spent many a full service in restaurants that have won every good-service award, I can say with confidence that it's almost unheard of for a service to go by without some unfortunate disaster or another unfolding. But let's be exceedingly conservative and say the service failure rate for the period (one month) at our hypothetical three- or four-star-level restaurant with excellent service is 50.
Now let's say that at a two-star-level restaurant the service failure rate is 150 for the period. Triple the other restaurant's service failure rate, assuming same size and number of sittings. In other words we're defining -- just for the sake of this model -- three/four-star service as a service failure rate of 50/5,000 and two-star service as a service failure rate of 150/5,000. And the one-star rate, let's call that 500. Of course this oversimplifies, but it's useful for the illustration.
Okay, so as a visitor taking a random sampling, how many visits do I need to make in order to tell whether a restaurant has a three/four-star service failure rate, a two-star service failure rate, or a one-star service failure rate? I think we can all agree without resort to any high-level math that 1 instance of service failure has no bearing whatsoever on predicting whether we've just dined in a restaurant with a service failure rate of 50, 150 or 500. How about 2 or 3 instances? The one mathematician I asked said: "Unless the good restaurant failure rate predicts less failures than the number of critics visits, not sure how you could assess differences in the rates from that small number. If the good rate predicts less than 2 bad nights per period and you observe 2 or 3, maybe you can sort of say something. But if good rate predicts 35 bad nights and bad rate predicts 70 bad nights, and you observe 3 bad nights, I don't think you can statistically classify into good or bad." Feel free to dispute that, but it makes sense to me.
All the same modeling can be applied to certain aspects of food preparation. For example when critics write that such-and-such is "consistently" overcooked, they simply are not rendering a mathematically meaningful judgment as to consistency. Again, if there's an overcooking rate of X per Y at the best restaurant and Z per Y at a mediocre one, your visits at least need to approach X before you can distinguish between the best and the mediocre on the consistency point. No critic makes anything near that number of visits.
As I've said before, if you want to judge consistency, use a mechanism like Zagat but with a more serious approach. When you get 1,000 people responding, you get some meaningful numbers on the consistency point. Critics shouldn't be in the business of judging consistency -- it's mathematically not possible for them to do so -- so they should focus on higher-level issues that don't depend on a false concept of consistency. Which is exactly what other arts critics do.