## Restaurant histograms of the day

I have a column at Grub Street today looking at some check-by-check level data for five New York restaurants. I got the data from the good people at Bundle, and NY Mag turned it into pretty charts, complete with a red line marking the median amount spent at each place.

But of course there’s much more to these charts than could be fit into a Grub Street column. So here they are again; this time I’ve added two more datapoints to each one. The blue line — which is always to the right of the red line — marks the *mean* cost of a restaurant meal. That’s the number you’ll see if you visit the Bundle website. And the blue Z marks the amount that Zagat thinks a diner is likely to spend, with tax, tip, and one drink. At Per Se, for instance, the mean cost is $878, while the Zagat cost is $303. (This is a slight apples-to-oranges comparison, since the Zagat price is for one person, while the Bundle data is not per person but rather per credit card or debit card. But both are intended to give an idea of how much the restaurant is going to cost, and the Bundle data is surely much more accurate on that front.)

Zagat reckons that the “cost” of a meal at Megu is $87 — which is surely meant to mean *something*. But few people pay much attention to Zagat cost estimates, for good reason — in many cases, it’s actually impossible to get out of a restaurant for the amount of money listed in the Zagat guide. At Per Se, for instance, even with no drink at all, the $295 prix-fixe menu, plus tax, will run you $320.

So how much does Megu cost, in reality? It turns out that question is pretty much impossible to answer. On the Bundle page for Megu, we can see that the average amount of money charged per credit card is “about $200 to $210”; that’s based on a mean expenditure per card of $198.82. But if you look at other kinds of average expenditure at Megu, they look very different.

The mean expenditure, $198.82, is basically the total amount spent there divided by the number of cards used to pay for it all. So if someone pays for a massive blow-out party there, that’ll raise the mean expenditure for everybody else. The median expenditure at Megu is substantially lower than the mean — it’s $126.87. Finally, there’s the mode. If you put all the charges at Megu into $10 buckets, instead of the $25 buckets in these charts, then the mode charge at Megu is between $70 and $80. More than 7% of charges at Megu fall in that range, which means that if you charge your card at Megu, there’s a 1-in-14 chance that you’ll spend seventy-something dollars on that card. That doesn’t make it exactly probable, but it’s more likely than any other amount.

But why try to reduce everything to a single number? This is one of those cases where a picture — or a histogram, rather — is worth a thousand words.

The Megu chart is actually about as simple as Bundle’s restaurant histograms get. Megu was not picked at random. It was picked because it gets lots of customers, and therefore generates a lot of datapoints in the Bundle database; because it is open only for dinner, which means that the numbers aren’t complicated by mixing up a relatively low-spending lunch crowd with a higher-spending dinner crowd; and because it doesn’t have much of a bar scene — if you drink there, you’re likely to eat there too.

But even so, the range of expenditures at Megu is enormous. More than 4% — one in 25 — of the card charges at Megu are for less than $20. And at the other end of the spectrum, more than 1.5% of the card charges are for more than $800; in fact, according to the Bundle data, you’re just as likely to spend over $800 at Megu than you are to spend between $600 and $800. What’s more, if you look just at the people spending more than $800 at Megu, their average expenditure is a whopping $1,894. The tails, in other words, are long.

I’ll admit that I was hoping to see some humps in Bundle’s histograms — what statisticians call a bimodal distribution. If Babbo’s histogram, say, has one spike at $100 and another spike at $200, then that would be a pretty good indication that eating at Babbo is likely to cost you about $100 per head. The $100 spike would be people paying for themselves; the $200 spike would be people paying for someone else as well. And then maybe we’d see another spike at $400, too, where people picked up the check for a party of 4.

But I had no luck on that front. If you squint and hope and delude yourself a little, maybe you can find those spikes at $100 and $200 and maybe even $400. But what about that spike at $250?

The main message I get from the Babbo chart is just that there’s an extraordinarily large range of checks at Babbo — you have a pretty good chance of coming up just about anywhere between $60 and $270. Which is not particularly helpful if you’re someone trying to anticipate how much the restaurant is likely to cost.

In many ways, though, the most interesting of all these histograms is the one for Per Se. Here, everything is set: the menu is a fixed price, the service is included, and while some people are sure to push the boat out when it comes to wine, you can pretty much expect that most checks there are going to be much of a muchness. Can’t you? Actually, no, you can’t.

One in every 35 visitors to Per Se spends less than $75 there — how is that even possible? The mean, median, and mode are relatively close together — $878, $768, and $800 respectively — which implies to me that if you take one other person there for dinner, it’s very easy to end up spending about $750 to $800 altogether. Except, that seems to be very much on the low side. Food alone can run you as much as $610 per person, and most people will spend hundreds more on wine.

At the far ends of the spectrum, fully 18% of the people spending money at Per Se are spending less than $325, which barely seems possible, even if you take into account the 3-days-a-week lunch menu at $185 per person. And that spike at the end representing people spending more than $3,000 is pretty substantial — those checks account for less than 2% of the payments run by the restaurant, but fully 10% of all its dining revenues.

In between, there’s all manner of activity going on. There are two spikes at $600 and $800 — people like to put round numbers on their cards. 44% of all spending takes place in the range between $575 and $1,100 — but that just means that 56% doesn’t.

All of which leads me to conclude that the very idea of a typical meal at a restaurant — or the idea of what a restaurant “costs” — just doesn’t stand up to scrutiny. At Mr Chow of Tribeca, Zagat — which we can use as a guide to the minimum price — says a typical meal will run you $77. Bundle says the “real price range” is $200 to $210. The median amount charged to a card there is $145. And 2.1% of customers spend more than $800, while 17% spend less than $70. What will you spend if you go there? Pick a point on the chart and guess. One thing’s for sure, though: you’re wrong if you think that the diners at Mr Chow Tribeca are some kind of homogenous and interchangeable mass. They might look like that from the outside, but in fact there’s a lot of variety there.

It would be nice indeed, then, if there were some neat formula where you could take the price of the average entree, say, multiply it by three, and get a typical all-in price per person. Sadly, there isn’t. Some restaurants make most of their money on cocktails; others concentrate more on the food. Some allow diners to eat cheaply, others don’t. But the big picture is that the differences between restaurants pale in comparison to the differences between diners. Some people are just going to spend a lot, others are going to get away with spending much less.

The next best thing, at least for people like me, would be a look at these histograms. If we had that, along with the ability to easily drill into the data, it would be an invaluable addition to Bundle’s service. Bundle’s $200-$210 number for Mr Chow of Tribeca, for instance, is interesting, but fully two in three people picking up a check spend less than $200 there.

If Bundle doesn’t want to show histograms, then at least they should switch from mean to median. But in any case, their service is really exciting, since it’s the first opportunity we’ve ever had to be able to make like-for-like comparisons between restaurants when to comes to the question of how much you’re likely to spend. It’s early days yet. But this could be the most important step in years when it comes to helping people know just how much different restaurants cost.

Wow — could feed a family for a week for the cost of the least of these places!

“This is a slight apples-to-oranges comparison…” seems like quite an understatement. Per check would most likely include and average of 2+ diners, and would also include things like bottles of wine and multiple drinks.

One factor to keep in mind for many of these restaurants—even those that do not have an active bar scene—is that small charges may in fact reflect the cost of drinks purchased at the bar while waiting for the table, but not transferred to the actual table check. Whether this occurs in the restaurants you listed is an empirical question, but I’ve been to enough restaurants—even fairly nice ones—that force you to close out of your bar tab incurred while waiting for the table. The bottom line is that I am inclines to discount (somewhat) the data on the lower tail of the distribution as not representative of an actual meal. It may also explain why the distribution is more like a chi-squared (k > 2), rather than a power distribution (which one may expect ex ante).

These charts are all pretty conclusive to me. They all say one thing. And that is that I shouldn’t eat at any of these restaurants.

Articles like this are great cases in point of the whole 99% to 1% concept.

Seems to me that you don’t dwell on the most important confounding factor: how many people are eating on each charge. Yes, you mention it and acknowledge it, but in the end, if you don’t know this, you cannot say much of anything. And this explains, better than anything else, why you cannot say much of anything. Why are you surprised?

Modes? Medians? Means? Chi-squared vs. power-law? All ridiculous to consider in view of the fact that what you are trying to determine — some notion of how much it costs *per person* to eat, say, dinner at one of these joints — is simply not possible to determine without knowing the number of diners that goes along with each check.

You cannot even say, except for your personal experience dining in some of these places where you doknow how many people were paid for, whether the mean at Megu is explained by the Zagat number together with the hypothesis that on average, people eat in pairs — or a bit more. Maybe each couple brings a baby?

As other have said, with no way to determine the size of the party for each check, this is junk data. Maybe the place that gets lots of $3,000 checks, gets those checks when it hosts birthday bashes with fifty people taking up the whole dining room, or whatever.

Seems like an awful lot of not very productive analysis when you could have just taken photos of their menus and we could see what they actually cost.

Median. Go with the median.

If you’re looking at wealth, for example, the mean tells you the wealth of the pocket the typical dollar lives in. The median tells you the assets of the typical person.

Look, there _is_ a lot of variance in restaurant bills. But if you want to _compare_ locations, and do so from the point of view of the “typical” visitor (and I know the typical visitor is going to vary from one location to another), you’re still best off with the median.