Optimizing the Pizza Selection When Ordering for Groups

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Optimizing the Pizza Selection When Ordering for Groups

Postby MFHodge » Wed Oct 31, 2007 6:22 pm UTC

The department ordered pizza for lunch today ( :D ). The order was two pepperoni and two supreme ( :( ). I think was the first on to walk up and I started looking around for the cheese-only pizza. I was stuck with pepperoni. The next guy looks around for anything vegetarian. He ends up with only salad.

This seems to happen all the damn time. Cheese is almost always the first one gone. The leftovers are almost always the one with tons of stuff on it. I suspect that anyone would eat a slice that has a subset of the toppings they like. For example, if your first choice is mushrooms and olives, you would probably be almost as happy with a pizza with only mushrooms or only olives. This leads to the conclusion that in the general case, pizzas with fewer toppings will have the greatest utility. Toppings should only be selected when there is a high degree of probability that sufficient people will prefer that combination as their first choice to account for the whole pizza.

I think with the collective intellegence of the xkcd fora, we can come up with an optimum strategy for ordering pizza for a group.

Here is my initial take, based on casual observation over my life:

  • 1/3 Plain Cheese
  • 1/3 Pepperoni
  • 1/6 Other single topping (Veggie before meat)
  • 1/6 Other multi-topping (Meat before veggie)

These are my suggested cases, based on total count.

3 -> 1 Cheese, 1 Pepperoni, 1 Single Veggie
4 -> 1 Cheese, 1 Pepperoni, 1 Supreme, 1 Single Veggie
5 -> 2 Cheese, 1 Pepperoni, 1 Supreme, 1 Single Veggie
6 -> 2 Cheese, 2 Pepperoni, 1 Supreme, 1 Single Veggie
7 -> 2 Cheese, 2 Pepperoni, 1 Supreme, 1 Single Veggie, 1 Sausage
8 -> 2 Cheese, 2 Pepperoni, 1 Supreme, 1 Single Veggie, 1 Sausage, 1 Veggie Supreme
9 -> 3 Cheese, 3 Pepperoni, 2 Supreme, 1 Single Veggie, 1 Sausage, 1 Veggie Supreme
etc.

Thoughts? Improvements? I'm working on an Excel function for it . . .
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby Bakemaster » Wed Oct 31, 2007 6:30 pm UTC

I would weight cheese more heavily, myself, for a better margin of error. There aren't a huge number of people who like pizza only with toppings and won't eat plain cheese. Plus, the more slices one person is going to eat, the more likely they are not to care if one of those slices (the last one, I'd assume) is "leftover" or "other". Beacuse they are hungry and they want pizza.
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby TigerX » Wed Oct 31, 2007 6:33 pm UTC

I think you have to account for the specialty pizza as well (i.e.: Pineapple and Ham).

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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby MFHodge » Wed Oct 31, 2007 6:34 pm UTC

TigerX wrote:I think you have to account for the specialty pizza as well (i.e.: Pineapple and Ham).

I thought about that and came to the conclusion that they had no place in the Group Order System. That's why they are "specialty". If you have a huge number, then I guess they could take the place of a meat-based multi-topping.
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby 22/7 » Wed Oct 31, 2007 6:42 pm UTC

Yeah, as much as I love me some Hawaiian Pizza, they have no place in the "general case." I think your original pattern looks good, but with introduction of the vegetarian supreme, sausage, etc. you are creating a pain in the ass for the Excel spread sheet (unless there's a "round down" function in Excel I'm not aware of).

Of course, I'm one of the people who you'd love to have at the party, because unless taco or Hawaiian pizzas are present, I pretty much eat whatever there is the most of after the first round. However, if taco or Hawaiian are present, I generally eat as much of that stuff as quickly as possible, occasionally resulting in an ingested hand or shoe. Luckily, none of them have been mine to this point.
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby MFHodge » Wed Oct 31, 2007 6:44 pm UTC

Here is my revised theory with some good math behind it.

For "n" Pizzas:

Cheese = CEILING(n/3)
Pepperoni = ROUND((n-Cheese)/2)
SingleTop = CEILING(n-(Cheese+Pepperoni)) [Odd Singles are Veg, Even Singles are Meat]
MultiTop = FLOOR(n-(Cheese+Pepperoni)) [Odd Multis include Meat, Even Multis are Veg Only]

Gives:

Code: Select all

 n   C   P   S   M
-----------------
 3   1   1   1   0
 4   2   1   1   0
 5   2   2   1   0
 6   2   2   1   1
 7   3   2   1   1
 8   3   3   1   1
 9   3   3   2   1
10  4   3   2   1
11  4   4   2   1
12  4   4   2   2
13  5   4   2   2
14  5   5   2   2
15  5   5   3   2
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby Robin S » Wed Oct 31, 2007 6:45 pm UTC

Are you looking to maximize expected utility, or minimum utility? If the latter, just go for all cheese, every time (unless you happen to know exactly what toppings everyone likes).
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby 22/7 » Wed Oct 31, 2007 6:46 pm UTC

Dammit, now I want pizza. Looks good. I'm not familiar with the "ceiling, round, and floor" functions though.
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby MFHodge » Wed Oct 31, 2007 6:49 pm UTC

Robin S wrote:Are you looking to maximize expected utility, or minimum utility? If the latter, just go for all cheese, every time (unless you happen to know exactly what toppings everyone likes).

Looking to maximize general human happiness. With all cheese, everyone gets fed, but if you have more than a handful of people, you have a fairly good expectation that there is enough interest in a pepperoni pizza that it will be utilized and therefore give a higher return than a plain cheese.

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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby Sprocket » Wed Oct 31, 2007 7:05 pm UTC

Bakemaster wrote:I would weight cheese more heavily, myself, for a better margin of error. There aren't a huge number of people who like pizza only with toppings and won't eat plain cheese. Plus, the more slices one person is going to eat, the more likely they are not to care if one of those slices (the last one, I'd assume) is "leftover" or "other". Beacuse they are hungry and they want pizza.


I don't like pizza without toppings. ::shrug: I'm unusual. As a kid I didn't like peperoni because it was too spicy, later I really liked peperoni, and today I only generally like veggie of some kind, but plain cheese pizza sorta makes me go "blech"
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby Robin S » Wed Oct 31, 2007 7:07 pm UTC

Personally, when it comes to pizza I will eat more or less any topping I am likely to encounter. However, I still have preferences and so if there is competition for slices I will still follow the basic rule that Bakemaster outlined.
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby Bakemaster » Wed Oct 31, 2007 7:11 pm UTC

That may be in part due to a surfeit of really good pizza places in this area. There's pizza I like, and there are specific specialty pizzas I adore, like the Urban Cowboy—bacon, red onion, grilled chicken, sliced tomato with a blue cheese-based white sauce—but I have yet to find a really stunning traditional cheese pizza. The Sicilian pizza at Pinnochio's is pretty good, and Upper Crust makes a good effort. I haven't explored the North End, which I probably should if I ever want to be authoritative on Boston area pizza.
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby 22/7 » Wed Oct 31, 2007 7:16 pm UTC

Who makes this urban cowboy? It sounds delicious.
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby PictureSarah » Wed Oct 31, 2007 7:17 pm UTC

I think the pizza of last week was pretty damn good. A tad puffy, but tasty. Not applicable to discussion of mass pizza ordering I suppose, though.
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby Azrael » Wed Oct 31, 2007 7:40 pm UTC

Hodge, I like the numbers laid out above, but suggest a couple of non mathematical bounds:

I wish to suggest that you remove Supreme entirely - I feel that people who want supreme will be satisfied with other options with a 90% happiness ratio.

Besides a Veggie Supreme, no pizza should have more than 3 toppings total. All multi-category pizzas (category = meat, veggie) should have three toppings in a 2:1 ratio of one type category to the other, probably favoring a 2 veggie to 1 meat.

On a side note, we've had this exact discussion before 'round the lunch table. One time we had a 200 person pizza lunch. One of the chosen pizzas was ... garlic. And I think they got a half dozen of them (out of maybe 70 total). Re. Tard. Ed.

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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby Bakemaster » Wed Oct 31, 2007 7:49 pm UTC

22/7 wrote:Who makes this urban cowboy? It sounds delicious.

The Urban Gourmet restaurant in Somerville, where I used to work. Unfortunately the owners sold the place along with the menu, and then it burned down and the guy who bought it is still rebuilding. They reopened a new place in another part of the city and while they can't legally call it the "urban cowboy" anymore, they still are probably the only ones who know how to make it right so they call it "chicken club" which is a much lesser name. I wouldn't want to eat any pizza that's named after a sandwich involving mayo.

Back on the topic of ordering pizzas, Hodge, your 2.0 is much improved. I think 2 cheese for 8 total pizzas was a dangerous proposition. What about the danger of getting only one of an interesting and uncommon specialty pizza in a large group where more than 8 people want to try a slice? Should we take that into consideration for cases of a certain size?
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby MFHodge » Wed Oct 31, 2007 8:04 pm UTC

Bakemaster wrote:Back on the topic of ordering pizzas, Hodge, your 2.0 is much improved. I think 2 cheese for 8 total pizzas was a dangerous proposition. What about the danger of getting only one of an interesting and uncommon specialty pizza in a large group where more than 8 people want to try a slice? Should we take that into consideration for cases of a certain size?

Agreed about 2 Cheese / 8 Pizzas . . . that was a bad one.

Local specialties might just have to be a case-by-case. If it is true that most people would want at least on slice of it, then it should probably be handled before any algorithm. I generally think you get one pizza for every 3-4 people (depending on your crowd and party type). If you have twenty people, you probably get two or three specials and then just apply the four or five pizza system for the rest.

Also: I'm now thinking that pepperoni may be over-emphasized here. It is the most popular topping, but should it be 1/3 of overall?
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby bbctol » Wed Oct 31, 2007 8:12 pm UTC

Just eat a damn sandwich.

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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby MFHodge » Wed Oct 31, 2007 8:13 pm UTC

bbctol wrote:Just eat a damn sandwich.

Don't even get me started on ordering sanwiches!
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby Tractor » Wed Oct 31, 2007 8:14 pm UTC

Bakemaster wrote:Back on the topic of ordering pizzas, Hodge, your 2.0 is much improved. I think 2 cheese for 8 total pizzas was a dangerous proposition. What about the danger of getting only one of an interesting and uncommon specialty pizza in a large group where more than 8 people want to try a slice? Should we take that into consideration for cases of a certain size?


This leads to other questions on numbers:
What size pizza are we talking about here? 8-slice? 12-slice? Party square-cut style? Other?

I think for groups less than around 10, 8-slice would be optimal. I'm not sure where the cutoff from 12-slice to party style occurs though, may be on a per-case basis, not size-dependant.

How many people merit multiple pizzas?

I think optimal use of the chart doesn't start until you have at least 5 people. 4 or less and you can stick to 2 pizzas, having half-topped pizzas where necessary. From my experience, it tends to be that a person will eat about 4 pieces of pizza. This should probably be the general idea when deciding how many pizzas to order, rounding up of course.
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby Azrael » Wed Oct 31, 2007 8:20 pm UTC

For the sake of this thread, all pizzas are standard national size -- 16" round with 8 slices

And I've found that 2.5 people per pizza works fairly well.

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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby hendusoone » Wed Oct 31, 2007 8:38 pm UTC

Regarding the Pepperoni issue:
Break it into its own group, single-topping meat. Every Odd number pizza in this group is Pepperoni, every Even number is some other meat of choice - ham or sausage, never anchovies, possibly chicken.

Number of pizzas can depend upon the time of day, with culture taken into account. In areas where the large meal is dinner, do 1 pizza for every 3 people at lunch and 1 pizza for every 2 people at dinner. The other way around when the large meal is lunch.
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby 22/7 » Wed Oct 31, 2007 8:41 pm UTC

Thanks Bake. If ever I'm in Boston(ish) I'll look you up so you can point me in the right direction.

VTHodge wrote:Also: I'm now thinking that pepperoni may be over-emphasized here. It is the most popular topping, but should it be 1/3 of overall?


Agreed that the pepperoni is over-emphasized, but that's probably just me (I'll eat it, but it's not my favorite, by any stretch). I would tend to slide the second pizza of a new set down to the single topping or multi-topping first, but again, I don't particularly care for pepperoni enough to eat 4 or 5 slices of it. That said, what about *not* separating pepperoni from the other single topping pizzas, and deciding the content of those single topping pizzas based on a group consensus, and when one is not available, maybe make it 1/3 or 1/2 (of the single toppings) pepperoni and then separate the rest among things like sausage, onion, pineapple, goat anus, etc.

Edit: Ninja'd

hendusoone wrote:Regarding the Pepperoni issue:
Break it into its own group, single-topping meat. Every Odd number pizza in this group is Pepperoni, every Even number is some other meat of choice - ham or sausage, never anchovies, possibly chicken.


This doesn't really change the ratio of pepperoni to non-pepperoni single topping pizzas from what it is now, as it's currently at (approximately) 1/2 of all single topping pizzas, if not a little more.

Edit 2.0: Just kidding, I was going off the first one. This would indeed decrease the number of pepperoni pizzas from Hodge v2.0. And I'm ok with it.

Edit 2.1: I just got back from lunch. I had pizza. This thread is to blame.
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby Narsil » Wed Oct 31, 2007 9:21 pm UTC

I order all pepperoni.
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby Ptera » Thu Nov 01, 2007 12:02 am UTC

I'm allergic to cheese, but I can get by pretty well by taking apart my pizza, and then reassembling it cheese-free. For my case, it's nice to have something with toppings, otherwise I'm just eating saucy bread. (Sauc-ay!)

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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby wing » Thu Nov 01, 2007 4:34 am UTC

Based upon EXTREME amounts of pizza ordering for nerds on a college campus, I have the following rules:

For groups of 20 or less:
2 people per large pizza.
50% cheese. 50% pepperoni. Add one Meatpocalypse (Every meat on the menu except the ones that swim) for every 10 people.

For groups of 21-50:
3 people per large pizza
33% cheese 66% pepperoni. Meatpocalypse rule is strictly optional.

For larger events:
5 people per large pizza
50% cheese. 50% pepperoni. NO meatpocalypse

For paid entrance events:
Take an informal poll at the least - at best, take ORDERS. I've ordered 90 individual-person medium pizzas before.

For recurring events where the same people are expected (i.e. meetings, etc.):
On the first occurance, follow the appropriate rule above, and somewhere on the agenda MUST be "Arrive at pizza consensus" where the group selects the toppings and quantity of pizza required for the future.
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby Zohar » Thu Nov 01, 2007 1:42 pm UTC

Just a note, as a vegetarian, I wouldn't eat a cheese-only slice from a pizza with meaty areas. Since it usually only gets complicated if you have a group larger than three people and then you order multiple pizzas, why not completely seperate vegetable and meat pizzas?

Also, I was in Spain and I had pineapple and banana toppings on a pizza. It was yummy and weird (my favorite is pineapple + onion).
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby Toeofdoom » Thu Nov 01, 2007 1:57 pm UTC

I'd usually go with ordering half a pizza for each person, asking their preferences then adding a couple of margheritas on the end (thats what "cheese" pizzas are called around here. also this reminds me I need to make another one of those macaroni cheese pizzas, in a couple of weekends when my family is away maybe.) I mean, you cant really get too much pizza anyway.
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby idont_know12 » Thu Nov 01, 2007 9:41 pm UTC

Bakemaster wrote:I have yet to find a really stunning traditional cheese pizza.

I don't know about "stunning", but I once had a cheese pizza that had an alfredo sauce instead of traditional. It was good.
That's probably on an individual basis though.

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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby 22/7 » Fri Nov 02, 2007 8:23 pm UTC

So far I've found almost every pizza tastes better (to me) with barbecue sauce rather than the traditional tomato sauce. Of course, this is highly dependent upon the type of barbecue sauce being used.
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Re: Optimizing the Pizza Selection When Ordering for Groups

Postby Bakemaster » Sat Nov 03, 2007 8:52 pm UTC

@idont_know12: I was talking specifically about Boston area restaurants. I've had a really incredible homemade pizza and one example of great traditional neapolitan restaurant pizza somewhere I was traveling years ago... I was visiting family, so that narrows it down to Chicago, Richmond, or the general L.A. area. Not much help.
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