Math Problem Time: Netflix and Broadband

There's no complicated geometry or number theory this time, just multiplication. Urban sophisticate Ezra Klein preaches the virtues of the Roku Netflix box for the 20% of Americans with high-speed Internet connections. Klein notes that "One of the effects of $200-a-barrel oil will be that anything that can possibly be transported electronically will be." That's close, but not quite right: anything that can be transmitted electronically cheaply will be.

But is it cheaper to have users download movies than pay business class postal rates? This provides a convenient excuse to do some multiplication.

1. Suppose a DVD case is 5"x5"x.25". How many DVDs fit into a single 40'x20'x10' shipping container?
2. each DVD contains 4.7 gigabytes of data. What is the total storage capacity of a container full of DVDs? (Note: the abbreviations beyond giga- are terabyte  (1000 gigabytes), petabyte (1000 terabytes) and exabyte (1000 petabytes).
3. Suppose that freight moves at an average speed of 50mph. How many seconds does it take for freight to travel from Bellingham, WA, to Key West, FL?
    
4. Divide the result from #2 by the result from #3. This gives you a measurement in the form of bytes per second. What is the bandwidth of a shipping container full of DVDs across the country? Is this faster or slower than most consumer-grade broadband connections? What if we used Blu-ray discs instead, which contain 50 GB worth of data?
    
5. Suppose the per-mile costs of freight is $3.50 (I did A Google and came up with $3.25, so we'll highball it). What is the cost per megabyte of shipping a container full of DVDs across the country? 5a: A consumer-grade broadband connection of 5 megabits per second, running full-tilt all the time, would yield a cost of $0.0006 per megabyte. Which is cheaper?

I will leave finding the actual numbers an an exercise to the reader, but the bottom line is that sending dense physical storage by mail is significantly faster or cheaper than using broadband, even with oil at $200, $300, or $1,000 per barrel.

Comments

[John]

Most commercial DVDs are recorded on dual-layer discs, meaning they hold 8.5 GB, not 4.7. The data shipping just got even cheaper.

Wonder how cheap it is to move, say, 500GB on a detached hard drive...

[Scott K]

Tsk, tsk... whatever happened to factoring in the various negative externalities into the cost?

[Mike Jones]

This is the phenomenon we used to call "never underestimate the bandwidth of a station wagon full of tapes".

The other question, of course, is latency. If you want to watch the movie *now*, the Roku wins hands down.

[nathan]

Plus, this does not include infrastructure for sorting and processing the DVDs at the Netflix warehouse. I imagine the cost of maintaining servers is less than the cost of processing, sorting, and routing all those disks.

A station wagon full of tapes/truckful of dvds has exceedingly high bandwidth, but who's going to sort through all of them?

As far as externalities go though, don't forget the HUGE! positive externality- that netflix is singlehandedly supporting the USPS.

[Turbulence]

I don't think this analysis gives us any insight into the relative costs involved. Consider:

Why should we assume the cost you supply for bandwidth? I mean, if I fail to download a movie, does that mean I will be billed less for bandwidth that month? Of course not: as with most users, my network provider charges me a fixed price regardless of how much I download.

There's no reason to assume that you have to move all 4.7 GB to satisfy users. All existing services stream compressed video, which satisfies many users already.

One does not ship disks across the entire country; Netflix has a number of regional distribution centers ensuring that for most subscribers, discs travel a much shorter path.

Modeling fuel consumption assuming a single container perfectly packed with discs is ridiculous. As with bandwidth, transport costs at the last mile probably dominate. If subscribing to Netflix causes my mailman to stop and idle his vehicle while he delivers discs more often, there's a cost right there. If he has to stop and idle in order to pickup returning discs more often than he normally would, that cost is compounded.

You could recast this same analysis to prove that costs dictate that most correspondence will be sent using postal rather than electronic mail. After all, a paper letter might have an infinite number of colors and may contain a vast amount of data, so we should assume that each paper letter requires a gigabyte...

[AmIDreaming]

Maybe bulk transfer isn't the question.

More appropriate, maybe: How much will it cost me to get one particular 5GB chunk of data into my hands by 8PM, assuming I didn't know at 8AM that I would need it? A lot, probably, if you can even get it here on time.

Physical shipping may be cheaper, but only in volumes larger than individual-consumption quantities, and only if you know far enough in advance.

[Nicholas Beaudrot]

But it's not even close. It's four thousand times cheaper to ship physical media. even if the last mile costs are huge, the cost of everything but the last mile is much much lower.

And running the CDN to distribute streaming media is not a cheap task.

[Turbulence]

Yes, it is thousands of times cheaper IF you make patently ridiculous assumptions about bandwidth costs. My bandwidth costs do NOT change regardless of whether I download movies from Netflix.

[Chris O.]

I find this highly problematic. I would want 5+ Mbps Internet service whether or not I streamed any movies online. Therefore, on the margin, hardly expensive at all.

[Nicholas Beaudrot]

AmIDreaming: You're looking at the shipping from a single Netflix customer's perspective. You need to look at it frm USPS's perspective.

From their perspective, every day, every house gets some stuff in the mail. Likewise, from Netflix's perspective, they need to add parcels to the set of stuff in the mail that some household is already getting. USPS can do this, at cost, at $0.41 retail. It's probably less for businesses. It's also probably less for businesses, like netflix, that can put their own barcodes on the envelopes, can guarantee that packages won't travel more than 150 miles (except in really sparsely populated areas), etc.

Meanwhile, bandwidth is the reverse: if you want really high bandwidth, you pay more per Mbps than you do for slower connections. At the retail level of a 5 mbps connection, it's $.11 to download a movie; between bandwidth costs and the content distribution network, surely netflix would pay close to their shipping costs for pushing the movie over the internet.

[Nicholas Beaudrot]

Chris O: how much is your free time worth? It will take you 30-40 minutes to buffer enough of the movie.

[Nicholas Beaudrot]

Also I was really trying to ballpark NFLX's bandwidth cost.

[Turbulence]

30-40 minutes sounds like a great deal compared to waiting 3-4 days for postal delivery.

[RiChard]

Except in the 3-4 days waiting for postal delivery I am living my life, probably not waiting impatiently every moment for delivery as I would be more likely to with the 30-40 minute download.

[Turbulence]

RiChard: is there some reason you can't live your life while waiting for a movie download to buffer?

[Jaycal]

Netflix dvds are shipped on a PER MOVIE basis through the post office, not bundled together, meaning the 5.4 Gig cost is measured against their bulk rate mail pricing, whatever that is. In addition, the price for the broadband lowers with time as more data is transmitted over the physical infrastructure, while the deliveries increase along with the fuel, personnel costs, etc.

I agree with Ezra Klein on the long-term prices for downloading vs. delivery. Information transmission is a much smaller infrastructure for the amount of data than roads/trucks using physical storage... think about every local post office those movies have to pass through.

[AmIDreaming]

Nicholas -- the single customer's perspective is the one I care about, obviously! I'm not competing with Netfix, I'm buying their service.

It pays to remember what business Netflix is in. They're an on-demand data provider. The "on-demand" part is as important as the "data" part. If my demand is for immediate delivery, it doesn't matter an iota how much cheaper it is to ship overland. The working window for "on-demand" is at least 24 hours.

That's where the analysis fails. The *price* to me as a consumer may start a little high with online delivery, but it goes up slowly, and as pointed out elsewhere here, the costs are spread over other activities. There's a brick wall where physical transport fails completely, but the incremental gain in price to me as a customer is still very small with online delivery.

[J.W. Hamner]

Netflix's service, while low quality... on the order of Hulu probably... does not require any noticeable buffering even on low end DSL lines like mine. Getting movies off of Xbox Live, which I've also tried, is a longer endeavor since they're much higher quality (many 720p if I'm remembering correctly) so can be 5+ GB. I presume Unbox and iTunes are similar in this regard, though I've never tried them. The difference between "right now" or an "hour or two" is fairly large in my opinion... perhaps not much better than "in a few days". I think downloading a movie in its entirety, to rent for a day or whatever, is a dead end. I can watch better quality movies than a DVD using Xbox Live, and it require no extra equipment to do so... but it doesn't seem that great to need to decide what movie I want to watch several hours in advance... might as well "set and forget" a Netflix queue.

However, I tend to think Blu-ray is the next laser disk... something that is mainly the provenance of videophiles. It is totally going to be lapped for the convenience of streaming whatever you want to see whenever you want it. I don't know how long it will take them to thread the country with fiber optics, but I imagine when you see it get serious penetration that will be the end of the disk as media for most.

One thing I would note is that you haven't considered the cost of making and buying all those disks to ship about the country. A 'net operation needs only hard drives and bandwidth, which are getting cheaper all the time.

[Damion Hankejh]

Wow, this is a horrible analysis. Why? Well, Nathan's comments above already stole the thunder: "ridiculous."

Seattle does have good beer, though.

[Sir Charles]

It really irritates me that on a matter of obvious controversy I have no opinion and am unqualified to give one.

[Blar]

One point that no one has mentioned yet is that shipping movies through the mail requires transferring them twice, once from Netflix to you and again from you back to Netflix. So at retail the USPS shipping cost would be $0.82 (actually $0.84 now) rather than $0.41, although of course it's less for Netflix. With broadband the data only gets transferred once, since they don't need to get it back.

[Paul Camp]

Ummmm . . . I get 8000 cubic feet for your container and .003 cubic feet for your individual dvds. That gives me on the order of 2x10^6 dvds in your container. That means 2x10^6 "last miles" compared to your collective 3600 mile long distance shipping. No way that the dude in the white truck costs $3.50 per mile, but even if he did there are way more last miles than there were first ones. Consequently, the last mile costs are enormous, as they must be for anything that is essentially a handmade product. You can amortize the first part of the trip over the entire container full of disks, but the last mile belongs to each individual disk going to each individual house.

[Chris O.]

DOES a Netflix movie buffer for 30 minutes? It definitely does not take that long on Hulu, which is quite simply a website of awesomeness, even if it does have ads. Obviously if it did that for every movie it would be a huge problem, but I would hope that my high-speed connection would solve that.

[KCinDC]

Not only that, Paul, but are there really 2 million DVDs to be delivered on a single day within 1 mile of the endpoint of the shipping container's journey?

[J.W. Hamner]

DOES a Netflix movie buffer for 30 minutes?

No it doesn't. I'm not going to bother and check, but it might take a minute at most on a DSL line. I've watched all of season one of Heroes on it twice, and maybe half a dozen movies on it. I have a 31" monitor, and I can't say it's a super purty thing to look at, but I'd say it's broadcast TV quality at least. The real problem with it is that I feel there is nothing left to watch but Heroes for the 3rd time.

It's free to check out if you have a regular Netflix plan.

[Kaleberg]

Shipping containers are 40' x 8' 6" x 8' external dimensions, just in case you ever wanted to know. They are great references for photogrammetry.

For bulk shipping, physical delivery still makes sense, but most people barely ship enough data to make it worth while. Even Netflix customers only get one or two DVDs a day. On the other hand, when Jared Benedict (redjar.org) bought all of the USGS topographic maps, he shipped them to archive.org on a hard drive rather than trying to upload them. I forget what his transfer rate was, but it was pretty impressive.

[Crissa]

No, Netflix doesn't help with the 'now' bit - only works on PCs.

[cw]

Another basic problem with this analysis is that netflix does not load up tractor trailers of discs and ship them all to one location. So the number of discs that could theoretically fit into a trailer (without boxes or packaging evidently, if I read Nick's math right) is irrelevant. The better question is the marginal cost to the postal service for shipping one disc, and as some commenters pointed out, that is near zero, because postal carriers visit every house every day, regardless of of the volume of mail. The infrastructure is already in place, and adding one small piece of mail doesn't make that much difference. But you have to consider that each disc is going to a completely different location, requiring sorting and handling multiple times. That's where the cost comes in.

[Adrock]

We have this problem in our industry as well. Customers want their data backed up instantaneously and complain about bandwidth. When we tell them they could put it on tape and ship it for less cost and overall bandwidth being cheaper, they still balk. But they have good reason. They want that stuff in a vault RIGHT NOW, which you can't get with tape. Which is all to say, there are a lot of different factors consumers consider when purchasing "bandwidth."

[Stuart Eugene Thiel]

You omit the relative merits of watching said movie on your 19" monitor or on your 31" TV. To be sure, I could buy a new monitor to even things up, but that's a big expense.

[Turbulence]

Stuart,

Inches matter less than angular field of view and since people typically sit much closer to their computer monitors than they do to their TV, they probably have a wider field of view with their monitor. I ran some rough numbers and verified that for my setup (21 inch monitor 18 inches away versus 37 inch television 6 feet away), the monitor has a wider field of view.

[Patrick Minton]

Forgive me if someone mentioned this, but this completely ignores economies of scale.

1) $.0006 may, in fact, be the current price of sending a megabyte, but it is almost certainly not its marginal cost. That is, I could almost certainly broker a better deal with a provider here.

2) Someone already pointed out that this calculation ignores many costs: the cost of the manufacturer to ship physical inventory to the wholesaler, the wholesaler's shipping costs to Netflix, the inventory costs, the factory costs of the production of DVDs, etc. All of which add up to many millions of barrels of oil, both in terms of the oil used to build the factories and in terms of the oil used to keep the factories/trucks/etc running.

[J.W. Hamner]

I hate to have been turned into the Netflix cheerleader here, but I should point out that the Ezra Klein post that started all this is about the Roku box which is meant to deal with the 19" monitor vs. 31" television issue. It's only $100 vs. an giant LCD monitor.

[ohwilleke]

The real competition in the case of Netflix is not USPS v. download, but Blockbuster v. Netflix.

A typical urbanite is probably within 5 miles of a local Blockbuster and pays a little under $4.50 for the rental, plus almost as much for the cost of driving to the video store and back twice, once to get the video and once to return it. But, getting the movie from your local video store to your home can be accomplished in under 15 minutes if one is decisive about it.

With my (not quite bare bones) DSL connection downloading video form iTunes or Amazon Unbox takes something like 50% to 90% of the time it takes to view the video -- maybe Netflix is better, but Blockbuster still wins the bandwidth fight.

USPS first class mail can't compete with the speed of Blockbuster and probably costs closer to $1.50 there and back (I think a DVD in a jewel box is more than once ounce); even express mail doesn't cut it (at about the same cost one way as a round trip to Blockbuster). Even with regional distribution, the bandwith of shipping a DVD to a particular residence doesn't begin to approach either renting a video or getting it via electronic transmission.

From a customer's perspective, given that a broadband connection, the computer, the TV and the electricity are usually fixed overhead costs incurred whether or not a video is downloaded, Netflix via broadband is effectively free in terms of transportation costs, and the downloading speed is far more competitive than USPS with Blockbuster, although it lags a little. But, if you rent more than one video a month, the marginal cost of Netflix by broadband is far less than the marginal cost of Blockbuster.

This discussion does suggest two easy ways to economize in the video business, however. One is to have rental DVDs that expire after a date certain, eliminating the need to return them. With $4 a gallon gas, a round trip to the video store can easily cost $2.50; as gas prices rise, the marginal cost of returning a video makes this part of the deal uneconomical.

The other is to have video stores burn their own disks. While a container load of DVDs may be cheaper to ship than to download, the typical video store gets just a handful of new releases each week. Downloading a single copy of new releases once to a computer at (or sending them by mail to) each video store, and then burning them locally, may be cheaper than shipping multiple copies of the same DVD from a central location to each video store.

One of the key flaws in the calculation above is the calculation of the bandwidth of a shipping container full of DVDs. If each one is different the bandwidth of a shipping container full of DVDs is huge. But if you ship multiple copies of the same film in that shipping container destined for multiple destinations (and since only a handful of new titles come out each week, there is a real limit on how many new titles can be shipping in a container without being redundant), then the amount of data in a shipping container of DVDs is a mere 4.7 GB, which happens to be highly redundant (the same is true of electronic transmissions -- all modern downloading code contains significant redundancy to prevent errors in transmission, although far less redundancy than a shipping container full of the same DVD).

[JR]

Hi:

Long ago (by internet years!) I read an interesting story about astronomers, using the very highest speed Internet connectivity, instead decide to UPS boxes with hard drives inside, because of the high data density.

You see, astronomy yields an unbelievable amount of data to analyze, at observatories in high mountain ranges in the most remote parts of the world, where it's dark at night.

No, I mean really, Really dark at night.

Their biggest problem is customs, who won't believe that what is being shipped is the data, not the computer/hard drive. There's no duty on data, but hi-end hard-drives on the other hand...

So this isn't new news, it's old news.

Sorry!
JR

[Dr. Psycho]

Until recently, Mrs. Psycho and I had various options for watching a movie: we could eight blocks to a rental place, we could go six blocks to a McDonald's and use the DVD vending machine, we could go four blocks to the library, we could go upstairs and download a movie with our broadband connection, or we could just turn on the TV.

We could turn on the TV, that is, until we concluded that we just weren't watching much television lately, mainly thanks to all the time we spend browsing the Internet.

The most recent feature film we watched we got from the library. The most recent video we paid for we got at a dollar store about a mile and a half away.

Oh, we could also go about two miles to watch a film in a theater, too.

Or we could watch one of the hundreds of films and TV episodes we have stored on VHS and DVD, many of which we bought years ago and still haven't watched.

But as I said, we spend more of our time these days on the Internet. There sure is a lot of stuff online....