Dot Physics

There was a Buzz Out Loud episode in the not-to-distant past where the discussion of youtube came up. I can’t remember the exact details, but the main point was that it would be impossible for google (the owners of youtube) to review all of the videos that were submitted.

And here is my calculation. How much would it cost google a year to do this? First, I need to pick some variables (and I will first do this symbolically – then you can put in your own values if it makes you happy).

  • Submission Rate (s): This is how many minutes of video are submitted each minute (so the units would be minutes/minute). Just as an example, if only one person was using youtube and streamed their whole life – s would be 1 minute/minute.
  • Pay Rate (p): How much do you pay a reviewer per hour (units: US Dollars/hour)
  • Reviewer efficiency (e): How much of a reviewer’s time is spent switching videos and stuff. This is a unitless quantity that must have a value over 1. For example, if a reviewer spent 10% of the time on stuff not related to reviewing, then e = 1.1. Also, this probably would depend a lot on the system that delivers videos to the reviewers.
  • Number of Reviewers (n): I think this one is clear.
  • Movie speed (v): I just thought of this one. What if the reviewers watch a video at a compressed rate. Movie speed of 1.5 means that a 1 minute video would only take 0.67 minutes.

Now for the calculation. No wait, how about a diagram?

i-dd5fb6c883ff2e75f4e74a501bfd61bd-2010-03-01_untitled_1.jpg

The main point of this diagram is that whatever videos come in, have to be reviewed. The Law of Conservation of Videos.

Ok – let me start with an example. Suppose that 20 minutes of video are submitted every minute. If there was only one reviewer (with no movie speed ups) it would take the reviewer 20 minutes to review that video. So, what would happen for the next 20 minutes? You would need 20 more reviewers, where each one would start to review a movie and be unavailable for at least 20 minutes. In terms of my variables, this would be:

i-e0fc162c6e70b9f0c402e5aa7454d5a2-2010-03-01_la_te_xi_t_1.jpg

Note that the units work out fine since both s and n really don’t have any units. Now, what if I want to include the efficiency? The greater the percent of time spent on administration stuff, the more people you would need. Then:

i-4b54ea66bd038aae45442bb03e992516-2010-03-01_la_te_xi_t_1_2.jpg

Units are still ok since efficiency also is unitless. What about the movie speed? The greater the movie speed for reviewing movies, the fewer reviewers google would need.

i-9f1ccb6b95ba9b638f0339fe67a211c6-2010-03-01_la_te_xi_t_1_8.jpg

Units are still ok. To get the cost, I need n. Note that n is not how many people they need to hire, but how many people they need working (at any given time – assuming the video submission rate is constant).

i-b73391e6a2a765dc6a75de34d00bd570-2010-03-01_la_te_xi_t_1_9.jpg

So, how much would this cost a year? If the payrate (P) is in dollars per hour, then the yearly cost would be:

i-d11b389ba1f7012acc127797b88191f6-2010-03-01_la_te_xi_t_1_10.jpg

Now for the estimates

  • P = $15/hr. I know this is much greater than minimum wage, but I am assuming there are other benefits costs and stuff.
  • s = 20 min/min. Seems this is what they said on Buzz Out Loud. Of course, you could probably find a better value for this.
  • e = 1.05. Total guess here. So 5% of the reviewing time is wasted. But maybe this should be even lower. What are the reviewers going to waste their time on? Watching youtube? I guess they could still play solitaire.
  • v = 1.5. I picked 1.5 times for the playback speed because this is what the ipod does for podcasts if you want to listen faster. Works ok.

With these values, I get a yearly cost to google of 1.8 million dollars.

Update

Ok, I guess my guess of 20 minutes of video every minute was pretty wild. According to Youtube’s fact sheet, they claim that 20 HOURS of video are uploaded each minute. This would change my estimate to 108 million dollars each year.

Thanks to the readers that pointed out my poor guess.

Comments

  1. #1 Z
    March 1, 2010

    With all due respect, with a result like 1.8 million dollars you should probably re-examine your assumptions. I can’t begin to tell you where the flaw is, but based on some semi(?)-reliable real numbers there’s definately a problem.

    Here’s some Kansas State University stats from 2008 about youtube uploads, etc: Digital Ethnography » Blog Archive » YouTube Statistics

    Here’s the youtube blog from Wednesday, May 20, 2009, where they claim to have 20 Hours of video uploaded every minute. That’s:

    20 hr/min x 60 min x 24 hr x 365.25 d/year =

    10,519,200 hours of video to be viewed per year, or 1,200 years per year. And those are full 24hr days, or at least 3 shifts with 1,200 people each to watch it all, with no days off.

    Back of the envelope guess, ~5,000 employees working 5 days a week for 8 hours a day doing nothing but viewing videos and clicking YES or NO could manage the load.

  2. #2 Rob
    March 1, 2010

    Z:

    It’s pretty easy to reconcile Rhett’s and your figures. If your 5000 people cost $30K/year (all up) each, then you’re looking at $30,000*5000=$150,000,000/year. Rhett figured 20 minutes/minute uploaded, you found 20 hours/minute. 60 minutes in an hour means that you’ve determined that 60 times as many people are needed as Rhett estimated. 60*$1.8 million is $108,000,000. Close enough for a Fermi problem.

    By the way, dimensional analysis is more powerful than is commonly known!

  3. #3 Z
    March 2, 2010

    Yes, I realized a bit after posting that I could have saved myself a lot of trouble by just multiplying by 60. That’s why I’m not a mathematician. My “with all due respect” was sincere, because I checked the math and it worked.

    There’s still a lot more to it than $150,000,000/yr though. You need supervisors (1/25?), managers (who knows how many), HR to manage the constant turnover, some infrastructure, plus you’ll need to ensure you’ve got 70-100 languages covered by those 5,000 people. Then there’s cultural senstivity–what if something is offensive to Americans but funny to the Japanese?

    Who’s going to go through X billion videos and mute every instance of “Happy Birthday to You”?

    Then there’s the law: Who’s law, and when (and where)? Last I checked, chewing gum is illegal in Singapore. The multi-national lawyers’ bills alone would run into the billions for writing a policy document so convoluted and cumbersome it would make a joint EU and UN government look responsive.

    It may not be impossible–with enough time and money most things are possible–but it’s a logistical black hole, which is why “Report it and move on” is the order of the day.

  4. #4 Rhett Allain
    March 2, 2010

    @Z,

    The goal here is to just get an order of magnitude. I completely guess about the 20 minutes of video each minute – that was way off.

  5. #5 Rob Monkey
    March 4, 2010

    I really don’t have much to say other than I LOVE these kinds of posts! I’m excited to read the bicycle/wind speed one now, but thought I’d say thanks first, these are totally fun little thought experiments. Someone should pay you to include these in their physics textbook, none of my example problems back in the day were anywhere near this interesting.

  6. #6 Rhett Allain
    March 4, 2010

    @Rob,

    Thanks for the feedback – I agree. Someone should pay me to put these in a book – just kidding. Actually, I saw a book somewhere with a whole bunch of these types of problems (probably if you search for fermi problem, you will find a lot)

  7. #7 Cedric
    December 3, 2010

    So from your 20 minutes estimation it would be possible for youtube to do that since 1.8 million isn’t that much. But if it’s going to be 108 million, it changes everything. They claim that they are barely making any money as it is so I don’t think they could afford to pay that much money.

    But great calculations anyways. Keep up the good work.

    Cedric from Super Traffic.