Mathematicians - I Need A Couple Of Formulae, Please

  1. I need a formula to figure out how long a show needs to have been on the air before I can start watching it on my DVR and not have to watch commercials. For example: assume that The Walking Dead comes on at 9:00 PM. Between 9PM and 10PM, 60 minutes will elapse. Only 47 of those minutes will be show content; the other 13 minutes will be commercials.

Assuming that the commercials are spaced evenly throughout the show, and assuming that the amount of time I spend fast-forwarding through the commercials is not relevant to this formula, at what time should I start watching the show in order to guarantee that I will have enough time built up (for lack of a better choice of words) to avoid having to watch commercials?

  1. When I download a movie via a streaming service, the download takes longer than the movie itself thanks to my crappy internet. So say that for ever minute of real time, I get 1.5 minutes of movie time. How long after beginning the download (say, in a 100 minute movie) do I have to wait until I can start the movie and be guaranteed that it will be fully downloaded by the time I finish it?

For 1, it seems clear. If there are 47 minutes of actual content, then you can begin watching at 9:13, watch all the actual content, and you’ll be synced up with the broadcast by 10pm when it finishes.

In 2, I think you’ve got a contradiction in your premise. If for every 1 minute of real downloading time, you get 1.5 minutes of movie time, then the download would take a shorter time than the movie’s running time. Did you mean the reverse, that it takes 1.5 minutes of real time to get 1 minute of movie time?

If so, and if we assume that it’s downloading from beginning to end and not skipping pieces in the middle, then we’ve got a full download time of 150 minutes for a 100 minute movie, and you can start watching it after 50 minutes of downloading, when the progress is just past 33%.

The formulae in both are just simple ratios.

Yes, that’s what I meant, thank you.

Agree with **chrisk **in both the above.

The first scenario is actually a bit more subtle, in that the optimal answer depends on the distribution of commercials.

E.g. imagine all 13 minutes of commercials were run in a lump at the very end. You could start watching immediately on time at 9:00pm and simply quit when you got to minute 47 at 9:47 and the commercials began. There’d be no need to wait at all.

Conversely, what if all the commercials were run in a lump at the beginning? You would need to wait to 9:13pm, when the last commercial ended, then you could start watching the content and finish at 10:00pm.

So in the real world, where the commercials are scattered throughout the show you need to wait something more than zero but less than 13 minutes. Any commercials which air immediately after the last live content can be ignored; you just tune out at 9:58:30 pm or whenever when the content ends and the trailer commercials begin.

There’s no asssurance the rest of the commercials are evenly spaced through the show. I’m sure there’s a lot of science in how they space them for maximum effect.

Bottom line: without knowing the specific time distribution of commercials through the show you can’t do better than waiting the full 13 minutes. You can probably reduce that by 1 or 2 minutes to 11-12 minutes and at worst you’ll be stuck sitting through the last 30-ish seconds of commercials just before the climax.

And of course you’re just guessing that 13 minutes is the actual quantity of commercials per hour. It might be more like 20 minutes worth. Different shows have different standards. To be sure if you often watch a series on a particular channel & time slot, you could time the commercials in one episode and have a pretty good number for other episodes of the same show.

So long as there is any content at all after the last commercial, the answer remains the same: You need to wait out an amount of time equal to all of the commercials. In any event, you are spending 47 minutes watching the show, and you are ending on the hour (the same as the live viewers), and so you must have started watching 13 minutes after the hour.