Everyone makes mistakes, and as much as they make us all cringe to look back on, there's a lot to be learned from them. It's "We Said What?" week on Industry Focus, and all the hosts are looking back at some of the biggest mistakes they've made on the air.

Wrapping up the week, in this Tech episode, Dylan Lewis and Michael Douglass look at some back-of-the envelope math that Dylan did on Apple's (NASDAQ:AAPL) Music segment a few years back -- which turned out to be incredibly overzealous. Find out why they got this so wrong, how investors can do better and more accurate back-of-the envelope predictions, a few exercises you can try to stretch your prediction muscles, and more.

A full transcript follows the video.

This video was recorded on Aug. 25, 2017.

Dylan Lewis: Welcome to Industry Focus, the podcast that dives into a different sector of the stock market every day. It's Friday, Aug. 25, and we're wrapping up "We Said What?" week with a mega-mea culpa. I'm your host, Dylan Lewis, and I'm joined in the studio by my good friend, fool.com's Michael Douglass.

Michael Douglass: Howdy!

Lewis: Way to give me something to work off there. 

Douglass: [laughs] I'm glad to be here, Dylan! Thanks for having me! Happy Friday!

Lewis: [laughs] As an aside, I'm very proud of the "mega-mea culpa" phrasing!

Douglass: It has a nice alliteration, and it has strength to it.

Lewis: Good mouth feel, the phrase. Listeners might realize at this point that I pretty much have Michael Douglass on the show whenever I'm not talking about nitty-gritty, nuts-and-bolts tech stuff. You're one of my good friends, and I just have a blast with you in the studio. But you coming in, it's a favor, really!

Douglass: [laughs] A favor to me, really. Because I enjoyed the podcast, and then I didn't get to do as much. So it's nice to hop in from time to time and subject everyone to my vocalized pauses.

Lewis: But it is time out of your day.

Douglass: Sure.

Lewis: You're a busy guy. You have a lot going on.

Douglass: Aren't we all?

Lewis: We are. But when I approached you for the show, I said, "Hey, Michael, I'm going to be talking about how I was totally wrong about something. Are you interested in coming on the show?"

Douglass: I was like, "Yes, yes, please, let's do that!"

Lewis: And I think that's a testament to your friendship! [laughs] And your good-heartedness! So we're going to wrap up "We Said What?" week. We're actually going to be going through an estimate I made about Apple Music back in the summer of 2015. Austin, do you mind rolling the tape?

(Lewis): As of 2014, this is the most recent data I can get, there were roughly 800 million iTunes accounts that were active. I want to say conservatively, maybe 5% to 10% of those people are converted over to paying Apple Music subscribers.

(Sean O'Reilly): That was the other question I had, was cannibalization.

(Lewis): Yeah. Well, I think they're monetizing people who would otherwise not get monetized. That's my feeling generally. I'm not comfortable saying they're going to convert 20%, like the Spotify breakout is now, because a lot of the people who are currently using iTunes are using it just to host music. They're not buying things off that platform. So I think, just to be on the conservative side, let's say they convert 10% to paying Apple Music subscribers. So, 80 million subscribers roughly, say a mix of individual and family accounts, maybe the average subscription winds up being around $11 a month. That puts Apple Music annual revenue around $10.5 billion, which would be a 4% bump on trailing-12-month company revenue. 

So I was back-of-the-envelope-ing here, but that was a really bad ballpark. If you look at a couple of numbers, I think they illustrate why. Two years later, Apple has roughly 27 million paid music subscribers, and at an average sub of $11 a month or so, based on the individual plans and family plans they have, that makes Apple Music roughly a $3.5 billion business annually, which is a third of the size of the number that I originally tossed out.

Douglass: And, listen, I tried to help. I'm an Apple Music subscriber, so I was trying to do some numbers here, but you didn't get terribly close.

Lewis: A truly good friend, trying to help out my estimates.

Douglass: [laughs] Got your back.

Lewis: It's really hard to make estimates for nascent products and new segments. But I think, even in my walk-through, I probably should have done a quick gut check and seen how ridiculous that 80 million sub number was. One of the big reasons, really, was that at the time, Spotify had 20 million paid subscribers on a overall base of 75 million users. So I incorporated that number into my analysis, but I did it by looking at the proportion of paid subscribers on their overall base, not really considering the aggregate number of paid subscribers. A major limitation there. And I think a far more sensible thing to do might have been, Spotify has this 20 million user base. If Apple Music can hit that at an average sub of $11, like I said, that's roughly a $2.6 billion business annually. That's basically what the service came out to at the end of 2016. So using a more sensible and much less complicated approach would have been way better here.

Douglass: In your defense, it is incredibly difficult to predict the product launches. My background is in healthcare, where predicting product launches is something that analysts do all the time and routinely get wrong. Even predicting what will happen with drugs that are already out on the market and have been for a while can be very difficult. I actually made a big mistake with Gilead Sciences, which is a company that Dylan and I both own, and I kind of convinced him into owning. I really messed up my attempts to understand what was going to happen with their hepatitis C franchise. I just wrote an article about it. If you're interested in reading it, you can send us a note and I'll pass it along to you. Or just Google "I Was Wrong About Gilead Sciences." That works, too.

Lewis: Yeah, if you're interested in getting the article, industryfocus@fool.com. And I appreciate that you decided to hang yourself out to dry a little bit, too --

Douglass: Yeah, you know, what are friends for?

Lewis: -- and didn't just leave myself out there. Because you could have! [laughs] That was an option. So this example from a previous show that I did, that article, these are just one-offs. But the reality is, the investment industry is full of estimates. You have company guidance, you have Wall Street analyst expectations, you have DCF models from analysts --

Douglass: Discounted cash flow, that is.

Lewis: Thank you. I was getting a little in the weeds there. Then, as an individual investor, you might have the things that you put together on your own. This is such a large part of the space that we cover, and I think it can be very easy and very misleading to look at these numbers, especially on a company guidance and analyst expectations side, and take them as scripture. That's really not what they are.

Douglass: Right. One of the problems here is, these numbers tend to be very precise. They will say, "Analysts are estimating $1.35 per share of earnings in 2018." That precision, I think, often gives the false sense of accuracy. Like, "Well, they've got it down to the penny; they must have some perfect system for getting it." Really, it's a lot of estimating, it's a lot of inputs, it's a lot of guesswork. Which, yes, it provides a precise number, but one that can be pretty wildly off.

Lewis: And my Apple Music example, I think, is the perfect example of a situation where an estimate is only as good as the inputs that go into it. And if they're bad, like they were with the one that I made, then it really doesn't matter. It might be precise, but you can't hang your hat on that six months later and be like, "What is going on? Where's the revenue?"

Douglass: It was precise and very inaccurate.

Lewis: Right. [laughs] 

Douglass: As was mine! As was mine with Gilead Sciences! It's fine! [laughs] 

Lewis: I was going to say, thank you for emphasizing that, Michael. I don't have any ego left. There is this temptation to quantify things, and it can be a very helpful exercise. We want to level set expectations a little bit. But I think with a lot of what the investment industry does with projections, the important thing to realize is, it's creating a set of circumstances. And maybe, in a lot of situations, the better thing to do is to look at a bull case, mid-case, bear case type analysis for these things, because that will give you a better sense of the range of possibilities, the range of outcomes.

Douglass: And just to plug that article one more time, I actually laid out that for Gilead Sciences after having mea culpa-ed and said, I really messed this up. So if you want that article, email us at industryfocus@fool.com.

Lewis: You know, I didn't even know that when I said that. I really teed you up.

Douglass: We're just reading each other's minds!

Lewis: You're really plugging that article. I hope someone writes in. I would love to just give a shout out to a bunch of listeners who wrote in last week when I put out a call saying I was interested in how they're using wearables, because it wasn't a market that made all that much sense to me on the consumer side. I don't have a use case for it. But a lot of people wrote in about the health benefits of wearables. We love getting those emails in our inboxes. You actually got them in your inbox, even though you're no longer doing the show.

Douglass: Yeah, exactly, it's an opportunity for me to see what's going on, give people kudos, because frankly, when listeners are engaged and investing better and making better decisions because of things that they're hearing and are being educated, that's a really cool thing. That's part of the company mission. So I'm really excited to even just tangentially read those things and say, "Gosh, that's awesome! I'm glad we're doing that!"

Lewis: Yeah, and it's great to connect with people one-on-one. We do that with email. We also do that with the Motley Fool podcast group, which is on Facebook, if you want to connect with the hosts there.

To bring it back around with what we were talking about with projections and estimates, and the idea of a case-by-case look at things, really you're getting a ballpark, which is helpful. But the next step, I think, is super important. And that's, OK, I have this number -- what does this number mean? And I think to slightly let myself off the hook with this Apple Music projection that I made, I talked about in that episode how, yes, this is revenue contribution, but on what exists right now for Apple's main revenue, their core business, it's really not all that meaningful. It's not significant, it's not the thesis-driver for this business. It's a nice tack-on. So that next level on these numbers is always good context to add, because a number devoid of any context is just a figure and it doesn't mean anything.

Douglass: Right. 

Lewis: We're going to talk about some ways to get a little bit better at ballparking, something clearly that I need to do --

Douglass: And me, too!

Lewis: Michael, we talked about how I was totally wrong.

Douglass: We were totally wrong! [laughs] About different things. I'm just going to keep not letting you completely ...

Lewis: I appreciate that.

Douglass: Yeah, you know, what are friends for?

Lewis: I wrote this outline and prepared this show of the mind that you were not going to be as self-effacing as you have been.

Douglass: I guess there can be miracles from time to time!

Lewis: There can be miracles! That's a joke. Michael is one of the most egoless people I know at the Fool. But we both need to get better at this, as it turns out. And I'm guessing there are some other folks out there who want to as well.

So something that I think might be a great practice exercise for people who are interested in this are Fermi problems. This is something that I think people who have an engineering background or have done interviews at consulting firms might be familiar with. The idea is, these are estimation problems, and they're pushing people to make back-of-the-envelope approximations and try to simplify a very large problem into little steps, or make it smaller in scale so you can then extrapolate out. So one of the most famous Fermi problems is how many piano tuners are in New York City? Michael, I'm not going to ask you that one.

Douglass: I appreciate that, thank you!

Lewis: Well, I was telling you, maybe just look it up on the internet and then run through this amazing explanation.

Douglass: Yeah, if you search "Fermi problem," that's the first one you come to, and it's like, OK, cool, that makes sense.

Lewis: It's on the Wikipedia page. So I couldn't ask you that. But what I am going to ask you, and I'm going to have you walk through your logic for this as an example of how to approach this type of thinking is, it's Pizza Day today, which is one of my favorite days of the month.

Douglass: Yeah, last Friday of every month.

Lewis: Last Friday of every month at HQ. We get a bunch of pizzas.

Douglass: For free.

Lewis: We're not going to say how many pizzas, because I'm going to ask the listeners a Fermi problem as well, and I don't want to give them too many hints. I'm going to ask you, because it's Pizza Day, how many calories have you consumed from all the Pizza Days you've had in your entire time at the Fool?

Douglass: I'm going to go ahead and assume that I've already consumed today's pizza, although I haven't yet. It's actually right after the taping. I'm very excited! But by the time you get this, I will have.

Lewis: To give listeners a better sense of Michael Douglass, I Slacked him this question, and he immediately responded, "Does that include today or not?" That's how detail-oriented Michael is.

Douglass: [laughs] False precision. So Pizza Day happens once a month, on the last Friday of every month. I've been at the Fool for 44 such Fridays, since starting in January 2014. I actually started on a Pizza Day in January 2014. Yay! So I've been for 44, except that on the last Friday of every November and the last Friday of every December, I'm out of HQ. Last Friday of November is the day after Thanksgiving. Guess what? I'm not here. I'm with family. Last Friday of December, I'm usually skiing in Vermont. So I'm out for both of those. So I've really been at the Fool for 38 such Fridays. Also, I take other vacations from time to time. I'm actually about to go on one. And I also get sick. So I'm assuming I missed another two Pizza Days for vacations and sickness, so let's say 36 Pizza Days. Like many people confronted with free food, I overindulge on the initial several free Pizza Days, and then gradually ramp down. I would estimate that from January 2014 through September 2015, I averaged 3.5 slices of pizza per Pizza Day.

Lewis: To add some context, the Fool 15 is a thing that gets thrown around the office pretty often, much like the Freshman 15. We have some very nice amenities. We have a food pantry; we have things like Cake Day and Pizza Day. If you're not up on your wellness when you start out, there's a very real chance that you might put on an extra couple of pounds. It happened to me!

Douglass: And it happened to me! But, starting in October 2015, I decided to lose some weight, including my Foolish 15 and a little bit more. And I started eating less pizza as a result, in addition to other things. So I would estimate that from October 2015 through now, I've averaged 2.75 slices of pizza per Pizza Days. So my Pizza Days from January 2014 to September 2015, I would estimate that I had 63 slices of pizza across 18 Pizza Days. In my Pizza Days from October 2015 to now, I've had 49.5 slices of pizza across 18 Pizza Days, again, with the assumptions that in each group, I missed one extra Pizza Day due to vacation or sickness, and of course for the Novembers and Decembers.

So, on to the actual slice composition. I tend toward eating two larger slices -- yeah, you knew what you were signing up for!

Lewis: I forgot how in the weeds you were going to get with this when I asked you this question.

Douglass: [laughs] I tend toward eating two larger slices -- one from Bugsy's, which is very thick, and one from that other pizza place with the big slices that I can't think of the name of.

Lewis: Oh, I know the spot you're talking about. 

Austin Morgan: Valentino's.

Douglass: Valentino's, thank you. Austin with the save. Valentino's, which is sort of big New York style. Then, any incremental slices are usually Papa John's, usually meat lovers.

Lewis: And those tend to be smaller slices.

Douglass: Yes, they are. So I would estimate that the Bugsy's slice is around 500 calories, the Valentino's is around 600 calories, the Papa John's slices probably around 350. So that means, for the 18 Pizza Days before I started losing weight, I took in 49,050 calories. That is 39,600 calories from the Bugsy's and the Valentino's big slices, and 9,450 calories from the incremental Papa John's slices. For the 18 Pizza Days, including today, since I started losing weight, and have mostly kept it off, yay, I took in 44,325 calories. That is 39,600 calories, again, from Bugsy's and Valentino's, because that hasn't changed, and 4,725 calories from the incremental Papa John's slices. That totals up to 93,375 calories ingested, plus or minus.

Lewis: And I am not asking you this question to shame you in any way, because my counts are probably just about the same. And Michael just threw a lot of numbers out there. It's a numbers dump, doing these types of problems and working through them. But I think that's a great illustration of how to take what is a massive problem and a massive question and slowly unpack it into much more digestible bites.

Douglass: And that's an important thing, not just in investing, but also in process building, in really trying to do anything in a business or work environment. You have a big problem, and you break it up into manageable chunks and get those done. I find that blocking and tackling like that, particularly when I'm faced with something big and imposing, actually really helps me both psychologically, like, I can do these things, and also map out, what does the schedule look like for making this happen?

Lewis: To turn it to what I teased before, with the listeners, I will put to you guys: I'm curious -- how many Fool Pizza Days could be paid for by the cash Apple holds in the United States?

Douglass: That's a good one!

Lewis: So when you did your problem, you did not look up anything.

Douglass: No.

Lewis: That is the purist Fermi problem way of doing things. But I will say to our listeners, you can go through and use the internet to inform how you do this. I would love to have some people write in with their logic flow and what they get as an answer. I'm going to say up front I don't know what the answer is. But this is an exercise to work through general logic and approximation.

Douglass: I wonder if we should help them out by giving them an estimate of how many Fool employees are at HQ.

Lewis: That is available online, I believe. I know there's a ballpark. But what's our count at, roughly?

Douglass: At HQ, I would guess it's around 250. Does that feel right?

Lewis: I think that's about what I've seen. Maybe it was Glassdoor, or something like that. But there is an approximation out there. To be fair, I will run through this myself, and we will post it on the Motley Fool Industry Focus Twitter account, @MFIndustryFocus. So I would love to see some people write in and go through this exercise with me. I figured it would be a nice way to rope in listeners for the show. I'm sure, at this point, Austin Morgan just wants to go eat pizza. [laughs] 

Douglass: I sure would! I sure do!

Lewis: Austin, what's your favorite slice provider of all the Pizza Day pizza shops we have coming in?

Morgan: I don't know if I have a favorite. I usually just grab some random slices. Like, "Oh, that looks pretty good." I never really look at the box. I just look at the pizza.

Lewis: I have to say, I was not expecting that answer!

Douglass: Yeah, I'm surprised!

Lewis: You seem like someone who has a strategy and a tack to Pizza Day. I do.

Douglass: Well, because it's a very target-rich environment. You have to block and tackle it.

Morgan: I literally never remember it's Pizza Day until we film the show and you tell me, "Hey, it's Pizza Day!" "Oh, man, it's Pizza Day!"

Lewis: I'm so excited that I can't help but talk about it.

Morgan: I literally forget every Pizza Day.

Douglass: What a great surprise every Pizza Day.

Lewis: Free lunch!

Morgan: "What am I going to get for lunch today? Oh, it's Pizza Day! Sweet!"

Lewis: Well, we'll wrap quickly so that we can get downstairs. Before we do, I want to mention that if you like this type of thinking, listeners, I would recommend checking out Superforecasting Philip E. Tetlock. It's a book that goes through the strategy and logic behind some of the world's most accurate forecasters. And a lot of them are not experts. They're actually amateurs, folks doing it in their spare time, looking at these various socioeconomic and political issues and coming up with approximations for them, and beating the experts in many cases. It's actually a book that we read for our editorial book club that we do with our writers. So I really enjoyed it. It was cool. And much of the book focuses on things we talked about in this conversation where, looking at data, logic for predictions, trying to curb any bias that you might have, thinking about probabilities a little bit, unpacking your question into a bunch of smaller parts and working there. One of the big things they do harp on in the book that we'll tie back to the point of this show and the point of this week is, keeping a record of your predictions so you can track accuracy, and the importance of doing that, because what's the point of having an opinion if you can't be held accountable for it?

Douglass: That's very true. It's almost like I wrote about that in an article that I was pitching earlier. [laughs] 

Lewis: Yeah. It's almost like I've been podcasting about it for two and a half years.

Douglass: [laughs] Yeah. Sorry, I couldn't resist.

Lewis: Michael really wants to read this article. Just a heads-up, listeners.

Douglass: I'm really excited to be publicly shamed for my terrible predictions.

Lewis: Well, thank you so much for hopping on the show again, Michael.

Douglass: Always my pleasure.

Lewis: Listeners, that does it for this episode of Industry Focus. If you have any questions or you just want to reach out and say hey, like we said, shoot us an email at industryfocus@fool.com, or tweet us @MFIndustryFocus. If you're looking for more of our stuff, subscribe on iTunes or check out The Fool's family of shows over at fool.com/podcasts.

As always, people on the program may own companies discussed on the show, and The Motley Fool may have formal recommendations for or against stocks mentioned, so don't buy or sell anything based solely on what you hear. Thanks again to Austin Morgan for all his work behind the glass. For Michael Douglass, I'm Dylan Lewis. Thanks for listening, and Fool on!

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.