Why you’re unlikely to find the perfect exercise program, and how you can find good enough

Posted on April 12, 2017

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There is a famous problem in mathematics-

You’re hiring a secretary and want to pick best the one. You’re a thorough person. You’re not going to merely look at resumes “He has the best typing score. Done.”  You’ll judge who is best as you interview them.

You interview randomly one at a time.

The rub is you have to pick as you meet them. Either hire or pass, and not be able to go back. By the time you would get to go back, that person has already taken another job. It’s a hot market for secretaries.

The perk is whomever you pick will accept the job. These secretaries don’t like to dick around.

You have 100 candidates, but hiring merely gets in the way of the real work. You don’t have time, or at least you don’t want to spend the time, interviewing 100 people.

What can you do? How can you get the best bang for your buck time wise, but still maximize your chance of getting the best candidate? The risk is picking too early, as well as picking too late.

If you randomly pick one of the secretaries, you only have a 1 in 100 chance of getting the best one. That’s not great odds. Can we do better?

The optimizing math on this works out to something called the 37% rule. Interview 37% of the applicants, then using whomever was the best in that first 37 as your benchmark, hire the next person who exceeds that benchmark.

…but you only have a 37% chance of picking the best candidate. That’s a lot better than 1 in 100, but it’s still not that high. However, these are the best odds.

-> It’s good to recognize math is not something we all love. In fact, probability is a subset of math many who like math don’t enjoy. It’s not the most intuitive subject, but this is a famous problem in mathematics in a research area called optimal stopping. While you might not intuitively grasp the numbers here, or enjoy them, they’re proven in the same manner a+b = c is.

Now the analogy. Instead of hiring a secretary,

You’re picking an exercise program. Obviously you want to pick the best one. Ultimately, much like you can’t judge a secretary solely by resume, you can’t know how well a program will go until you try it.

Once you pass on a program, you can’t go back to it. Time only marches forward, and if there’s anything we know about life is it changes. We’re talking the best program here. What was optimal then won’t be now. Injuries, age, training history, scheduling workouts, changes.

The extra rub in our exercise program case is while the secretary couldn’t reject the offer, the program CAN be rejected. By you! Let’s say you either like or dislike it. The program may be optimal for strength, but that doesn’t mean it’s optimal for your psychology.

From browsing the internet, there are 100 programs you think should be considered. To judge the effectiveness of a program, you have to do it for a month.

You don’t have time, or don’t want to spend the time, to do 100 programs.

How do you choose? Picking a program you think will be the best early on means fear of missing out on a potentially better program out there.

Because the program can take part in rejection, our 37% odds go down to 25%. It’d be like us having to find the best secretary who will also be willing to work for us. You might find the best program, but that doesn’t matter if you’re not willing to do it.

And even if you 100% can always make a program work, that the best program actually means fitting every single criteria and finding the overall best fit, then we’re still back to that 37%.

And in the case of judging a program we can’t judge it after a brief interview. We need an extended one e.g. month per program. (Six weeks is ideal.) If we’re examining 100 programs, that means it’s going to take us 37 months just to get our benchmark. Who knows how much longer it’ll take until we do the program which exceeds our benchmark!

Even worse, there is a chance you go through all 100 programs!

-> If in the first e.g. 37 you happened to do the best program, then in the next 63 you won’t find something which exceeds your benchmark. Probability is a bitch.

This isn’t going to work.

 

An alternative to the best program is picking one that’s good enough. What do we need to do for that? There’s a nice little formula:

  • sqrt(number of programs)

So going back to our 100 programs, if we take the square root of 100, which is 10, then we would do 10 programs, subsequently picking the best program which exceeds the best within those first 10.

We’ve gone from 37 programs down to 10. But still, 10 months is a while, and at what cost have we done this? Not that much actually. Instead of the perfect program, in this case we’re down to the 90% perfect program.

If we say we’re only willing to do 10 programs, then

  • sqrt(10) = 3.16

we need to do three or four programs. But the tradeoff here is we only have a program which is 75% perfect. That might not be good enough.

 

Takeaways

1) Give yourself time when getting into this. Even the best algorithm isn’t going to be hitting home runs most the time.

2) Have a more specific goal.

What does “best” program actually mean? It’s a vague description. If you can instead be more specific, such as “increase bench press from 200 to 300 pounds” then that becomes more analogous to our “hire a secretary solely by typing ability.” In that case the odds of success in finding the best program go up to 58%.

3) Hire a trainer

There are three benefits of the trainer.

They can guide you as to what perfect enough will be. You might think you need to have every single thing optimized, but in reality you need 75% to get to where you want. You say, hire a trainer for a few months, get that sense of direction and now have an increased ability to filter what’s out there due to better knowing what will be sufficient. The trainer guides you to look at 10 programs rather than 100.

Next, the trainer can give a specific goal. You might think you need extra strength everywhere, but the trainer can convince you to focus on your lower body. (When it comes to physical goals, the average client doesn’t get too specific. They’ll say “feel better,” or “be stronger.”)

Where then the trainer acts as a perpetual filter. You think you need to consider 100 programs, but you hire a trainer who knows there are actually only three that should be entertained. You are paying the trainer for not only their experience in doing programs themselves, but from what they’ve seen other people in your situation do. They’ve already put the time in.

Similar to how a recruiter might be able to guide an employer into looking at three applicants instead of 100. The odds of success of finding the best applicant go way up in that scenario:

Source: Algorithms to Live By.

What we’re hoping for is something which can get our number of options down from 100 to under 10. Moving from 1000 to 100 only changes things by less than a percent. Moving from 100 down to 50, still not even 0.5%. To make a dent, we need a significant reduction.

This isn’t outside the realm of what a good trainer should be able to do for somebody. But it’s going to be outside the realm of what an inexperienced trainee can do on their own. The trainer hopefully can get you on the best program (or 90% perfect) within a few months. On your own? For a newbie? Not inconceivable it takes a few years. (The fear of missing out on other programs makes many switch even if they have a great thing going. By the time they go back to that great thing six months later? It’s not as great!)

 

The AI connection

Because we don’t know if a program is perfect until we try it, it seems plausible to say at best we could limit our consideration to two programs. Either this or that. If we only do one program, we have nothing to compare it to. We might think it’s the best, but we don’t know. A reference program would be ideal. Similar to if we only interview one secretary, they might seem perfect, but having a reference secretary would help.

In that case, even if the AI is 33% better at filtering than a human, bringing us from three programs to try to two, the odds of picking the best program are the same. 50%.

-> This is a gigantic assumption of the AI. There is a misnomer out there AI can do anything. That math can always find the best solution. When we consider the real world, where finding solutions always have a time constraint, then cracks in the armor show.

When it comes to optimizing scheduling, think picking the best sequence to perform tasks, 7% of all problems have no known solution. 84% of the known solutions are intractable- they can’t be solved in a reasonable amount of time. One way to make a scheduling problem intractable is make each task depend on the other.

What’s part of picking the best program? Picking the best sequence to do exercises in. When each task depends on the other (sounds like exercises depending on the other (you can’t shouldn’t do accessory exercises until you’ve done compound; you can’t lift until you’ve stretched, etc.), we may very well have an intractable task.

Because by the second program we make a decision. If it’s better than the first, we use it. If it’s worse than the first, we pick the third. There are six possible orderings of our three programs.

  • Best program – second best – third best
  • Best program – third – second
  • Second best – best – third
  • Second best – third – best
  • Third best – best – second
  • Third best – second – best

In three cases above, if we make our decision by the second program -we either stay with what we have or keep going- then we succeed three times out of six. (Bolded.) 50% chance of picking best program. The same as if you’re only considering two programs, where you have a 50/50 shot of picking the best.

Meaning an AI could be demonstrably better in one arena, say filtering programs, but zero percent better in the practical ramification- picking the best program.

-> One thing the AI would be better at here is lessening the time it took to get the best program. With two programs to consider, it would take two months. In some cases above, it could take three months.

There is no doubt there are variations of looking at this, nor do I know this is the best way (I did ask my computer science degree having brother and he thought it was worth doing), but hopefully the above gives some insight as to why something like exercise apps are so bare bones.

“Push-ups”

…30 seconds later…

“Squats”

…30 seconds later…

Why some of them you pick the exercises. Where you’re effectively making the program. Because doing this right is tough. Doing it algorithmically is tougher. (Most trainers cannot explain their programming in any mathematical sense. Though I think they should be at least somewhat able to!) Doing it binarily is nobody even knows how hard. To give a sense, Amazon had a couple thousand people working on Alexa for four years before releasing it. While yes, she’s cool, think about how remedial she is.

-> Our business issue is cropping up again. How many other companies can make that type of investment? Amazon’s volume is so high they’re cool with a 1% profit margin…

Is she any better than a DJ at picking a song for you? And if you ask her why she gave you a certain answer? What she’s basing the next song choice off of?

When it comes to potentially having to explain why an AI picked an exercise program? AI is worse! In fact, it’s incompetent.

 

Hire a trainer here.

Credit to: Algorithms to Live By: The Computer Science of Human Decisions. Check it out for other ways to assess the best way of choosing various elements of life. 

Credit for good enough math: http://www.slate.com/articles/technology/technology/2014/12/the_secretary_problem_use_this_algorithm_to_determine_exactly_how_many_people.html

 

Nine part series-

 

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