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Thread: Mathematical Modeling of Attempt Selection

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    stef is online now Community Organizer (Administrator)
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    Default Mathematical Modeling of Attempt Selection

    by Jeff Russell

    One Saturday afternoon you decide to head to the gym and max out your squat. Maybe itís been a while, and you want to see if you can set a new personal record - a number youíve had your eye on. Once you arrive, you put on your shoes and begin to warm up the lift. After a few sets and some singles, you have your PR attempt loaded on the bar in front of you. You steel yourself, get under the bar, walk it out, squat down andÖ

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    A person could collect various data points to develop their own logit function - if they will succeed at the weight.

    Fascinating thought...

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    I like the article, but to be true to it's mathematical foundation, it should consider (in bold)

    The change in likelihood of a successful lift vs. lifter proficiency with all other factors being constant. At least the diff. eq. professor stuck in my head from grad school many years ago kept telling me as I read the article.

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    seems complicated

    1st attempt: something you can triple/have tripled
    2nd attempt: something more the 1st
    3rd attempt: something a little more than a 2nd

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    Quote Originally Posted by OZ-USF-UFGator View Post
    ...with all other factors being constant.
    Agreed. This phrase would make a good tattoo, if anyone's interested.

    Quote Originally Posted by Fulcrum View Post
    seems complicated
    I had the same impression when I wrote it.

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    Are there datasets that contain this type of information?

    I would think the key pieces of information would be the amount of the weight the lifter trained (last group of 5's), time since last trainings session along with previous pr's. Essentially, this is creating the performance curve that Rip talks about in his lectures. The challenge is the accuracy of the curve.

    I'm also thinking the probability estimates would be conditional. If a person misses his first attempt, it would change the odds of making the next attempt. (I'm not smart enough to figure out these revised calculations.) The key premise is being to choose an aggressive - but not too aggressive first weight - and then determining the jump from weight 2 and then weight 3.

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    Attempts to construct the logit curve for a given lifter are likely to be essentially hopeless. Why? Suppose a lifter has a 50% chance of making a lift. The number of trials, n, you have to run in order to establish P(making lift) to within a 10% standard deviation is given roughly by sqrt(0.25/n) = 0.1, which gives 25. How often do you test a ~ 1 RM? Is the timescale for 25 such attempts short or long compared to the evolution of your own true logit function? Probably long. In which case, you're measuring something that's almost certainly already changed because your proficiency has changed.

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    Quote Originally Posted by stlrick View Post
    Are there datasets that contain this type of information?
    I couldn't find any. They're hard to produce with much quality, for reasons mentioned in the article and that K9ZAZ describes here.

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    Quote Originally Posted by K9ZAZ View Post
    Attempts to construct the logit curve for a given lifter are likely to be essentially hopeless. Why? Suppose a lifter has a 50% chance of making a lift. The number of trials, n, you have to run in order to establish P(making lift) to within a 10% standard deviation is given roughly by sqrt(0.25/n) = 0.1, which gives 25. How often do you test a ~ 1 RM? Is the timescale for 25 such attempts short or long compared to the evolution of your own true logit function? Probably long. In which case, you're measuring something that's almost certainly already changed because your proficiency has changed.
    Isn't the goal trying to develop something useful for the lifter to determine how much weight he should put on the bar? If he is a competitive lifter, he should be gathering as much data as possible to best determine the amount of weight to be put on the bar. Although there may not be enough data for an individual logit, I would have to think their is enough for the population of lifters.

    As an individual, there certainly should be enough data to create a regression. Yes - the data will change as the person changes - but correct me if I'm wrong but the curved line that is drawn appears to mimic an equation with elements raised to a power.

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    Quote Originally Posted by stlrick View Post
    Isn't the goal trying to develop something useful for the lifter to determine how much weight he should put on the bar?
    That may be the goal, but practically, it's not going to work. There is so much uncertainty on the true value of P(z=% of 1 RM) for any given z that you aren't going to get reliable results unless you, as I said, gather a lot of data points. Practically, this isn't possible for one person because their function will evolve too much over the course of collecting the data.


    Quote Originally Posted by stlrick View Post
    If he is a competitive lifter, he should be gathering as much data as possible to best determine the amount of weight to be put on the bar.
    Granted, but this formalism doesn't really help with that. It's a mathematical exercise limited in practical application by the objections raised in this thread.

    Quote Originally Posted by stlrick View Post
    Although there may not be enough data for an individual logit, I would have to think their is enough for the population of lifters.
    This is a more interesting idea, but you have to think that there's enough variance in individual responses to training that it's not useful for the individual lifer.

    Quote Originally Posted by stlrick View Post
    As an individual, there certainly should be enough data to create a regression. Yes - the data will change as the person changes - but correct me if I'm wrong but the curved line that is drawn appears to mimic an equation with elements raised to a power.
    We don't actually know what the functional form of P(z= % of 1 RM) is, and there's no theoretical reason to pick one over the other really. Without that guidance, you have to rely on the data themselves to build the function; a regression won't work.

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