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Little things about starr's 5x5 from math modeling

majutsu

Well-known member
I am going on vacation soon. When I come back, I will start a Starr 5x5 program (thanks to madcow for his posts). I started playing with some ideas and found some neat things about 5x5. Some of these discoveries actually affected my plans for the next two weeks. I don't know how many people will like this (I know Samoth will :) ), but nerds of all flavors may find it interesting.

In this graph below:

Dual Factor Graph

The x-axis is the number of days. Day 0 (zero) is Monday, the first workout. The fitness level and fatigue levels are maximal the second you finish your set. The red line is fatigue. The blue line is fitness.

As expected, fatigue decays three times faster than fitness. To do this, I needed a decaying function. I went with Fatigue= ae^(-bx) where a and b are constants and x is the number of days. The constant a doesn't really matter, since it would just change the fatigue unit of measurement, "fatiguitons". Constant b can be set so fatigue falls to zero within the parameters of my experience. In my experience, if I workout Monday, Tuesday I'm beat, and Wednesday kind of ready. But if I skip two days, I'm totally ready. So I picked a fatigue constant so the fatigue level fell to about zero in 3 days. This means fatigue = e^-x. Fitness, according to dual factor theory, falls about a third as quickly as fatigue. So Fitness = e^(-x/3).

The first little brown scallop shaped curve is fitness-fatigue, or e^-x - e^(-x/3).

Next, we reload on day 2 (wednesday). That means from day 2 to day 4 (Wednesday to Friday), we have workout 1 + workout 2 as a total training benefit. In other words, e^-x - e^(-x/3) + e^-(x-2) -e^(-(x-2)/3). We keep patching workout functions together in this way for three weeks . . .

So the multi-peaked curve is the benefit of training over time curve.

I only ran it three weeks in this graph. Notice that your fitness gain is starting to level off at three to four weeks! This is because the cumulative fatigue level is really starting to anchor you down. This graph assumes that all your workouts are maximal stimuli. If you are a newbie, or have a low work capacity, it would take about six weeks to peak! It's interesting how much agrees with anecdotal observations.

Also note that by deloading after the fourth week, you can drop some of that fatigue anchor. Furthermore, by switching say to a 3-rep range, there is much more CNS involvement, more of a power rep-range. In essence, you are training a different aspect of strength training (power versus hypertrophy), so you can expect a new multi-peaked training benefit curve in a new training modality or skill.

Also, notice in this graph, that the last workout is day 18. At day 25, a week later, we have so good training benefit left, well over our baseline when we started. But even 3-5 days later, we're plummeting back to zero. So for my vacation, I'm going to do one or two workouts of total body compound moevements, like 3 sets of 8, to leave just one week of complete inactivity and to boost fitness maintenance. Two weeks of total rest is too long to maintain steady progress.

;)
 
Can you run the graph again for 4 weeks with a 3-day rest period after 4 weeks, i'd like to see how far it drops after another 4 weeks.
I guess I could do it with your formulae.... but i'm lazy.
 
To be completely honest, I really don't understand half of the mathematics going on here -- but I think it's kick ass that someone took the time to plot this out!

Nice work majutsu.

-- KhorneDeth
 
This post should bring the nerds out of the woodwork. I like it, Majutsu, I always respect planning. I read it a few times, and it may be something I am missing, but what are the days you plan to train? I couldn't be sure whether or not you were going to train Wed.
 
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this post assumed M,W,F training like in the madcow version of starr's 5x5.

I will probably hit the same intervals (but not those exact days of the week).

It was just to see the dual factor idea graphed out. In the long run, I didn't really uncover anything new, but I did understand why some things are done (like deloading week 5).
 
Thanks for the reply. The graph was cool. It is nice to see it charted out as the fatigue fades quickly, the fitness slowly, and you are almost uncovering hidden gains.
 
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