PatrickDB wrote: ↑Tue Feb 06, 2018 6:43 am
damufunman wrote: ↑Tue Feb 06, 2018 5:49 am
Relating to the discussion above, I haven't done any reading or research on this, but how does an intensity-weighted tonnage sound to you guys?
[equation]IWT = weight \times reps \times \%1RM \quad (1)[/equation]
Which can also be represented as
[equation]IWT = 1RM \times reps \times \%1RM^2 \quad (2)[/equation]
This factors in the fact that lower intensities are less stressful for a given number of reps. For example, why 5 sets of 5 with just the bar as warmup isn't meaningful volume. Equation (2) has a [math]\%1RM^2[/math] term, that effectively gives more weight to higher intensities, which I think follows with what people experience of higher intensities are more fatiguing.
Note that this does ignore how the volume is distributed, ie 5 x 3 @ 80% vs 3 x 5 @ 80%.
Normalizing so 1 RM = 1, let's assess the bench hypertrophy and strength days using this idea.
Hypertrophy: 31*(.7)^2 + 15*(.6)^2 = 20.59
Strength: 15*.8^2 = 9.6.
Not looking good.
I need to look up what Nuckols thinks the shape of the regression curve should be for this. Then I could use Hanley's hypertrophy and strength day values to get a formula.
ETA: fixed calculation
Reps per set needs to factor exponentially I think, as does %1RM.
[equation]sets*(reps)^x*(\%RM)^y[/equation]
Find values of x and y that make sense based on experimental data. Let's try x=1.2, y=2.
Hypertrophy: 70%, 3x5 then 4x4
[math]3*6.9*.49 + 4*5.3*.49 = 20.5[/math]
Strength: 5x3 at 80%
[math]5*3.7*.64 = 11.8[/math]
Nah, I think rep count to a factor of intensity might actually be a better metric. Or (1-intensity) to a factor of rep count.
[equation]sets*(reps)^(\%RM)[/equation]
Hypertrophy: 70%, 3x5 then 4x4
[math]3*5^.7 + 4*4^.7 = 19.8[/math]
Strength: 5x3 at 80%
[math]5*3^.8 = 12[/math]
This is probably approaching correctness. I don't think it will scale linearly with set count though. Hmm. Lets square root the sets.
Hypertrophy: 70%, 3x5 then 4x4
[math]3^.5*5^.7 + 4^.5*4^.7 = 10.6[/math]
Strength: 5x3 at 80%
[math]5^.5*3^.8 = 5.4[/math]
Intensity to a factor of reps? No, normalizing this to sane values is dumb. Eh it's probably just something like (bar speed as %1RM barspeed) * %1RM of weight used. Could also be that 5x3@80 really isn't as fatiguing. If you jack y up enough in the early equation you could make it work. Maybe x should be less than 1? Ok one more try.
[equation]sets^.5*reps^.5*\%RM^2[/equation]
Hypertrophy: 70%, 3x5 then 4x4
[math]3^.5*5^.5*.7^2 + 4^.5*4^.5*.7^2 = 3.9[/math]
Strength: 5x3 at 80%
[math]5^.5*3^.5*.8^2 = 2.5[/math]
These seem close. Ugh I lied I thought of something else, but it would require converting reps @ percents into RPE. Something like
[equation]sets^x*(RPE/10)^y*\%1RM^z[/equation]
Solve for x, y, z.