The Strength Matrix II: Graphing and Analyzing Your Set Data

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In Part I of my series, we talked about the benefits of adding a strength training routine to your training program.  We also showed you how to log the details of your strength training in the training logs at BT. 

This article will walk you through some of the many graphs, what they mean and how they can be useful in analyzing your strength routine.  This is a BIG article.  I start by just going over examples of different types of strength sets.  Then I will go over some math of how we get the values for the graphs and what the values mean to you.

Triathlete strength set composition
Many triathlete strength programs are periodized so that you first do a conditioning phase with light weight, high reps at a constant amount of reps/set: 3 sets of 15-20 or even as high as 20-30 reps.  This lasts a number of weeks and serves to get the muscles and tendons ready to to go to higher loads.  The next several phases decrease (or increase) the number of reps per set while increasing (or decreasing) weight to then develop muscle strength, endurance and power to parallel the swim, bike and run training phases. 

Throughout the many triathlete routines on this site and elsewhere, the reps/set stay relatively constant within a training period and the only things changing from one period to the next are increasing the weight and decreasing the reps/set or decreasing the weight and increasing the reps/set.  It all depends on the phase you are in for you triathlon training be it base, build, peak or taper.

Most triathlete strength routines do not go so far as to create lots of extra muscle mass just by the nature of the sets-as you would rarely do low rep/high weight sets and you would never do many low rep sets to fatigue consistently.  Many triathlon routines will have your maximum load for an exercise as a % of your bodyweight so you will reach a maximum where you do not add on more weight but rather just increase the reps per set.

Bodybuilding set composition
In contrast to a triathlete's routine, a general newbie bodybuilding set consists of 15 reps at very light weight for a warmup set, adding weight to get 10 reps for the second set.  Then sets 3-5 are at 6-8 reps going to fatigue.  So within a set, the reps/set decreases as the weight increases.  To further shock and stress the muscles into growth, once or twice a month one would have 'heavy' days where you do a warmup of 15 reps at light weight then pile on the weight for a 2nd set of 6 reps, then sets 3-5 are 1-2 reps to fatigue.  THEY HURT!  You are sore for several days following a routine.  One of the many reasons bodybuilding routines don't mix with triathlon and endurance training.

So you can tell that a triathlete's and bodybuilder's set composition are radically different.  Triathlete's prefer the same number of reps for every set (narrow set spread), the weight stays relatively constant and the repetitions per set rarely go below 3-5 reps.  During an actual racing season, set reps usually never go below 6 reps so that soreness is not an inhibitor to racing and training.

Getting stronger
How do you know if you're getting stronger?  How does one gauge improvement?  There are many different ways to setup a weightlifting set. 

  • For a phase in a triathlete's routine, is an increase in strength from increasing weight at a constant number of sets and reps? Example, Bench Press 3 sets @ 10 reps each (3x10) but increasing by 5pounds each week assuming you can always hit 10 reps per set.  In this type of set, you should see your cumulative weight, average rep weight and your strength factor increasing for every set.
     
  • How about keeping the same weight on the bar but adding on more reps and possibly more sets every week? An analogy is it is like muscular endurance at a given weight.  Example: 3 sets of Pullups (your bodyweight): Week one is 2,2,3=7rep total.  Week 2 is 3,3,3=9rep total.  Week 3 is 4,4,2=10rep total at the same rep weight.  So for this type of routine, your cumulative weight lifted per set will hopefully be increasing.  Your total reps per session will also be increasing signaling strength improvement in this exercise set. (But the strength factor will decrease, more on this later)
     
  • A typical bodybuilding routine is 5 sets of decreasing reps but increasing weight.  For instance if you can get 5 sets of 15,10,8,8,8 reps for week one.  Week two you add 10lbs to the bar on the low end and get 15,10,8,6,6.  Are you getting stronger the second week even though you added weight but decreased your reps on the final two sets?  Will cumulative weight or total reps be of any use?  What about the average rep weight and the strength factor?

Strength metrics that can be graphed:
All users get to use the first 5 graphs.  Performance members are able to use the full list of strength graphs for their performance analyzation.

 

Definitions
This is the math part, I apologize in advance.  Most concepts are simple algebra and summations.  There are only a few concepts (the number and weight averages) that mimic polymer systems that I have found to be strikingly parallel in concept to our strength training sets and can serve as good indicators of improvement.

Each definition will be followed by some sample graphs of a live persons strength data to demonstrate.

Total sets = The total number of sets within selected time period.  Set data per 'Total Exercise' over a time period can really show you how many different exercises you do per bodypart and the sets you devote to them.  Are you a 2 exercise per bodypart person or a 4-5 exercise per bodypart person? 

 

Likewise, you can see the total set distribution of all exercises over your entire body.

 
 
Total reps = The total number of reps within selected time period.

 

 
 
Reps/Set = (Number of Reps)/(Number of Sets) in selected time period. 

 

The above three metrics of total sets, total reps and reps/set only signify the trend in the composition of your sets.  They don't necessarily mean you are getting stronger or weaker as they are independent of logged weight.
 
Cumulative weight = The sum of the (#Reps X Weight) of all sets within a time period.

An increase in this number just means that per the time period, you are working more by lifting more total weight.  A good metric to gauge increase in strength if your set composition (#Reps/Set) remains fixed.

 

  
 
Average Total Set Weight = (Cumulative weight of all sets)/#sets.

An increase in this number can signify an increase in strength as within a particular set composition, the weight that you lift is increasing.

 

 

Number Average Rep Weight = (Cumulative weight of all sets)/#Reps.

Weight Average Rep Weight = (Cumulative RepXWeightXWeight)/Cumulative Weight 
    
This is a tricky equation but this Weight Average is more 'weighted' towards a higher average weight per rep over the Number Average Rep Weight.

 **Number Average Rep Weight < Weight Average Rep Weight
***Number Average Rep Weight = Weight Average Rep Weight ONLY if the weight you use per set per rep stays the same.

 

 

Both Average Weight/Rep numbers will tend to increase as you increase the weight of your set assuming the composition (#Reps/#Sets) remains relatively constant.  An increase in this number will tend to indicate and increase in strength per time period.

Strength Factor = (Number or Weight Avg Rep Weight)/(#Reps/#Sets)

The Strength Factor is for advanced analysts and can be tricky in it's interpretation if you can't figure out the math.  It's a number that can do two things and is highly dependant on total set composition:

1 - It will tend to decrease as you increase the total reps of your set.  For example, you increase the #reps of your last 3 sets OVER the previous workout at the SAME set weight-the denominator gets smaller.  NOTE, this does NOT mean you are getting weaker since your cumulative weight is still increasing. (#sets/#reps is still constant)

2 - It will increase if your (#Rep/#Sets) remains constant but you are adding more weight across your sets to give you a bigger Avg Rep Weight.  You are getting stronger.

In general given a fixed denominator (#Reps/#Sets), the more weight you use in your sets, the bigger the number will be.  You will see that Squats, Bench Presses and Deadlifts will have far larger 'Strength Factor' numbers over Bicep Curls and Front Deltoid Raises.  Just notice the below difference between Bench Presses and Pulley Pushdowns.

 

 

As you progress weekly with your weight routine, the Strength Factor can tend to 'dip' periodically depending on your sets as you are able to achieve your goal #Reps per Set before you increase your weight across the set for the next time. 

Lets analyze the 'Average Weight per Rep' and the 'Strength Factor' numbers for these two exercises and compare them to the four graphs above.  Here are the raw logged set data representing four workouts.  This data represents workouts of one that is just getting back into lifting and starting to add weight every week to build strength.

6/25
 

7/2
 

7/9
 

7/16
 

In all cases, the first two weeks yield the same 'average weight per rep' and 'strength factor' numbers as the sets are identical.  This person is just getting used to the weight.

The last two weeks indicate and increasing average weight per rep.  We see this in the set data as in the case of the bench press, the weight of the last four sets is increased by 10lbs.  In the case of the pulley pushdowns, the reps increase THEN the weight increases.

"Why the dip in the third week for the pulley pushdown strength factor?"

Remember, the Strength Factor = (Number or Weight Avg Rep Weight)/(#Reps/#Sets). In the third week, the # of reps went from 6 to 8 in the final 3 sets.  That means the denominator increased causing the number to decrease some.  THIS DOES NOT mean that the person is 'getting weak' since the 'strength factor' number is lower, but the person is just doing more reps at the same weight (cumulative weight and average weight/rep WILL increase)  The strength factor increases again in the fourth week as the weight increases by 10lb on the final 3 sets-even though the reps on the last two sets are lower at six-the numerator overides the denominator and growth in this number occurs.

Exercise Factor = (Weight Avg Weight Rep)/(Number Average Rep Weight)

This number only signifies how 'spread apart' your set is.  It's an indicator of set composition of how the weight is distributed between the sets.  When the Exercise Factor is 1.0 (minimum), this indicates that you are using the SAME weight for every set regardless of the number of reps OR the number of sets.  The more this number increases from 1.0, the more your set has a weight spread between the sets.

 

This is the same data as used in the 4 weeks of bench press and pulley pushdown log data above.  The last two sets are higher in number as we can see from the data that the last sets are increasing in weight while the first set stays remains the same.  There is more weight variance between sets. 

*People logging strength data where the weight is the same for each set will only get values of 1 for the Exercise Factor!

Max Weight - 1Rep = This is a useful tool for bodybuilders that will ONLY look for your max weight of 1 rep within the exercises of the time period.

Max Weight - 1Rep+ = Will just look for the maximum set weight per exercise for the lowest number of reps over the time period.

 

This data is taking only the maximum set weight from the prior four weeks of logged data.

# Reps per Weight Histogram = For each exercise, this will display a plot of all set weights lifted versus the number of reps for those weights.  Interesting insight on set composition over time.

 

And finally, everyone LOVES pie!

 

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date: July 26, 2006
 






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