Powerlifting Relative Strength Calculator
Scroll down for introduction and usage instructions.
UPDATE: A thorough bug fix with plenty of added functionality was released on February 4, 2007. See the development history below for further details.
About
What relative strength is - and isn't
Maximal strength is dramatically affected by such variables as the bodyweight, age and gender of a lifter. If you want to be picky, you could add anything from muscle fiber proportion and individual leverages to mental factors, such as whether you are wearing your lucky Mickey Mouse underwear or not, but since blaming a poor total on your leverages is not generally acceptable and since the formulas we are about to discuss only concern themselves with the major differences of bodyweight, age and gender, we need not concern ourselves with minutiae. Let's just say that an 80 kg/177 lbs bench press would be a mediocre lift for a 100 kg/220 lbs 28 year-old male lifter, but an awesome lift for a 50 kg/110 lbs grandmother aged 78. We could say that the masters lifter is very strong relative to her strength potential whereas the man isn't anywhere near his. That's relative strength in a nutshell.
This is probably a good time to point out that even when reduced to only bodyweight, determining relative strength is not as simple as directly comparing lifts with bodyweight (as in a "double bodyweight bench press"). Relative strength is simply not linear with bodyweight. In fact, the best weight to achieve good results compared to bodyweight appears to be around 60 kg/132 lbs for men and 50 kg/110 lbs for women, after that the added bodymass will make it progressively harder to reach an impressive bodyweight compared result.
A few words on relative strength formulasOver the years, a number of formulas (or formulae if you prefer that spelling) have been developed to assess and compare relative strengths in heterogeneous groups of lifters. The formulas have generally been created by fitting a mathematical formula to world class level meet results in all weight classes over a certain time. It is important to realize that what equipment is allowed and the position on drugs varies from federation to federation as well as over time which might cause a certain degree of bias towards certain weight classes when used to rank competitors lifting under circumstances different from those the formula was developed under; see the NASA formula for notes on how formulas based on drug using lifters will skew the results for natural heavyweights, a similar skewing might well occur when formulas based on equipped lifters is used on RAW lifters as body size is likely to somewhat affect how much stretch, and thus pounds, one gets from the equipment (generally, lighter lifters get proportionately more out of their gear). Typically, each lifter's total is multiplied by a bodyweight/gender specific coefficient with a separate coefficient being used to adjust for age (typically masters lifters above 40 years of age and sometimes teen lifters up to 22 years of age). Not all formulas support all handicaps, but bodyweight is the common denominator. As an illuminating example, applying the Wilks formula with handicaps for bodyweight, gender and age on the bench press example above, the old lady would soundly beat the male lifter with a 201.5341 score against his 48.6871 as she gets much more favorable coefficients due to her senior age, female gender and respectable age (a 1.284638 bodyweight/gender coefficient AND a 1.961 age coefficient against his single 0.608589). To beat the grey powerhouse, the man would have to bench a whopping 332.5 kg/732 lbs! That's how heavy 80 kg/177 lbs is to granny.
Relative strength formulas are commonly used to determine the overall champion across all weight classes and in open meets, but are also invaluable tools for comparing the progress of a single lifter whose weight fluctuates over time (e.g. to see how a diet cycle has affected relative strength). At this time, there is no universally accepted formula with different powerlifting federations using different ones. The formulas are usually broadly in agreement, but when the competition is tight the formula selected might mean the difference between a gold and a fourth place finish. For Master lifters (aged 40 and over) an additional bias is introduced by the use of different, or no, age adjustment formulas, which can easily give or take 20% off their relative strength adjusted totals depending on formula.
How does this calculator work?
This calculator allows you to quickly compute the relative strength based on the totals (combined weight for squat, bench and deadlift) of one or more lifters using the most common formulas. Only the bodyweight handicap is selected by default, the others depend on whether the relevant fields are filled (if there is at least one female lifter involved the gender handicap is triggered, if the age is given for any lifter the age handicap is triggered). In the event that a formula can't take all requested handicaps for one or more lifters into account either by design (Siff and NASA do not have separate coefficients for women) or convention (for example, NASA is never age adjusted in NASA meets), the affected lifters are clearly written in red with the variable that couldn't be accounted for striked out. For example, if a 52 year old lifter is compared using NASA and Wilks, his age will be striked out for NASA since that formula does not take his age into account (for official NASA results not hampered by the strikes, just omit the age).
Sometimes it may be desirable to remove the age adjustment bias to compare formulas head-to-head; this can be done either by not entering age at all or by asking the calculator to use the same age coefficients for all formulas, whether conventional or not (all age adjustment formulas are based on percentages and can thus be used interchangeably). No matter whether the defaults or a specific formula is selected, the age coefficients used will always be noted together with the results to minimize the risk of confusing official with hacked results.
Ultimately, the calculator can only make educated guesses as to what the "official" combinations and practices are, leaving it up to the user to verify the options if using the calculator to score meets. Note that the script author does not accept any responsibility for miscalculated results. If you suspect a bug or formula mistake, please report it asap (e-mail at the bottom of this page).
Most formulas have a name for their coefficients, but in the interest of making the results easier to compare these have been dropped.
A closer look at the supported formulas
The formulas are presented in a rough chronological order, oldest to newest. The available background information for some of them is scant, more information would be highly appreciated (again, e-mail at the bottom of this page). Please let me know if there is any formula you think should be added.
Each formula presentation is linked to the formula table on the Internet that was used in creating this calculator. Mistakes have since been uncovered in most of these formulas (see the Development history for the gory details) which have been fixed in this calculator according to the best of my ability; corrected tables can be retrieved using the formula dump function above. At the end of each presentation, the characteristics of each formula is briefly listed together with the default handicaps conventionally used for that formula. You will note that most formulas by default adjust for age using the independent Foster Age Coefficients for Teen lifters and the McCulloch Numbers by Eugene McCulloch for Masters lifters (this formula was revised some time ago to be more conservative, here's what I believe is the old version).
- Schwartz/Malone
formula:
In the 1970s, Dr. Lyle Schwartz created a classification
standards for men. Dr. Schwartz was a lifter and official
associated with both the Amateur Athletic Union (AAU),
which pioneered powerlifting meets by officially
sanctioning the sport in 1964, and The United States
Powerlifting Federation (USPF) formed in 1980 as the new
national governing body. Later Pat
Malone, a champion for women's powerlifting, created the
Malone formula to give women a fair scoring. With agreement
from Dr. Schwartz, the two formulas were henceforth combined
into the male/female Schwartz/Malone formula that allows men
and women to compete in the same arena. The Schwartz Masters
Formula coefficients, probably of later origin, allow handicaps
for Master lifters between 40 and 80 years of age (to my
knowledge, there are no teen coefficients). The popularity of
the Schwartz/Malone formula decreased as the Wilks formula was
popularized, but many federations still consider this to be a
less biased, and hence, better, formula. This calculator uses
what I believe is the original pounds formula; an Excel
spreadsheet with a kilogram formula also exists, which
appears to have been created by converting the bodyweights into
kilograms and then interpolating to an accuracy of 100 grams.
In effect, this formula uses the pound coefficients with
kilogram totals leading to a result that is roughly 2.2046
times lower than when using the pound table (this is supported
by testing the accompanying Schwartz-Malone
kilogram calculator).
[Granularity: men 90-362 lbs (40.8-164.2 kg), women 90-250 lbs (40.8-113.4 kg), 1 lbs (0.45 kg) jumps. Default handicaps: bodyweight, gender, masters 40-80 years] - Reshel
formula: Created by American Powerlifting Federation
(APF) Technical Officer Greg Reshel for use in APF/World
Powerlifting Congress (WPC) meets. Since replaced by the
Glossbrenner formula.
[Granularity: men 50-175 kg (110.2-385.8 lbs), women 40-119 kg (88.1-262.3 lbs), 0.25 kg (0.55 lbs) jumps. Default handicaps: bodyweight, gender, teens 14-23 (Foster's), masters 40-90 years (McCulloch)] - Siff
formula: The origins of the Siff formula goes back to
1971 when South African sports scientist Dr. Mel
C Siff and McSorley, a South African engineering student,
created equations to fit all world records up to the 110kg
class for the last three years in weightlifting. In 1998, Dr.
Siff adjusted the formula by statistical regression of "the
mean of the ten best lifts ever achieved in each of the 11
bodymass classes in weightlifting history for bodymasses up to
about 165 kg". At the same time, Dr. Siff also created formulas
for powerlifting based on data up to 1987. Unlike the other
formulas, there are separate formulas for the three individual
lifts (available in a
separate calculator). The equations are presented in
Siff's classic book Supertraining
(see chapter 3.3.5) where example data can also be found for
verifying that the calculator is correct. Whereas most other
formulas give an adjusted total, the Siff value is a percentage
of a World Record performance; for example, a Siff total score
of 89.2 means that the total was 89.2% of a world record total
in that class. Supertraining goes on with extensive discussions
on adjusting for gender and age, but unfortunately only in
reference to weightlifting. Even if the formula fits the data
well on paper, it has not gained much of a following in
powerlifting (no federation I know of relies on Siff). Read this (or in
French) for Siff's take on other handicapping systems,
especially on Wilks.
[Granularity: mathematical formula, supports any bodyweights. Default handicaps: bodyweight] - Wilks
formula: Developed by Robert Wilks of Australia, the
Wilks formula was adopted for use in the The International
Powerlifting Federation (IPF) in January 1997 and a year
later for USA Powerlifting
(USAPL) meets. Similar to most of the other formulas, the
Wilks adjusted total is usually calculated using a coefficient
table (in pounds),
but this calculator uses the actual
mathematical formula. This makes it preciser, but might
lead to minor discrepancies when compared to table generated
results, especially if bodyweights are not given as increments
of 0.1 kg/0.25 lbs. For those interested in research, here's
a paper that
validates the formula for use with bench result and totals.
[Granularity: mathematical formula, supports any bodyweight. Default handicaps: bodyweight, gender, teens 14-23 (Foster's), masters 40-90 years (McCulloch)] - NASA: The
NASA Outstanding Lifter (OL) & Drug Free Lifter Coefficient
Standard is used in Natural Athlete Strength
Association (NASA) meets. I am grateful to NASA founder
Rich Peters for providing
me with detailed information on this formula and for allowing
me to use it despite it being copyrighted. In Mr. Peter's
own words:
I developed the co-efficient formula myself. I noticed years ago that all of the formulas of the day were based on lifters that had used or were using Steroids. Thus, heavier body weights translated to more muscle mass. But, in reality, in drug free lifting, heavier bodyweights mean more body fat in almost 90% of all instances. This has to be taken into consideration when developing a formula for Drug Free Lifters.
We first changed all our records and drug tested ALL of our new records starting in 1996 and then we tested ALL AR's for the next 2.5 years. This established a pattern and a standard for Drug Free Lifters that were truly Drug Tested and passed. We felt that by also dividing the actual weight lifted by the lifters bodyweight that it would lend more credibility to the performance by each lifter. After we did this, we included the new Formula as the multiplier.
What we found was that our OL's went from the customary 181-220 lb winners to OL'ers from all weight classes based on their performance. Some have questioned the fact that our top 100 Lists are heavy with 181-242 lifters. I have pointed out that by comparison and percentage or NASA lifters, the numbers are quite even. Yes, we have many 181-242 lb lifters in our top 100, but their percentage of our Total Membership is equivalent to their representation. Lifters should also remember that our larger lifters also come from a variety of other "strength" sports such as wrestling and football.
Those that helped me with these calculations were Mike Ewoldsen (math) and David Oyler (selecting mean numbers. We invested about $40,000.00 in testing developing this formula and it has been a very effective method of test selection and OL coefficients.
It is important to realize that when doing OL'ers, a meet director will notice a distinct line in the sand with these formulas. this line lies between the 140-170 lb. bwt lifters. To adjust for this, we usually split our OL'ers are given for light and heavy portions of the meet that day in the smaller meets.
Either way you use our formula, a lifter that goes over 10.0 in NASA is a hell of a Drug Free Lifter. In the Lighter weights, a 9-9.6 coeff is awesome as well.
Is our system perfect? NO! None of the OL coefficients are. But is ours the most efficient for Drug Free Lifters? We think so, we actually did the research to develop the system.
What many do not take into consideration when developing these formula's and what the "old timers" didn't address, was the drug free lifter into the equation. You cannot have an efficient Coeff if you are mixing drug free lifters with non-tested lifters. This is the main reason I copyrighted it in 1998.
[Granularity: 119-326 lbs (54-147.9 kg), 1 lbs (0.45 kg) jumps. Default handicaps: bodyweight] - Glossbrenner
formula: Created by Powerlifting USA statistician Herb
Glossbrenner in 2004, this formula is an average of the
Schwartz and Wilks formulas. The reasoning behind combining
these two is that Schwartz formula allegedly favors lighter
lifters and Wilks heavier lifters, hence an average should
balance things out. Replaces Reshel in the APF-AAPF-AWPC. Note
that Glossbrenner supports any bodyweight above the listed 231
kg for men and 169 kg for women via interpolation, but this is
not as of yet baked into this calculator.
[Granularity: men 40-231 kg (88.1-509.3 lbs), women 40-169 kg (88.1-372.6), 0.05 kg (0.11 lbs) jumps. Default handicaps: bodyweight, gender, teens 14-23 (Foster's), masters 40-90 years (McCulloch)]
Development history
March 26, 2007: Fixed an error in the Glossbrenner Women's Formula where the 149.5 kg coefficient was inflated to 0.64586. This error is present in both the source table and the WPC-WPO Russia calculator, but replaced it with a logical 0.64536. A BIG thanks to Mika Pesonen for reporting the bug. Hopefully it was the only one that slipped through the February anomaly scan; if not, scream!
February 4, 2007: Fixed several bugs, a few of them severe, and added new functionality.
A. NEW FUNCTIONALITY:
- Formula dump. The errors revealed in most formula tables found on the Internet prompted the addition of a separate function to write out the coefficient values the calculator is actually using in real-time. This serves as a handy way to print out bug-fixed formula references and helps anyone verify the tables (a little tip is to set the column width to 1 to allow easy pasting into Excel or OpenOffice Calc). The formula dump also allows conversion of tables between kilograms and pounds, plus can create coefficient tables out of the mathematical formulas (Wilks and Siff) for easy reference.
- Option to use any combination of Teen and Masters formulas. To cater for those cases where a powerlifting federation may not be using the conventional combinations of relative strength formula and age formulas, and to allow removing the bias of mixing age formulas, the calculator now supports overriding the defaults. In many cases this will produce unofficial results.
- Added original McCulloch formula: The original McCulloch coefficients have commonly been replaced with a more conservative version. The original formula was added to allow recreation of meet results scored under the old formula (and for those wishing to adjust more liberally for age).
- Added % of Winner column: In addition to rank, all results now also indicate how many % of the winning total each lifter scored. This makes it easy to see how results were distributed for each formula at a glance.
- Added a datestamp to results and dumps: This makes it easy to verify if a result might have been generated before some as of yet unknown (and hopefully, non-existing) bug was fixed.
B. BUG FIXES:
Fixed several bugs revealed by graphing out the coefficient tables and comparing each value with its neighbours to find coefficients that caused a sudden shift upwards or downwards. When a coefficient is either higher or lower than both its neighbours, it is with 100% certainty a bug since lighter bodyweights should always receive higher handicap than heavier bodyweights (for example, a coefficient series from heavier to lighter of 0.551700, 0.511650 and 0.551600 shows that the middle one is a bug since it is not anywhere between the two values but far below them). If coefficient bugs remain, they are values that are wrong but still fall between their immediate neighbours; although academically distressing, these errors will always be very close to the correct value (in example above, taken from the an actual bug in the Glossbrenner formula, the error margin is no larger than 0.000099). A few bugs of this minor order replaced serious coefficient errors when there were no means of reliably retrieving the correct values from another source or by analysing the logic of the formula; in these cases, an average of the neighbouring values was used to provide a reasonable value.
With the exception of a few mistakes in the calculator source code, the coefficient errors found originate in the formula tables used to create the calculator. Since the mathematical formulas (Wilks and Siff) cannot per definition have a bug if the formula is correct, I only had to run through the table based formulas comprising Glossbrenner, Reshel, Schwartz-Malone and NASA. Out of these, NASA was the only formula in which no obvious bugs were found. Glossbrenner had the most typos in the source table - perhaps not surprising since the 0.05 granularity gives Glossbrenner the most coefficients on the order of just above 3,800 values for the men's table alone; in this light 9 mistakes for men and women combined is not a lot. Alarmingly often, the errors were replicated in all the coefficient tables found online suggesting that they all have been copied from a single source. When taken into account that many obvious coefficient mistakes (such as misplaced decimal signs and extra zeros) were corrected during the initial coding of this calculator, there are good grounds for urging caution when using many of the coefficient tables found online... even if it is an official table found on a powerlifting federation's site; possible exceptions are Wilks (did not test the coefficient table since the calculator uses the mathematical formula) and NASA (no obvious mistakes). The mistakes are not many, but if a lifter hits one of the affected bodyweights serious distortion could result which, in a worst case scenario, could award the trophy to the wrong lifter. I am contacting the relevant parties to inform them of the mistakes, but this is naturally no guarantee that the affected values will actually be corrected.
Below is a breakdown of the issues fixed.
Coding mistakes in the calculator
- Rounding bug affecting bodyweight submitted with decimals and internal conversion between pounds and kilograms: This bug affected the Glossbrenner, Schwartz-Malone and Reshel formulas only. Important calculations done before January 22, 2007 should be resubmitted to have possible errors weened out. Apologies for any inconvenience this bug may have caused.
- Results in rare cases not sorted correctly.
- Glossbrenner formula lacked data for women's 112-125 kg bodyweights.
- Glossbrenner Women's 58.40-58.95 kg: A find and replace gone horribly wrong had resulted in seriously inflated values due to missing zeros and decimal signs; easily corrected by referencing the source tables.
- Glossbrenner Men's 111.55-111.95 kg: Line in source code was messed up causing these values to be low on the order of 0.01.
Glossbrenner errors in source table
These are errors found in the
official formula published on the WPC site (archived
copy with current bugs) that this calculator's
implementation was based on. As an aid in debugging, the new Glossbrenner
calculator offered by WPC-WPO Russia was used (to retrieve
the actual coefficient, just add 1 as total). Unfortunately,
besides not working in browsers other than Internet Explorer,
it had a host of coefficient mistakes of its own (for example,
all values for women's 116.90-133.30 kg classes have a bug
caused by a shifted value) causing it to be of little use in
solving some bugs.
- Men's 64.75 kg: Dipped to 0.77502; Glossbrenner calculator indicates that also the 64.8 value (0.77540) is wrong. Changed accordingly to 64.75 = 0.77540, 64.8 = 0.77502).
- Men's 108.10 kg: coefficient dipped to 0.53530; Glossbrenner calculator confirms this as 0.56530.
- Men's 119.30 kg: coefficient dipped to 0.51165; Glossbrenner calculator confirms as 0.55165.
- Men's 128.45 kg: coefficient inflated to 0.591875; Glossbrenner calculator confirms as 0.541875.
- Men's 132.75 kg: coefficient dipped to 0.437645; the value is also wrong in the Glossbrenner calculator (0.57645), should most likely read 0.537645.
- Men's 139.05 kg: coefficient dipped to 0.531057; Glossbrenner calculator confirms as 0.531957.
- Women's 133.30: coefficient inflated to 0.68185. Should probably be 0.66185 based on spacing between neighbouring coefficients. Glossbrenner calculator of no use due to a bug in this weight range.
- Women's 137.55 kg: coefficient inflated to 0.65965; should most likely be 0.65695, Glossbrenner calculator failed to verify due to a bug in this weight range.
- Women's 145.9 kg: coefficient dipped to 0.64826; 0.648360 is likely correct since it represents a 0.000050 drop from the previous (145.85 = 0.648410) and next (145.95 = 0.648310) weights which is the same as the drop shown in the surrounding classes.
Schwartz-Malone errors in source table
These are errors found in the Schwartz-Malone coefficient table on the APA-WPA site (archived copy with current bugs) which this calculator's implementation was based on. Note that the bug fixes for Schwartz-Malone contains a few corrections which, although logically bugs, could be correct values. Confirmation on these values from an independent source would be warmly welcome!
- Women's 136 lbs: was 0.8101 on all charts found on the web which cannot be correct as the 135 lbs coefficient is 0.8462 and the 137 lbs 0.8358 causing a sharp dip for 136 lbs; in lieu of finding the real constant an average between the 135 and 137 lbs coefficients has been used (0.8410).
- Women's 249 lbs: dipping coefficient 0.5556; corrected to 0.5656 in accordance with this version.
- Women's 157 lbs identical to 156 lbs: the only instance in the whole formula where a value is identical between two bodyweights strongly suggests a typo. Found no instances online with another value in here, used an average of the 156 and 157 lbs coefficients to produce 0.7487.
- Women's 178 lbs (0.6811) nearly identical to 179 lbs (0.6810): The difference is abnormally small (0.0001) whereas the drop between 177 (0.6866) and 178 lbs is unusually drastic (0.0055) suggesting that the 178 lbs coefficient is a typo. Inserted an average (0.6838) between the coefficients for 177 and 179 lbs.
- Men's 193 lbs: coefficient dipped to 0.5878; assuming a reasonable typo of 0.5978.
- Men's 225 lbs: heavy peak at 0.5994. This is wrong on all charts found on the Internet, assuming a typo of 0.5494.
Reshel errors in source table
These are errors
found in the Reshel
coefficient table (archived
copy with current bugs) used as a source for this
calculator.
- Women's 41.5 kg: coefficient dipped to 2.195; this version (pdf) verifies it as a typo (2.915).
- Women's 70.75 kg: the 1.695 coefficient was much higher than the other 70 kg coefficients in the source table; corrected to 1.595 as per this version.
- Men's 58.00-58.25 kg: both coefficients dip too low (1.460 and 1.451); corrected to 1.497 and 1.488 in accordance with this version (pdf).
May 15, 2006: Released the calculator.