The MeenaMethod Math

This post outlines the math of the MeenaMethod framework, ultimately resulting in the calculation of objective performance points for Metric Sports.

As previously stated in “Rethinking Performance Methodology in ‘Objective’ Sport”, the MeenaMethod framework compares performances against a benchmark to establish a relative scale that evenly distributes performance points across a linear slope.

Additionally, adjustments can be added for a gamification effect as long as they, too, are objective. Therefore, unless otherwise stated, all performance points are considered to be unadjusted.

So, now, let’s dive into the framework…


THE FRAMEWORK


Benchmarks

A foundation of the MeenaMethod is the utilization of benchmarks, defined as “a standard or point of reference against which things may be compared or assessed”. And, to be more precise, the benchmarks used must be measured objectively (e.g. in meters, seconds, or kilograms), which effectively means the MeenaMethod focuses on Metric Sports.

The reason for using objective benchmarks is because they are unbiased and universally regarded as accurate. Said differently, objective benchmarks are not influenced by human emotion.

  • For example, everyone agrees that Usain Bolt’s 100–meter dash world record of 9.59 seconds did, in fact, take 9.59 seconds to complete.

    • Therefore, when calculating relative comparisons for male running sports, using Bolt’s world record as a benchmark is universally agreed as applicable and therefore serves as an objective benchmark.

  • However, and again, just as an example, in the modern era of professional baseball (i.e. since 1900) the number of perfect games thrown is 21, but some might argue that the correct number is 22, because the Armando Galarraga “28–Out Imperfect Game” should be included.

    • However, since Major League Baseball rules do not allow for video replay confirmation, or even umpire admission of guilt, to overturn a call, a batter was awarded a base hit and Galarraga’s perfect game was null.

    • Therefore, since human emotion dictated the result of this perfect game benchmark, it is subjective.

The point is, while subjective benchmarks can still be relevant, they are outside the scope of the MeenaMethod because they are subject to factors that are arguably impossible to quantify (e.g. human emotion).

On the contrary, objective benchmarks are primarily unadjusted, and even in the rare cases when adjustments are required, they can be quantified (e.g. drag or altitude).


Scales

While benchmarks are used as the comparison metric for which to calculate performance points, they must be used in context on a defined scale. Different benchmarks create different scales, and performance points do not transfer across scales. Said differently, scales can also be considered as cohorts and since they are dependent on the benchmark, they are therefore named after the benchmark.

  • For example, in previous posts the benchmarks used for reference were the World and NCAA records, so the scales for each would be labeled as the “World Record Scale” or the “NCAA Record Scale”.

Benchmarks, and thus scales, can also range in their scope of who is included in the cohort. From very broad to very narrow, benchmarks used in the MeenaMethod could be, for example:

  • Very Broad: a world record, which can apply to any competition and any age group

  • Broad: a Division 1 NCAA record, which can apply to any Division 1 NCAA competition

  • Narrow: the fastest performance, or the average of all performances, in a given competition

  • Very Narrow: a personal record, which applies to one individual but across any competition

Regardless of the benchmark used, in all cases of the MeenaMethod the scale applies 100.00 points to the benchmark, and if a performance beats a benchmark, then it achieves more than 100.00 points.

What this means is, as previously mentioned in the footnotes of “Rethinking Performance Methodology in ‘Objective’ Sport”, the MeenaMethod agrees with the statement that “not all records are created equal” but disagrees with the statement that “not all records are considered equal”.

Under the MeenaMethod all benchmarks on a scale are equal to 100.00 points, and thus equal to each other. Therefore, all world records are considered equal, all D1 NCAA records are considered equal, and all personal records are considered equal. Furthermore, in the case where benchmarks are competition specific (e.g. equal to a first place performance or average of performances), all benchmarks produced from events within the competition are considered equal.

  • Regarding “not all records are created equal” - this is true.

    • A faster record-breaking performance can earn less points than previous record-breaking performances under the MeenaMethod.

    • For example, Caeleb Dressel earned 100.25 points for his 39.90 SCY 100 Freestyle NCAA breaking performance at the 2018 D1 NCAA Swimming Championships, but he earned 101.14 points for his 40.00 SCY 100 Freestyle NCAA breaking performance at the 2017 D1 NCAA Swimming Championships

  • Regarding “not all records are considered equal” - this is false.

    • All benchmarks (measured under the same conditions) must be considered relatively equal (or far, or fast, or heavy) as each other.

    • Just as one must assume the financial capital markets operate efficiently and thus use benchmarks (or indicators) such as the S&P 500 for equities or LIBOR for debt, the MeenaMethod does not allow for arbitrage.

    • If you want to know the true impact of a record, you should look at the points achieved when the record was set.

      • For example, Caeleb Dressel’s SCY 100 Butterfly NCAA Record of 42.80 may only be worth 100.00 points now, but it achieved 101.79 points when it was set at the 2018 D1 NCAA Swimming Championships.

    • Additionally, if a benchmark is under question (e.g. suspicion of doping or illegal/superior equipment), it is certainly a viable concern and, from a statistical perspective, a way to validate the concern is to compare the benchmark under question to other unquestionable benchmarks.

Lastly, as stated earlier, performance points do not transfer across scales so it is important to note that a world record is not considered equal to a D1 NCAA record which is not considered equal to a personal record (unless all are held by the same participant, respectively). However, performance points do transfer across Metric Sports, as long as the same scale is used. This broad scope of benchmarks is used for universal comparisons primarily, but the assumption is, for example, that the world record for a male 100–yard freestyle swimming race is equally, and relatively, as fast as the world record for a female 200–meter dash running race.


Slopes

Since all benchmarks are equal to 100.00 points by default, similar to scoring 100% on an exam, then performance points can be calculated and evenly distributed using a linear slope assumption. However, even if the benchmark value is altered, the slope can still be linear using the MeenaMethod, but the significant digits of the point values might need to be expanded in some cases to ensure separate values are given to different performances.

Remember that word, slope? Or better yet, remember “rise over run”? This is a perfect descriptor as to why a linear slope is crucial to the MeenaMethod. A linear slope means that how fast/slow you run (for example) is directly and equally correlated with the amount you rise/fall on the scale.

Many Metric Sports already utilize performance points of some kind, but they are calculated using a non–linear slope equation. For example, a decathlon is scored in points based on an a set of performances; swimming utilizes FINA points based on a cubic curve; and Olympic Weightlifting adopts the Sinclair Coefficient method. Are these methodologies wrong? No. Are they outside the realm of the Meena Method? Yes.

Aside from the fact that a non–linear slope is difficult to comprehend and therefore loses the attention of the participants rather quickly, the compliance issue is that a non–linear slope favors a certain portion of the scale over others. On the contrary, by using a linear slope the MeenaMethod evenly distributes performance points across the entire scale to all participants.


Performance Points

To summarize the framework outlined above, performance points are a way to rank performances (e.g. distance jumped, time swum, weight lifted) based on a benchmark. Additionally, performance points can compare performances from different Metric Sports (e.g. the long jump vs. swimming vs. clean & jerk) if the same scale is used (e.g. the World Record scale, or the NCAA Record scale), and a linear slope is produced.

Additionally, the MeenaMethod framework is based on the theory that every benchmark on a dynamically adjusted scale is equal to the other benchmarks on that same scale, regardless of the sport or the date in which the benchmark was established.

  • For example, if every world record (i.e. the “benchmark”) in a Metric Sport is equal to each other world record, then Mike Powell’s Long Jump WR of 8.95 meters set in 1991 is equal to Katie Ledecky’s 400m WR of 3:56.46 set in 2016 is equal to Nijat Rahimov’s Clean & Jerk WR for the 77 kg weight category of 214 kg set in 2016.

  • Therefore, on the World Record scale, all three of these results are equal to 100.00 performance points.

    Note: ideally scales are most applicable when comparing to the same sport (e.g. long jump vs. long jump, or swimming vs. swimming)


Adjustments

As previously stated, all performance points are assumed to be unadjusted unless otherwise stated. Therefore, typically, adjustments come into play (pun intended) when performance points need to be gamified, for example, in a competition when first place is awarded extra points for winning.

Theoretically, adjustments can be ascribed any value but in order for them to qualify for the MeenaMethod they must be objective to maintain the consistency and neutrality of the unadjusted performance point calculation.

  • For example, an adjustment of adding 10 performance points for winning first place, regardless of the performance itself, is subjective and does not qualify for the MeenaMethod.

  • However, if a first place performance in a heat of eight competitors finished 9.95% ahead of the mean of the eight performances, a 9.95 performance point adjustment is objective and does qualify for the MeenaMethod.

Furthermore, adjustments can be applied against:

  • an individual benchmark such as, for example, a world or personal record and the adjustment could be calculated based off the amount by which the benchmark was broken or the time (in days/years) in which the benchmark was held.

  • a group benchmark such as, for example, the mean or median of a group of performances and the adjustment could be calculated based off the amount by which the benchmark was exceeded.

    • Note: this sort of adjustment could apply to multiple participants - for example those that exceed the benchmark could be awarded (i.e. added) an adjustment and those that do not meet the benchmark could be penalized (i.e. deducted) an adjustment

Lastly, not all adjustments are created equal so while adjustments are objectively measured they are effectively subjectively chosen, and should not be combined with other adjustments unless they are relatively equal to the other adjustments.


THE MATH


Now that the framework of benchmarks, scales, slopes, performance points, and adjustments has been outlined, lets walk through the actual math of the MeenaMethod.

There are two approaches of calculating a relative distribution scale (i.e. a scale that equally distributes performances). While both are similar, only one (Approach A) produces an identical result for distance, time, and weight based sports (i.e. Metric Sports). Approach B does not qualify for the MeenaMethod because it produces a non-linear slope for sports measured in time.

  • Approach A: “The Distance Approach”

    • Factors the relative space between two variables

    • Slope = linear for distance, time, and weight based sports

    • Note: for the purposes of this case study, Approach A is the MeenaMethod

  • Approach B: “The Size Approach”

    • Factors the relative size of two variables

    • Slope = linear for distance and weight based sports

    • Slope = non-linear for time based sports


MeenaMethod Math for a Distance Based Sport

The world record in Men’s Track & Feld Long Jump is 8.95 meters, set by Mike Powell on August 30, 1991

= Benchmark = B = 8.95 = World Record

= Result Tested = T = 8.50 = Carl Lewis 1996 Olympic Performance


MeenaMethod Math for a Time Based Sport

The world record in the female swimming 400 meter long–course freestyle is 236.46 seconds (aka 3:56.46) set by Katie Ledecky on August 7, 2016

= Benchmark = B = 236.46 = World Record

= Result Tested = T = 238.54 = Katie Ledecky 2017 World Championship Performance


MeenaMethod Math for a Weight Based Sport

The world record in Male Olympic Weightlifting Clean and Jerk for the 77 kg weight category 214 kg set by Nijat Rahimov August 19, 2016

= Benchmark = B = 214 kg

= Result Tested = T = 196 kg = Ihab Mohamed 2017 World Weightlifting Championships


Adjustments to Performance Points

Adjusted performance points are only applicable when the adjustments are objective. For example, adding 10 points to every first place finishers unadjusted performance point calculation for winning first place is subjective as the 10 points is an arbitrarily picked number.

Furthermore, as previously stated, adjustments can be broadly applied based off individual or group adjustments.

Examples of Individual Benchmark Adjustments

  • Distance Adjustment Relative to a Benchmark

    • Factors the relative space between two variables

    • Gives favor to a performance for breaking a benchmark

    • Note: this is the preferred adjustment for individual benchmarks under the MeenaMethod as it relates directly to the performance

  • Length Adjustment Relative to a Benchmark

  • Factors the relative time a benchmark stood before it was broken

  • Gives favor to benchmarks that are not broken as frequently

  • Note: this adjustments, while still objective, is not directly correlated to the performance and should therefore be used with caution

Examples of Group Benchmark Adjustments
Assuming a heat of eight performances

  • 1st Place Adjustment to the Mean / Median

    • Awards (i.e. adds) first place, and any other performances above the mean / median, points relative to how far they exceed the benchmark

  • 8th Place Adjustment to the Mean / Median

    • Penalizes (i.e. deducts) eight place, and any other performances below the mean / median, points relative to how far they are from matching the benchmark


Author: Elliot Meena

Published: May 23rd, 2019

Source: Baseball-Reference, Merriam-Webster, National Institute of Standards and Technology (NISU), University of Cambridge, FINA, International Weightlifting Federation

Note: all performances referenced are as of the date of this publication.