MeenaMoney

Published: April 24, 2022

Introduction

If absolute comparisons focus on quantity, then relative comparisons focus on quality. As such, under the premise that the financial capital markets operate efficiently, accurately, and with transparency (i.e., the efficient market theory), relative comparisons are commonly used to monitor the quality of performances for securities within those markets.

This efficiency theory that performance results are universally agreed to be accurate is the same theory that supports the MeenaMethod scoring methodology for Metric Sports.  Both theories use indicators for comparison purposes that are objectively, not subjectively, derived from the performance result.

These indicators are then used to forecast, or predict, a future performance result. For those that operate within an efficient market theory, forecasting is the practice of using what we know to predict what we do not know but believe we can achieve.  What have we produced thus far, and how can we improve? Whether it is regarding a company’s financial guidance or an athlete’s goal time, a CEO or a coach could ask this exact question to their team.

To objectively understand an activity with a small margin of deviation amongst peers (i.e., financial capital markets and Metric Sports), relative comparisons are the indicators to study.  These indicators offer an objective view of the past that can identify areas in need of improvement.  If these areas are successfully improved, a company or athlete could increase their margin of advantage over their peers or decrease the margin of advantage against their peers.

As a lifelong swimnerd, I have no doubt that my career evolved into a financial capacity because I spent my youth competing in a Metric Sport.  I always knew there were more ways to understand my progress in the pool other than absolute time standards, but sports math was never a subject in school.

Therefore, this publication outlines some educational concepts used in financial capital markets via relative Metric Sports math examples. The intent is not to preach or imply these concepts as the only way in which to view a sport, but rather highlight mathematical similarities between business and sport.

I feel one can learn a lot from relative comparisons, and when teaching relative math, perhaps examples using Metric Sports over financial corporations could broaden the scope of engagement from students.

A Metric Sport performance is, in some regards, a math equation.  Which means, it has a right answer. It can be solved. And the nice thing is, since no two athletes are the same then there can be multiple right answers.

Outline

In their simplest form, relative comparisons can be thought of as a ratio of X divided by Y.  As such, ratios are typically expressed as a fraction, but can also be shown as a number with at least one decimal or as a percentage.

In capital markets, ratios are used commonly to gauge the performance of a company AND to gauge how investors react to the performance of a company.  Whether it is an earnings multiple, a % of revenue datapoint, a stock price increase, or an interest rate reduction, every number tells a story.  Therefore, the more numbers you study, the more context, and thus confidence, you gain to predict the story (i.e., forecast).

In Metric Sports, ratios are helpful to understand the variables used within an individual performance, as well as the result of a collection of performances. Whether it is stroke tempo, prize money, or age group ratings, many aspects of Metric Sports can be addressed with ratios.

This publication will outline, across seven exhibits, some examples of how ratios used in the financial capital markets could apply to Metric Sports.  Note that many concepts are used together, but in this case each exhibit highlights a different lens through which to view swimming.

• Exhibit 1 – Tempo

• Exhibit 2 – Percentages and Multiples

• Exhibit 3 – Equivalency

• Exhibit 4 – Key Performance Indicators

• Exhibit 5 – Sports Betting with Odds & Lines 

• Exhibit 6 – Swimming Ratings as an Analogy to Financial Bond Ratings

• Exhibit 7 – Indexes

Exhibit 1
Tempo

To ensure companies maintain pace to achieve financial predictions, they will monitor progress over time via an assortment of indicators. Pace is important for efficiency in spending and can be measured with indicators such as days sales outstanding (DSO) or salary expense relative to revenue.

Within a Metric Sport performance, such as a swimming race, athletes aim to distribute their energy efficiently throughout the entire distance.  To execute an effective race at a healthy pace, swimmers’ study, among other indicators, stroke tempo.

Stroke tempo helps swimmers identify the fastest speed they can maintain while dispersing a minimal amount of energy, and is measured as:

• Stroke Tempo (aka Tempo) = Stroke Count / Time

If a swimmer is training for a particular goal time (i.e., their prediction), Tempo is a valuable indicator because it helps a swimmer reverse engineer the right stroke count, which is the only variable a swimmer controls (if time is the other variable).

In shorter races, stroke tempo is higher because maximum speed matters most.  In longer races, stroke tempo decreases because swimmers need to maintain a pace for longer periods of time, therefore their energy distribution is not as steep of a decline as in a shorter race.

In the following table for Caeleb Dressel, there are variations in tempo (and therefore stroke count) between his 50 and 100 LCM races.  Both distances are considered sprint distances, but his tempo variances indicate the distances have different strategies.  For example, in freestyle, his “easy speed” is <0.70 strokes/second, but his maximum sprint speed is >0.80 strokes/second.

Exhibit 2
Percentages and Multiples

As stated earlier, ratios are typically in the form of a fraction, but decimals and percentages also work and are sometimes preferred given the context. Furthermore, when referencing scale, decimal ratios are typically labeled with an “x” at the end and referred to as a multiple.

These relative multiples are important because not all companies are the same size, so conversions are necessary to level the comparisons.  This is true for both financial and athletic performance.

In financial performance, a common indicator referenced as a multiple is “Price to Earnings” (P/E) which indicates value as the price an investor is willing to purchase a share of stock vs. the earnings a company produces per share of stock.  This is referred to as an earnings’ multiple, and when compared in a group this ratio is used for investors to identify stocks that are under or overvalued relative to their peers.

On a similar basis for Metric Sport performances, relative multiples can be applied to a broad group of both swimming and running performances.

In the following exhibits, relative multiples will be used to address (not answer) the following question:

Question: How much faster are men than women?

By using world records in these exhibits, a baseline can be established to start a discussion of “on an elite stage, men are X% faster than women”.

From there, the baseline can be used as a healthy indicator when looking at other cohorts, such as studying the doping impact on athletes, or athletes with differences of sexual development (DSD).

As stated above, ratios are often compared with peers and sometimes even combined and divided to determine cohort averages.  In a cohort context, once all ratios have been measured, the result is often described as a range of the minimum to maximum values, along with the average value.  As in, this cohort ranges from X – Y with an average of Z.

To create an initial baseline in response to this question, one approach is to compare the world records of the male and female swimming and straight running (i.e., non-hurdle) events.

Swimming and Running World Records

Conclusion of the World Record Comparisons for Swimming and Running

In conclusion, the initial world record baseline shows that, on average:

• Male swimmers are ~9.4% faster than female swimmers, with a wider range than running at ~6.1% faster in distance events to ~10.6% faster in sprint events

• Male runners are ~9.8% faster than female runners, with a narrower range than swimming at ~9.5% faster in sprint events to ~10.7% faster in mid-distance events

• Blended, male elite athletes are ~9.6% faster than women

Arguably, this sort of analysis with these ranges could be used to determine discounts or handicaps applied to any future performances.  Metric Sports do not historically include fouls, just disqualifications, but if penalties, discounts, or odds (i.e., sports betting) are ever ascribed, relative ranges of a cohort will certainly be factored into the final value.

Again, this is just a discussion starter to establish an initial baseline, in this case, the world record baseline.  Another baseline could involve the average of the top 10 times ever, or each year.  This would broaden the performances for more data points and be an interesting comparison against the world record baseline.

Exhibit 3
Equivalency

In some financial scenarios, when multiple revenue streams are available, it may help at times to combine certain revenue streams.  However, if streams are valued differently, then a ratio must be determined to adjust (aka “weight”) the streams, so they are equally valued.  This is known as an equivalency or weighted adjustment.

For example, companies that produce gold may also produce silver.  But gold and silver have different financial values in a fair market.  Therefore, to convert silver ounces to gold ounces an equivalency ratio must be determined based on the price of the two metals, and that ratio is then multiplied against the silver ounces to produce a gold equivalency (aka “AuEq”) ounce number.

Another financial example of equivalency relates to currencies.  Currencies are often compared to other currencies to determine their “strength” at certain points in time.  You may have heard of tourists preferring certain travel destinations because their local currency might be stronger than the destination currency.  From a relative value perspective, this means the stronger currency is weighted more than the weaker currency.

Equivalency can also work in Metric Sports as a relative comparison, not absolute, to ensure playing fields are weighted equally (i.e., balanced).

For example, equivalencies will be used to address (and try to answer) the following:

Question: Are triathlons fair?

When it comes to certain Multi Sport events, such as Nordic combined or the heptathlon & decathlon, the scoring methodology is weighted appropriately so that each individual discipline is treated relatively equal to every other discipline.

Nordic combined uses the Gunderson Method which weights the skiing distance jumped in the first event to determine the starting line placement for the second event, which is cross-country skiing.  The athlete who jumped the farthest starts the cross-country event first and all other athletes are in a delayed pursuit, the time of which is determined by the distance they were outjumped.  The result, the athlete over the finish line first in the cross-country event is the overall Nordic combined winner.

In heptathlons & decathlons, the scoring system is very similar to the MeenaMethod whereas performances are weighted and scored relative to performance result, and not performance placement.  This equivalency methodology is used for every discipline so that all events are scored equally against a universal benchmark, and ultimately combined for a 7 or 10-event total, with the most points claiming first place.

But in traditional triathlons, the scoring methodology focuses on the total time it takes to complete three disciplines, at various distances, to ascribe placement.  It is an absolute, not relative, scoring methodology and nothing is weighted.

For this exhibit, the focus is on an Olympic distance triathlon, which breaks down as:

• 1,500-meter swim +

• 40,000-meter bike +

• 5,000-meter run

In total, this equates to 46,500 meters traveled, distributed by:

• swimming = 2.9%

• biking = 77.7%

• running = 19.4%

Based on these distances, distance ratios can be established. Furthermore, time ratios can also be established using the world record or world best times for the 1,500 and 10,000-meter distances.

Note that elite times like world records are used to set baselines and are not necessarily always the correct benchmark.  Also, all times are world records except the 10,000-meter swim (which is the world best from 2019) and the 10,000-meter bike (which is an assumed number based on a 40,000-meter record of ~47 minutes).

After analyzing the distance and time data, the following table shows the distance and time ratios.

Question: Are triathlons fair?

Answer: No

If “fair” is intended to mean equal, then no, triathlons are not fair.

Comparing distance ratios, the analysis shows the running portion of the Olympic triathlon is 6.67x longer than the swim.  However, regarding time, men running either a 1,500-meter 10,000-meter distance can finish ~4.20x faster than a man swimming the same distance.

Therefore, all else being equal (e.g., water tides, road elevation), if it takes an elite male athlete ~4.2x as long to swim as it does to run, but the relative distance ratio of the triathlon is ~6.7x longer to run than to swim, that arguably says either the swim is too short, or the run is too long.

So, without even broaching the cycling discipline, the math states that triathlons favor athletes who are faster runners, as opposed to swimmers, relative to the rest of the competition. For this reason, triathlons are not equally balanced, and thus not relatively fair to all participants.

Triathlon Alternatives - Balanced Distances

As an alternative to the current format of triathlons, there is a way to determine three fair distances for three separate sports.  This could be thought of as a relatively balanced triathlon. Or, maybe since it uses the math from the MeenaMethod it could be thought of as a MeenaMathlon?

In the tables below are:

• fixed distance ratios based on the world record and world best times

• suggested distances of a MeenaMathlon if using an Olympic triathlon distance

The distance ratios are used to suggest the proper distance of two sports, based on the chosen distance of the third sport. For example, if the swim is 1,500 meters, then the bike should be 15,000 meters (10x), and the run should be 6,000 meters (4x).  In every instance, the ratio of total time is ~⅔ bike and ~⅓ swim + run.

This approach maintains the traditional scoring methodology of ranking by fastest absolute time, but relatively balances the distances of each discipline based on objective benchmarks.

Triathlon Alternatives - Fixed Time

As an additional alternative to the current format of triathlons, one could measure the total distance in a fixed time, as opposed to total time over a fixed distance.

For example, an athlete swims + bikes + runs for 30-minutes each, totaling 90-minutes.  For each sport, their distance traveled is compared to a benchmark to derive a point value, similar to heptathlons, decathlons, and the MeenaMethod.  Once all three sports are completed, placement is determined based on the total point values across the three disciplines (e.g., on a 300.00 point scale).

This approach shifts the scoring methodology from time focused to point focused, which is more in line with the longer heptathlon and decathlon.

Arguably the energy expenditure may not be equivalent across the three sports for 30-minutes each, but neither is the current format of triathlons according to the math calculated in this exhibit.  From a novelty perspective, a fixed time breakdown may be more attractive to watch and / or participate. 

Exhibit 4
Key Performance Indicators

In some form, most corporations use a Key Performance Indicator, or KPI.  A KPI is typically a numerical figure that is trusted to show the quality of performance for a particular initiative relative to the variables inputted.

A common KPI is to understand how much money an initiative is costing during its lifecycle relative to the forecasted budget put in place before the initiative commenced.  Said differently, a company had an expectation for an initiative, and they want to know how close they are tracking to that expectation as the initiative advances through its lifecycle.

Therefore, going forward when any question of “how much will it cost?” is asked, the corporation can have a reference point for an acceptable amount to spend on a certain initiative.  Furthermore, incentives are sometimes put in place based on achieving certain KPIs benchmarks.  These incentives are typically put in place on either a fixed or sliding scale. Both scales set an incentive and threshold amount, but for a:

• fixed scale, 100% of the incentive is achieved if the threshold is either met or exceeded

• sliding scale, the amount of incentive achieved is related to the amount by which the threshold is either approached, met, or exceeded (meaning it could be <100%, 100%, or >100%) 

In sports, when it comes to salaries, reward money, sponsorship dollars, or scholarship allocations, KPIs are important to track both objectively and subjectively. Not only do they help athletes improve, but they ensure money is being allocated efficiently.

Objective KPIs are more straightforward as they only include objective inputs, such as dollars and times.   Subjective KPIs include factors like social media impressions, which is an informative number that absolutely has value, but largely driven by emotion which is difficult to standardize.

Here are some objective KPI exhibits using a fixed and sliding scale: 

Reward Money Per Performance

The 2019 Mare Nostrum swim series consisted of three competitions, held two weeks apart in June across Monaco, France, and Spain. Additionally, first place in every event was awarded 350 Euros, so call it $400 USD.

The following exhibits show select first place performances for women and men from each Mare Nostrum competition.  On every row, next to each performance time is the FINA and MeenaMethod point value, along with how much prize money could have been rewarded if allocated on a fixed or sliding scale.  Remember, each line is worth $400, but on a per-point basis, some swims were more valuable than others.

Conclusion

In conclusion, while each first-place performance earned $400 regardless of their point value (i.e., their time), not all performances were relatively equal regarding their FINA or MeenaMethod points. 

The following table shows the average $/point values from the previous 15 swims shown, by gender, to forecast the payout and appropriate savings.If the Mare Nostrum series used a sliding scale as their point methodology, they could have saved (or re-allocated) between ~3% to ~9% off the prize money.

This sort of KPI can be used by both an athlete and an event organizer.  An athlete can identify profitable competition opportunities by searching for a relatively slow field of participants – particularly on a fixed scale perspective. 

Event organizers, on the other hand, can look at this KPI to ensure athletes are producing the same caliber of performances. If an athlete is guaranteed a win, their effort level might not match a race with a faster field of participants. On a sliding scale, every hundredth matters so time is more important than placement.

Exhibit 5
Sports Betting with Odds & Lines

The sports betting world depends on ratios in a similar way as the financial capital markets.  Odds, or lines, can be set in fractions like bond prices or decimals like stock prices.

Odds are tied to an underlying “commodity” so to speak, typically a performance.  These odds are then set on a scale of low to high with the lower the odds correlating to the most likely outcome (i.e., the favorite places 1st), and the higher the odds correlating to the least likely outcome (i.e., the underdog places 1st).

When it comes to pure racing, nothing will ever top animal track betting, like horse and dog racing.  Plus, “speed” junkies already get their fix from stats like Beyer Speed Figures.  These markets are so advanced and loyal, that there is no point trying to re-create the wheel for pure speed racing with other Metric Sports.

Therefore, this exhibit is not necessarily a comparison but rather an idea of how to widen the attention for Metric Sports betting.  Sports betting is very similar to gamification, which was broached in the Gamification of Metric Sports, so similarly this exhibit incorporates a group of participants, not just an individual.

So, what if, for example, one could bet the field and not a single athlete?

In capital markets, investors follow individual securities and baskets of securities.  In Metric Sports betting, the individual securities market for speed racing is covered with horse and dog racing.  However, the basket of securities market remains open to exploration.

Said differently, rather than focusing on individual placement, audiences could bet the overall outcome of an event based on a group, or basket, of performances.

Swimming Example for Setting Odds & Lines

Note: odds are weighted based on the amount of money wagered, which is not factored into this exhibit, so instead the odds move directionally accurate and not precisely accurate

The possible betting scenario is the Male 50 LCM Freestyle swimming event from the 2020 Olympics, which was contested on July 30 and 31st, 2021.  This scenario sets a final time prediction and incorporates the performances leading into the event, then after Preliminaries, then after Semi-Finals to adjust the betting lines for the final time prediction and ultimate result.

To get to the Olympic final in the 50 LCM Freestyle, a swimmer must place in the top 16 in prelims to get to semi-finals, and then place in the top 8 in semi-finals to get to the final.

Therefore, if the odds are set before prelims, then adjusted after prelims, and adjusted once more after semi-finals, that generates three total lines available to bet.

So, here is an example of betting on an entire event as opposed to betting on an individual athlete:

Query: Will the average time of the 1st through 8th place finishers in the Male 50 LCM Freestyle at the 2020 Olympics be faster or slower than 21.655 seconds?

Line = 21.655 seconds

• Over = 21.66 or slower

• Under = 21.65 or faster

Initial Odds Before Preliminaries

• Over = 3:1

• Under = 7:1

• This would imply that leading into the Olympics, the average of the Male 50 LCM Freestyle final will be SLOWER than 21.655 seconds (so 21.66 or slower)

Odds Adjustment After Prelims

• Over = 2:1

• Under = 8:1

• The average time of the eight final swimmers after prelims was 21.72 seconds (see results table), so slower than the 21.655 prediction.  Therefore, this initial effort causes the lines for Over to decrease and Under to increase

Odds Adjustment After Semi-Finals

• Over = 8:1

• Under = 2:1

• The average time of the eight final swimmers after semi-finals was 21.63 seconds (see results table), so faster than the 21.655 prediction. Therefore, if they repeat this speed, the Under prediction will payout, so the lines for Under reduce and Over increase.

Final Payout

• Since 21.60 was the final average of the top eight finishers, the Under bets will be paid according to the values at which the bets were made (e.g., 7:1 or 8:1 or 2:1)

Considerations Of Betting The Field

From an attention perspective, betting the field might lower the barrier of entry for an audience that understands a sport but does not know specific athletes.

From an ethical perspective, there is always a concern about corruption when it comes to sports betting.  However, it is harder to manipulate an entire field rather than one participant, particularly with rules such as capping allowable times, etc.

From a technical perspective, given the objectivity of the results, handicaps can be quantified and can account for outliers regarding line re-adjustment (e.g., a participant is disqualified or found cheating).

Interestingly, the average of the 2nd place through 7th place times is 21.66 seconds, which is just over the betting line.  So that could be an argument to eliminate the fastest and slowest competitors in a field when it comes to setting lines.

Exhibit 6
Swimming Ratings as an Analogy to Financial Bond Ratings

When a public entity issues a financial debt instrument known as a bond, those bonds are rated (typically by Moody’s or S&P or Fitch).  The bond rating is an output that indicates the stability of the entity issuing the bond, based on multiple inputs.  The higher the rating, the more stable the entity.

As an analogy to bond ratings, this exhibit will examine motivational rating systems used for age group swimmers in the 100 SCY and 100 LCM races.  One is an absolute rating system used by USA Swimming, and the other is a relative rating system based on the MeenaMethod, dubbed MeenaMotivational.

Note: for this exhibit, all times are displayed as seconds.hundreths (ss.hh) and all percentages indicate the amount a time is slower than the referenced benchmark. Additionally, all data is as of 12/31/2019.

Absolute Rating System - USA Swimming

USA Swimming issues time standards for the under-18 age groups.  For every event for every age group, certain times align with certain ratings and the faster the time, the better the rating.  The goal of the time standards is to give swimmers a data point that motivates them to swim faster and move up in the ratings, which may dictate their ability to train in certain groups or travel to certain competitions.

These standards are selected based on, among other things, absolute inputs (e.g., number of swims and number of swimmers needed to achieve each standard).  A total of six standards are set for each age group for each event, corresponding with six ratings.

Under the current USA Swimming system, the six ratings are:

• B (slowest)

• BB

• A

• AA

• AAA

• AAAA (fastest)

Even though this is an absolute rating system, this is a relative exhibit.  Therefore, for each rating, the time standard is compared against the National Age Group Record (“NAG”, i.e., the fastest time ever in that event for that age group) and against the fastest time of the year in 2019 (“2019 Fastest”).  Said differently, the NAG record and the 2019 fastest times are the “Benchmarks” in all calculations.

Now since this is an absolute rating system, and relative variances are being measured, do not expect much linear correlation, but instead pay attention to the ranges. 

The overall detail tables are included at the end of the exhibit.  But, in summary, there is a wide range of relative values across the ratings when compared to benchmarks.

In some events, the B (slowest) standards were ~90% slower (so almost double the seconds) than the NAG record or 2019 fastest time. In other cases, the B standards were ~45% slower, but on average, B standards were ~55% slower.

On the other end of the rating system, for the AAAA (fastest) standards, those ranged between ~10 - 20% slower than the NAG and 2019 best times.

So, using a relative framework, if there are six ratings and the fastest is 15% slower than the benchmark, and the slowest is 55% slower than the benchmark, then a linear distribution would be something like:

• B = 55% slower

• BB = 47% slower

• A = 39% slower

• AA = 31% slower

• AAA = 23% slower

• AAAA = 15% slower

However, since USA Swimming uses an absolute framework, the ranges are between:

• B = 43 - 90% slower

• BB = 33 - 66% slower

• A = 23 - 41% slower

• AA = 18 - 33% slower

• AAA = 13 - 25% slower

• AAAA = 7 - 17% slower

When comparing the “expected linear” distribution to the actual distribution, there is a very interesting story being told.  The USA Swimming rating standards are highly influenced by absolute inputs, such as number of qualifiers, and this is an accurate approach from a motivational perspective.  The standards should be attainable, and if more people are swimming a particular event, then it makes sense when the standards may be relatively faster.

For example, since more people swim freestyle than any other stroke (particularly at an under-18 age), the rating ranges for freestyle are (and should be) tighter compared to butterfly which has a steeper developmental learning curve.

Relative Rating System - MeenaMotivational

As opposed to manually setting time standards by individual event, which is the result of an absolute rating system, a relative rating system with fixed thresholds can be dynamically updated.  A relative system eliminates any “noise” that comes with an absolute system and focuses solely on individual speed compared to an agreed upon benchmark.

By pegging relative percentage limits to benchmarks like the NAG record, or the top time of the previous year, ratings can automatically adjust so there is no confusion as to what and why the rating standard is at that moment in time. 

For example, the MeenaMotivational limits distributes ratings in 10% increments:

• B- = 60% slower than the benchmark

• B = 50% slower than the benchmark

• B+ = 40% slower than the benchmark

• A- = 30% slower than the benchmark

• A = 20% slower than the benchmark

• A+ = 10% slower than the benchmark

With a set discount for each rating, the math is straightforward.  If a 14-year-old female ties the A+ MeenaMotivational time in the 100 LCM Breaststroke, she knows she is relatively just as fast as an 18-year-old male who ties the A+ time in the 50 SCY freestyle.  

Absolute and Relative Data Tables

The following pages contain a total of 12 tables. Six for USA Swimming and six for MeenaMotivational, with three tables each for Short-Course-Yards and Long-Course-Meters.  The table titles are:

1. USA Swimming Time Standards – SCY

2. USA Swimming Time Standards – LCM

3. USA Swimming Relative Comparison Details – SCY

4. USA Swimming Relative Comparison Details – LCM

5. USA Swimming Relative Comparison Summaries – SCY

6. USA Swimming Relative Comparison Summaries – LCM
   
   

7. MeenaMotivational Time Standards – SCY

8. MeenaMotivational Time Standards – LCM

9. MeenaMotivational Relative Comparison Details – SCY

10. MeenaMotivational Relative Comparison Details – LCM

11. MeenaMotivational Relative Comparison Summaries – SCY

12. MeenaMotivational Relative Comparison Summaries – LCM

1. USA Swimming Time Standards – SCY

2. USA Swimming Time Standards – LCM

3. USA Swimming Relative Comparison Details – SCY

4. USA Swimming Relative Comparison Details – LCM

5. USA Swimming Relative Comparison Summaries – SCY

6. USA Swimming Relative Comparison Summaries – LCM

7. MeenaMotivational Time Standards – SCY

8. MeenaMotivational Time Standards – LCM

9. MeenaMotivational Relative Comparison Details – SCY

10. MeenaMotivational Relative Comparison Details – LCM

11. MeenaMotivational Relative Comparison Summaries – SCY

12. MeenaMotivational Relative Comparison Summaries – LCM

Exhibit 7
Indexes

An index is a “number derived from a series of observations and used as an indicator or measure”.

As such, in the financial capital markets, indexes are commonly referenced as indicators of the strength, value, or stability of a cohort relative the same cohort at other points in time.

Some financial indexes commonly referenced are:

• the Consumer Price Index (“CPI”), which follows the variances in consumer goods and services to monitor inflation

  • for example, a “basket of goods” may cost $1.00 today but $1.03 tomorrow, indicating a 3.00% increase in the cost of those goods

• The Dow Jones Industrial Average (“DJIA” or the “Dow”), which is an index that measures the performances of 30 purposely chosen stocks over time as a gauge of the health of the United States economy

  • for example, on any given day the movement of the Dow, whether positive or negative, typically reflects the movement of many of the publicly listed stocks in the United States, therefore, serving as a benchmark indicator for the health of stock markets

In Metric Sports, indexes can serve a similar purpose as those in financial capital markets. If interested in the progression of a certain cohort, such as an event or gender, then collect data at various points in time to determine the relative change over time.

Using swimming as the Metric Sport, specifically World Records, this exhibit will create indexes to address (and try to answer) the following:

Question: Have humans become physically faster over time?

To address the question of whether humans have become physically faster over time, then, for example, look at the world record progressions across four swimming events and two genders.

The four swimming events studied are:

1. the Female 50 LCM Freestyle progression

2. the Male 50 LCM Freestyle progression

3. the Female 1500 LCM Freestyle progression

4. the Male 1500 LCM Freestyle progression

Below are four separate charts highlighting important data points for the world record progression of each of the four swimming events.

The Female 50 LCM Freestyle World Record

• Progressed 12.30% from 1975 (26.99 seconds) to 2017 (23.67 seconds)

• A total progression of 3.32 seconds over a 42-year period, which equates to an annual improvement of ~0.08 seconds, or ~0.29%

• This World Record has been broken or tied 27 times in this period

The Male 50 LCM Freestyle World Record

• Progressed 12.36% from 1976 (23.86 seconds) to 2009 (20.91 seconds)

• A total progression of 2.95 seconds over a 33-year period, which equates to an annual improvement of ~0.09 seconds, or ~0.37%

  • This World Record has been broken or tied 28 times in this period

The Female 1500 LCM Freestyle World Record

• Progressed 11.42% from 1971 (17:19.20) to 2018 (15:20.48)

• A total progression of 118.72 seconds over a 41-year period, which equates to an annual improvement of ~2.53 seconds, or ~0.24%

  • This World Record has been broken or tied 21 times in this period

The Male 1500 LCM Freestyle

• Progressed 8.99% from 1970 (15:57.10) to 2012 (14:31.02)

• A total progression of 86.08 seconds over a 42-year period, which equates to an annual improvement of ~2.05 seconds, or ~0.21%

  • This World Record has been broken or tied 20 times in this period 

Question: Have humans become physically faster over time?

Answer: Index It

After gathering the historical world record today, the next step in an attempt to answer the original question, have humans become physically faster over time?, is to create an index.

Important to note that indexes can involve any number of participants (e.g., the S&P 500 includes 500 stocks), but for simplicity purposes, we are going to focus on the following two indexes:

• a “sprint” index using the Female and Male 50 LCM Freestyle world record progressions

• a “distance” index using the Female and Male 1500 LCM Freestyle world record progressions

These indexes will be weighted meaning the inputs (i.e., swimming times) will be converted to a MeenaMethod point value so they can be valued relatively equally based on their performance.

Next, the index for a given period (e.g., years) is calculated as the sum of the Female and Male point values for that period, divided by two (because there are two events in the index)

• Swimming Event Index Value = (Female Points + Male Points) / 2

The following charts show the indexes with a MeenaMethod point value as well as a relative percentage value.  Spoiler alert, the point values are the same as the relative percentage value (just different decimal placement).

Comparing the “Sprint” and “Distance” Index for Male and Female Swimmers

Sprint Swimming Index

• “Sprint Index” = 50 LCM Freestyle Index of Male and Female World Records progressed 12.33% from 100.00 to 112.33 points

Distance Swimming Index

• “Distance Index” = 1500 LCM Freestyle Index of Male and Female World Records progressed 10.21% from 100.00 to 110.21 points

Conclusion

In conclusion, under the two assumptions of:

1. the progression of swimming times is a fair indicator, and

2. all-else-being-equal (which is akin to the efficient market theory)

the answer is Yes, to the question of whether humans have become physically stronger over time. Based on the above two indexes, in the past ~50-years, humans have become ~10-12% physically stronger.

Understanding that factors like the number of events included or technological advancements certainly could have an impact.  Also, could phenotypes and genotypes influence the results? Definitely maybe. The math is available, but in order to calculate the impact would require additional indexes with additional contributing factors.

Footnotes

Author: Elliot Meena

Published: April 24, 2022

Sources: Merriam-Webster, Omega Timing, NBC Olympics, UCI Cycling, USA Swimming, World Athletics

Notes:

• SCY: Short-Course-Yards (i.e., a 25-yard pool)

• LCM: Long-Course-Meters (i.e., a 50-meter pool)

• For questions where it says “address (not answer)” or “address (try to answer)”, the purpose of these exhibits is to introduce mathematical examples of how to start a discussion on a Metric Sport related topic, not definitively answer a question.

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