The Zero-Sum Gamification of Metric Sports

Published: August 5, 2020

Introduction

This publication has five sections.  They are:

1. Defining Games

2. The International Swimming League

3. The Scoring Methodologies

4. Event Examples

5. Competition Results by Team

Section 1
Defining Games

What Are Games?

In regard to sport, if someone is referencing a game they are likely talking about a Match Sport. That is, a sport where participants are competing against other participants, in an offensive and defensive manner, typically involving shared contact of an object.

Question: what game (i.e., Match Sport) involves:

• running (a Metric Sport) +

• a ball (a shared object) +

• a goal (an offensive target and defensive barrier for participants) + 

• fouls (adjustments that make cheating legal)?

Answers include:

• soccer, football, basketball, rugby, and lacrosse

• if you swap the ball for a frisbee you have ultimate

• if you swap the running for ice skating you have hockey

• if you swap the running for swimming you have water polo

Point is, no pun intended, if you were to reverse engineer how Match Sports are created, the foundation of most is the concept of a Metric Sport. By layering adjustments (e.g., shared object, point values, time limits, fouls) onto a Metric Sport, the field of play can be gamified into arguably countless games. Remember BASEketball?

In some regards Match Sports could be considered gamified Metric Sports.  Or, said differently, from an equation perspective, Metric Sports + Adjustments = Match Sports.  

Furthermore, Match Sports bring the expectation that anything can happen.  In other words, they are exciting!  On any given Sunday, a Match Sport can create buzzer-beaters, walk-offs, brawls, point spreads, missed calls, or overtime. 

Metric Sports, on the other hand, are a bit calmer than Match Sports, at least on any given Sunday.  Metric Sports are exciting when stakes are on the line (i.e., a championship-esque performance) and the performances are personal record-esque.  Therefore, in order for these two factors to come together, Metric Sport athletes train for one or two competitions a year.  Typically these competitions are in a team championship format, with the expectation their training will produce personal records along with the expectation the other participants will produce personal records.  It is this “best-of-the-best” atmosphere that brings out the excitement in Metric Sports.

Why Are Metric Sports Not Games?

From a MeenaMethod categorization perspective, Metric Sports are not games (i.e., Match Sports) because in:

Metric Sports:

• physical contact between opponents is prohibited, and

• placement is dictated from either distance, time, or weight (DTW)

Match Sports

• physical contact between opponents is allowed, and

• placement is dictated by points

Having said that, scoring methodologies have historically attempted to gamify Metric Sports, but none have been objectively successful. From a gamification perspective, using swimming as an example, the existing subjective methodologies (e.g., NCAA, ISL) are wrong because they ascribe points relative to placement and not relative to the performance result.  Additionally, the relative methodologies that use an individual benchmark (e.g., FINA points, MeenaMethod NCAA Record points), favor an offensive “quantity over quality” strategy.

To be clear, these existing scoring methodologies are not wrong in terms of selecting placement, but they are wrong in terms of truly gamifying the sport because they do not objectively incorporate an offensive and defensive point-scoring strategy.

Understandably so, it is difficult to be defensive when opponents do not share any contact with one another, unlike Match Sports. That is why offensive-focused strategies have traditionally worked for Metric Sports.  There is nothing but literal upside available.

But even though Metric Sports are individual in nature (i.e., single lanes, personal records), they are scored in points when it comes to a team competition. However, offensive-only team competitions are not games.  Or at least not fair games. Games are supposed to give all participants a chance. Games are supposed to create that exciting “any given Sunday” moment.

How Can Metric Sports Become Games?

Metric Sport athletes traditionally build their training cycles around one or two competitions a year, typically referred to as a championship. Any other competitions that fall within their training cycle are considered in-season (or regular-season) competitions.

It is not expected that athletes can perform personal-record-esque performances any given day of the year, so it is not a fair indicator to compare in-season performances with championship performances.

As a result, also no pun intended, it is difficult to bring excitement to in-season Metric Sport competitions.  At competitions such as dual meets or invitationals, records, whether personal or higher, are not broken regularly.  Breaking records, and close races, are what brings excitement to Metric Sports.

Therefore, Metric Sports must be gamified to create an experience that includes an offensive strategy (i.e., scoring points) and defensive strategy (i.e., preventing others from scoring points). This back-and-forth methodology, highlighting strengths and weakness by participant and by team, is a large part of the excitement created from games, and can bring a new level of excitement to in-season Metric Sport competitions.

So, to objectively add an offensive and defensive component to Metric Sports, without allowing for physical contact between opponents, means both components must be tied to the same performance result.

Next, every performance in a cohort (e.g., an event) must be pegged against an objective indicator of the other performances (i.e., the benchmark) in that cohort to create the points.  That way, performances are not measured against an external benchmark like a world record, or even an individual record, but instead, they are only measured against other performances from the exact same in-season event.

As opposed to the individual benchmark methodologies historically used, which are purely offensive, adding a defensive component can be done by using a group benchmark. A group benchmark is derived from the collection of performances, and as opposed to offensive focused individual benchmarks, group benchmarks offer an offensive and defensive strategy.

Therefore, under the MeenaMethod framework referencing a group benchmark, an objective way to incorporate an offensive and defensive scoring methodology into a Metric Sport is to use a zero-sum game.

What Is A Zero-Sum Game?

Zero-sum means “of, relating to, or being a situation (such as a game) in which a gain for one side entails a corresponding loss for the other side” (Merriam-Webster).  Simply put, “my win is your loss”.

In a zero-sum game for a Metric Sport, the benchmark equals the average of all performances in a given cohort (e.g., an event).  Performance points are then ascribed to each individual performance relative to that average, so every hundredth of an inch, second, or pound literally matters.

Ascribed is the key word because for some performances this methodology awards above-average performances (offensive strategy) and punishes below-average performances (defensive strategy).

In the end, all points for an event total 0.00.  A la, a zero-sum game.

By utilizing a zero-sum methodology, Metric Sports can be gamified into a strategy of “quality over quantity” competitions that creates an objective and relative match-up between opponents.

As you are about to read, the International Swimming League is the perfect candidate to adopt a zero-sum approach to their scoring methodology.

All International Swimming League performances are considered in-season, which means the athletes are not expected to post record-esque times (although some do).  Therefore, as opposed to a traditional scoring methodology, it would be more fair, and more exciting, to score the competitions as a zero-sum game.

Section 2
The International Swimming League

The International Swimming League (“ISL”) “aims to create new groundbreaking projects, in both form and content, which explore the full potential of competitive swimming and secure sustainable commercial growth in the sport” (ISL.global).

Its inaugural season, which was held between October and December of 2019, brought attention and praise to the sport in a time when swimming was often overlooked (i.e., a non-Olympic year).

As a life-long swimmer and swimnerd, I thought it was a spectacular event.  From the world-class rosters, to the curation of the venues (especially the acrylic pool!), to the geographic reach, to the media-coverage, it was Olympic-esque. 

However, as “groundbreaking” as they and all the athletes claim the league to be, they unfortunately went the opposite direction with the point scoring methodology and chose an antiquated subjective model that indirectly ascribes points based on placement and not directly based on performance.  This methodology is outlined below.

Even with the introduction of skins races, cut-off times, penalty deductions, and the “split time rule” in 2020, the idea that a swimmer (or any athlete) should be awarded points that are not directly correlated to the time, and only to placement, is simply not groundbreaking.

To give the ISL some credit, they are not alone with this point system.  As previously stated, offensively awarding subjective point values is the most common way Metric Sport competitions are scored. Furthermore, I understand they did not want to use the FINA point system because the ISL was invented in direct contrast to FINA.

If the ISL really wants to “explore the full potential of competitive swimming” it should adopt a new, never been used before, scoring methodology that values every hundredth of a performance.

Lucky for them, the ISL is the perfect example for a zero-sum game scenario.  While technically zero-sum can work with any number of participants, there is less noise when all teams are represented equally.  The ISL is structured that, for each event, every team has two representatives.

The ISL Data Set

The following dataset was used for this analysis:

• Governing Body: The International Swimming League

• Season: 2019, October through December

• Matches / Competitions:

  • Knock-Out: 6 = Indianapolis, Naples, Lewisville, Budapest, College Park, London

  • Championship: 1 = Las Vegas

Each match consist of 4 teams and each team competes in 3 knock-out matches. The top 4 teams from the knock-out stage are invited to compete in the Las Vegas championship.

• Teams: 8 = Aqua Centurions (AQC), Cali Condors (CAC), DC Trident (DCT), Energy Standard (ENS), Iron (Iron), LA Current (LAC), London Roar (LON), NY Breakers (NYB)

• Gender: 3 = Female + Male + Mixed*

• Pool Length: all races are Short-Course-Meters, “SCM” (i.e., a 25-meter pool)

• Strokes: 5 = Fly, Back, Breast, Free, Medley

• Individual Events: 15 per gender per competition = 50 Free, 100 Free, 200 Free, 400 Free, 50 Back, 100 Back, 200 Back, 50 Breast, 100 Breast, 200 Breast, 50 Fly, 100 Fly, 200 Fly, 200 Medley, 400 Medley (note, the 100 Medley was not contested)

• Relay Events: 5 total = 2 per gender (400 Free, 400 Medley) + 1 Mixed (400 Free)*

• Skins Events: 1 per gender per competition = 50 Free

• Performances: 8 per event, 4 per team

*Note: there is only one mixed gender event, the 400 Free relay

Section 3
The Scoring Methodologies

Outlined below are the traditional approach adopted by the ISL, and the zero-sum approach following the MeenaMethod framework.

Traditional Scoring Methodology

A Traditional scoring methodology is one that uses a performance result to determine placement, but then subjectively awards points based solely on placement.  This methodology does not regard the relative value of the performance result, only the absolute value of the performance placement.

The ISL uses a Traditional scoring methodology that, in summary:

• for 1st place through 8th place, the base value of points is awarded as 9-7-6-5-4-3-2-1, and multiplied by:

  • 1x for individual events

  • 2x for relay events

  • 1x, 2x, or 3x (depending on the placement) for skin events

• will deduct points from a team if:

• a swimmer does not finish or is disqualified = 2 points are deducted

• a swimmer does not show up for their race = 4 points are deducted

• at the end of each match, the 1st place through 4th place teams are awarded 4-3-2-1 placement points, respectively

  • at the end of the 6 knock-out matches, the 4 teams with the most placement points go on to compete in the ISL Championship in Las Vegas

  • the champion in Las Vegas is determined by the most points from Las Vegas alone, not a combination of matches

Zero-Sum Scoring Methodology

The Zero-Sum game scoring methodology, under the MeenaMethod framework, compares each performance against the average performance of all participants in a given event.  In the case of scoring the ISL, the max (and most common) number of performances per event is 8.

• Performance Points Equation = P = [(1 - ((T - B) / B)) * 100] - 100

  • Performance Points = P (or “points”)

  • Performance Tested = T

  • Benchmark = B

• The point value is then, just like the Traditional method, multiplied by:

  • 1x for individual events

  • 2x for relay events

  • 1x, 2x, or 3x (depending on the placement) for skin events

• Scale (i.e., benchmark) = 00.00 points

• In this scenario, by using the average time as the benchmark, some performances will earn positive points (i.e., swam faster than the average) and some performances will earn negative points (i.e., swam slower than the average)

  • In any case, the total points across any single event will equal 0.00 (with an extremely small margin of error due to rounding)

  • Note, the sum is only 0.00 if all performances of a particular cohort are included in the average

    • If not all performances are included, the outcome would not total zero - for example, if the benchmark equaled the median of 8 performances - even though it would be the average of the 4th and 5th place performances, the result would not be a zero-sum

• In the end, the sum of all events in a given match will be 0.00, meaning some teams will have more than 0.00 points and other teams will have less than 0.00 points

  • At the end of the 6 knock-out matches, the 4 teams with the most combined points across go on to compete in the ISL Championship in Las Vegas

  • The champion in Las Vegas is determined by the most points from Las Vegas alone, not a combination of matches

Scoring Methodology Summary

While technically no scoring methodology is wrong, any objective MeenaMethod approach, such as a zero-sum game, produces a more accurate result than a subjective approach.

Furthermore, in this instance with the ISL since swimmers are not at the peak of their training cycles, considering a different methodology to the Traditional approach is fitting.

For end-of-season championships, purely offensive strategies may be the right approach because everyone is prepared to produce best times. However, for in-season competitions, group benchmarks are more applicable because times posted do not matter as much as racing the current competition. At championships, athletes compete against history.  In-season, athletes compete in the moment.

Section 4
Event Examples

Extrapolating all the variables from the data set will result in 7 total matches, each with a minimum of 37 events.  Therefore, rather than post 200+ exhibits for events and heats, the following exhibits are intended to illustrate the different scoring examples by select events.

For ease, all examples are from the first ISL competition in Indianapolis. Nothing “special” happened at the Indianapolis match that did not occur at other matches, but each of the events below highlights a difference between the Zero-Sum and Traditional scoring methodologies.

Event Exhibit Layout

All of the exhibits have the same structure of rows and columns, and the only line that shifts per exhibit is the average performance line

• Each exhibit represents 1 event

• Each event has 8 participants spread across 4 teams, so 2 participants per team

• Each of the 8 performances are included, with a line separating above average and below average swims

• All times are in minutes:seconds.hundredths or seconds.hundredths unless otherwise stated

• The individual time (T) and event average (B) are included, as are the points ascribed under a Zero-Sum and Traditional scoring methodology

• At the bottom of each exhibit, the total points per team are tallied

  • For the Zero-Sum method, some teams gain points and other teams lose points, but all points per match total 0.00

  • For the Traditional method, all teams gain points

Note: It is important to remember that these are team competitions, so the points per event should be viewed in isolation and should not be interpreted as the same outcome for the matches in total

Female 100 SCM Butterfly Individual

This first exhibit is explained in further detail…

The first event of the ISL was the Female 100 Short-Course-Meters (SCM) Butterfly in Indianapolis.  The times of the 8 participants were as followed:

1. Sarah Sjostrom (ENS): 55.65

2. Kelsi Dahlia (CAC): 55.88

3. Brianna Throssell (DCT): 56.81

4. Elena di Liddo (AQC): 57.71

5. Anastasiya Shkurdai (ENS): 57.91

6. Mallory Comerford (CAC): 58.04

7. Ilaria Bianchi (AQC): 58.11

8. Bethany Galat (DCT): 58.23

Summary

• The average (i.e., the benchmark) of the 8 performances was 57.29 seconds

• That means, for this event, 3 swimmers swam faster than the benchmark and gained points, while 5 swimmers swam slower than the benchmark and lost points

• ENS and CAC hovered the average close enough to walk away with positive points

• Overall, the placement of the team for Zero-Sum vs. Traditional remains the same, but the points are more tailored to the actual performance results (i.e., AQC swam slower than DCT so they lose more points in the Zero-Sum scenario but they are tied in the Traditional scenario)

• In this case, it breaks the tie between DCT and AQC by ascribing relative point values based on the performance, and not arbitrary point values based on placement

Male 200 SCM Freestyle Individual

• By getting both swimmers above the average, AQC and DCT remained atop the leaderboard in this event

• However, having one above average (i.e., CAC) does not guarantee positive team points, but it at least minimizes the dilution

  • On that note, given the framework of this scoring methodology, every hundredth of a second improvement will minimize the dilution

Female 400 SCM Freestyle Relay

• This event shows the difference in 1x and Tiered (2x for relays) points, but that does not make an impact on the Zero-Sum placement

• However, there is a difference in placement between Zero-Sum and Traditional

  • For Zero-Sum, CAC placing 2nd and 4th (both above average) earned more points than ENS who placed 1st and 5th (one above average, one below average) 

  • For Traditional, ENS earned more points than CAC because of the arbitrary bonus bump subjectively ascribed to 1st place for relays

Male 50 SCM Freestyle Individual

• This event, and the skins event (next exhibit), is pure domination by ENS

• With the fastest two performances, ENS is a good example to highlight the impact of a “point boost” that comes with the Zero-Sum methodology

  • ENS was the only team to receive positive points from this event, with the net impact point boost ranging from 6.06 to 6.62 points, the largest of any event in the match

  • What this means is, given the math of the Zero-Sum methodology, the point boost is equal to the margin of victory

  • In this particular case, with ENS being the only team with positive points, a fun analogy would be to call this a “grand slam” in the Zero-Sum arena

Male 50 SCM Freestyle Skins

• Similar to the 50 Free Individual (previous exhibit), this event is pure domination by ENS, but in a different way

• Because the two ENS swimmers are the two to make it to the C-Final of the Skin events, they:

  • earn triple points in the C-Final for the Traditional scenarios walking away with 48 total points (~4x over 2nd place)

  • negate their points C-Final points in Zero-Sum scenarios walking away with 0.00 points from that heat

• However, in the Zero-Sum method, every performance in each heat is scored, a rule the ISL did not adopt in 2019 but will adopt in 2020

• That means that ENS really earned their 7.89 points (~19x over 2nd place) from the A and B-Finals

• Therefore, similar to the individual event, ENS had another point boost in the range of 8.31 to 11.83, even though they negate their performances in the C-Final

Section 5
Competition Results by Team

Interestingly enough, under both the Zero-Sum and Traditional scoring scenarios, the top and bottom four teams are the same at the end of the six knock-out matches.  The order of 1st - 4th and 5th - 8th vary, but in general there were clearly four teams that, regardless of the scoring methodology, were going to place above average.

Outlined below are point summaries for each knock-out match and the championship match.  The summaries are separated by gender and event type, and separates the positive and negative points for the Zero-Sum scenario.  For the Traditional scenario, only the total points achieved are shown.

As you are about to read, even though ENS was the in-season and championship victor under the Traditional scenario, LON was the in-season victor and CAC was the championship victor under the Zero-Sum scenario.

All commentary will be from a Zero-Sum scenario perspective, since that is the new methodology being highlighted.

Let us dive into these comparisons by team…

Indianapolis - October 5 & 6, 2019

• ENS cames off the blocks hot for the first meet of the season, scoring the most points for the men and second most for the women in both scenarios

• CAC women carried the weight in Indianapolis as their men ended up with negative points, but overall CAC came out positive and finished in 2nd place

• AQC and DCT never stood a chance as both were only able to finish with positive points in one category each (Male Individual and Female Skins, respectively)

Naples - October 12 & 13, 2019

• Relatively (i.e., Zero-Sum scenario) CAC men swam much faster at Naples than at Indianapolis, and their women swam about the same which was enough for CAC to place 1st in the Zero-Sum scenario, even though ENS retained 1st place in the Traditional scenario

  • Interestingly enough, even though ENS men scored the most Traditional points, the only male team with positive Zero-Sum points was CAC

• AQC and DCT continue their trend of finishing below average in all three genders, and thus overall

Lewisville - October 19 & 20, 2019

• On the men’s side, the inverse impact of a point boost occurred for NYB as they were the only team with negative points - alternatively, LAC, IRON, and LON placed fairly close to each other on the positive side of the spectrum

• LON and LAC were the only teams to score positive Zero-Sum points in each gender, and thus, just like the Traditional scenario, LON and LAC place first and second while IRON and NYB placed third and fourth, respectively

Budapest - October 26 & 27, 2019

• As opposed to Lewisville the week earlier, in Budapest IRON was able to crack into positive point barrier, but still placed third, whereas NYB remained in negative point territory placing fourth

• LON and LAC retained their first and second places, although the gap of ~60 points in Budapest was greater than Lewisville with ~35 points

College Park - November 16 & 17, 2019

• Possibly the most dominating of matches from a positive point perspective as CAC easily placed first and LAC second for every gender

• NYB and DCT continued their struggles of finishing in negative point territory

London - November 23 & 24, 2019

• The London team placement was arguably the most balanced of all the competitions, meaning the point spread was the tightest / narrowest between first place and fourth place - in this case, the spread was 81.4 points (the only competition under 100 points)

• What this means is, more than any other competition, the swimmers swam closer to the average in their events and no one team really took control of the match

Regular Season Match-Up Summary

• After the six in-season competitions, for both the Zero-Sum and Traditional scoring methodologies, the same four teams move on to the Las Vegas championship

  • They are CAC, ENS, LAC, and LON - but the order of placement varies

• For placement points (i.e., 4-3-2-1 for 1st - 4th place; max of 12 points for three competitions):

  • LON is the Zero-Sum regular-season champion with 12 points (3 x 1st place)

  • ENS is the Traditional regular-season champion with 12 points (3 x 1st place)

• For event points (i.e., sum of all points for all matches):

  • CAC is the Zero-Sum regular-season champion (+251 event points)

  • ENS is the Traditional regular-season champion (1,500 event points) 

Las Vegas - December 20 & 21, 2019

• CAC continued their regular-season dominance by not only placing 1st at the Las Vegas Championship but also by being the only team to earn positive points

  • What that means is, on a relative basis, CAC swam faster than all the other teams by a considerable amount

• An interesting highlight, in the case of the Las Vegas Male Skins C-Final, Caeleb Dressel from CAC beat Florent Manaudou by 2.43 seconds (21.46 vs. 23.83)

  • The big variance in time is largely due to the fact that Manaudou was tired and perhaps did not complete the race with 100% effort like he started the race given how far ahead Dressel was at that point

  • Therefore, in the Traditional methodology, because of absolute point values ascribed to placement, Manaudou’s time did not matter because he received 21 points (3 x 7, for 2nd place) no matter what time he posted

  • However, in the Zero-Sum methodology, because the variance was so large, Dressel and CAC earned 47.10 points (3 x 15.70) whereas Manaudou and ENS lost 47.10 points (3 x -15.70)

  • In the end, this +/- of ~47 points could have switched CAC and ENS into 3rd and 1st, instead of 1st and 3rd

• That is the beauty of objective scoring - literally every hundredth of a second counts

Conclusion

In conclusion, if you can’t beat em’, join em’.  Meaning, if record-breaking is not an option, join the swims together and have them statistically compete against themselves.

If leagues want to be groundbreaking and forward-thinking, it is this version of gamification that can create an atmosphere in Metric Sports that has never been seen before.

Footnotes

Author: Elliot Meena

Published: August 5, 2020

Sources: International Swimming League (“ISL”), Merriam-Webster

Notes:

• SCM: Short-Course-Meters (i.e., a 25-meter pool)

• Due to the volume of the performances, this case study only focuses on a few select performances, not all of them - for those who would like to see an analysis of every performance, please send us an email request for the data

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