TL;DR
I used a simulator to analyze badminton games “played” by perfectly equally skilled players. A scoreline of 30-29 or 29-30 occurred .024707% of the time.
Abolishing the 30 point cap resulted in a maximum scoreline of 43-41 in 100 million simulated games. Games going to 31-29 or more came to .024281% of the games. Any games at 35-33 or higher occurred a mere .000744% of the time.
Abolishing the 30 point cap would not affect many games. The games that do go past the 30 point cap will feel more fair and even be considered epic for all the watching fans. Suspense is built up the most when extra points are being played and is when fans are the most engaged. If we still want to have a point cap, 45 points would pretty much never be reached in competitive play and would be a good candidate.
Introduction
As any serious badminton player knows, the current scoring system (as of 2024) consists of 3 games to 21 points with a 2 point gap required to win. This went into effect in August 2006. However, there is a cap at 30 points, where if both players/teams have 29 points, the next point wins the game. This is the so-called “golden point” system, which is supposed to end games that are really close so that they don’t go on forever.
When I was watching some games on BWF’s YouTube channel a while back, I remember hearing the famous Gill Clark ask why we have the 30 point cap at all. First, it’s so rare for a game to get to a score of 29-29 so it barely even occurs. Second, this is when the game is the mostexciting – especially if it’s the 3rd game! So why would you want it to end at 30 points? If it’s a professional game, fans on both sides would be at their peak attention!
Further, when the score hits 30-29, it always feels like the game is incomplete and almost just luck! For the winner, it feels like a half deserved win and for the loser it feels like you’ve been robbed.
The main reason why there is a 30 score cap is because of concerns that a game would go on forever. Theoretically, that can happen if players trade points 1 to 1 for eternity. However, the likelihood of even going to 40 points is ridiculously small – and I’ll prove it with some numbers.
First though, the scoring system in tennis already has something similar – where you have to “win by 2” for every game (they call it a “deuce” with “advantage” or “disadvantage”) – but they have no cap! So why in the world does badminton have a cap when it’s even rarer for badminton to ever get to 30 points at all?!
Analysis
Anyways, let me give you some numbers that I ran with my handy dandy BadmintonBites Match Simulator! It gives you a graph and table of how many points players end up with depending on the players’ point win rate.
For this experiment, we’ll use 50% for both Player 1 and Player 2 as this simulates the players to have the exact same skill level and gives the highest likelihood of the players reaching 30 points.
We’ll run the simulation 100 million (100,000,000) times. I put the “Number of Games Needed to Win a Match” to 1 so that we know that exactly 100 million games were played.
Player 1 won 50,001,865 games and Player 2 won 49,998,135 games.
Here are the probability distributions of the points.
This one shows Player 1’s score when Player 2 won.
And this one shows Player 2’s points when Player 1 wins.
Let’s look at how many times the score got to 30-29 or 29-30 in the simulation.
The 29-30 scoreline occurred 12,255 times and the 30-29 scoreline occurred 12,452 times. A total of 24,707 times out of 100 million games. This comes to a .024707% chance that a game will be determined due to the 30 point cap rule when the players are completely equal in all aspects.
Bonus – How Often Do Badminton Games Get to “Extra” Points?
Extra points mean that a game ended with 1 player having more than 21 points.
In our simulation, games with extra points occurred 12,142,521 times out of 100 million games. This means that badminton games go to extra points 12.1425% of the time when the players’ skill levels are completely equal.
Abolishing the 30 Point Cap
Ok, so now we see that in our simulation that only .024707% of the games played reached a score of 30-29 or 29-30. What would happen if we got rid of the cap or just increased it a bit?
I changed the settings of the simulation to have a 50 point cap instead and ran another 100 million games.
How many games do you think went to 50 points?
Well, the answer is…0! Not a single game got to 50 points!
The game with the largest scoreline went to 41-43, and that only occurred once!
In fact, it’s far more likely for a player to win 21 to 0 than it is to get past the 40 point mark for 2 evenly skilled players!
Let’s look at more of the results.
So, how often would games get past 30 points (for the winner’s score) if the rule was actually abolished? Let’s do the math.
In the simulation, games went past 30 points 24,281 times out of 100 million games. That comes to .024281%.
Any games past 35 points (for the winner’s score) occurred only 744 times, resulting in a mere .000744% of the time!
Conclusion?
So, if there was no 30 point cap, the maximum score we found in a 100 million game simulation between 2 perfectly even skilled players would be 41-43. Anything past 35 points only occurred .000744% of the time.
These games are so rare that these high scorelines should be embraced and not cut short. Yes, the game would practically feel like 2 games combined, but it would pretty much be the game of the century if it occurred in a competitive setting.
The pros outweigh the cons (if any):
- 2 point gaps to end a game feel more fair
- Professional games that go past 30 points get more fans and viewership since that’s when the pressure and intensity is the highest. Every additional point in the game increases the suspense.
What are your thoughts? Do you think we should get rid of the 30 point cap now that you have some simulated data?
Caveats
To get my data, I used a simulator to do so. This is not necessarily reflective of how humans play badminton and is only used as a model to help predict what type of distribution the badminton scoring system would produce.
Further, assigning 50% win rates on every single point is not human-like. It may be that the winner of a previous point spends more energy and therefore decreases their win rate on the next point. The win percentage probabilities are likely more dynamic and based off of stamina, focus, birdie quality and much more.
Bonus – Starting at 20 Points Each
What if players started at 20 points a piece? What would the distribution look like and what would the highest scoreline be? Let’s take a look!
The highest scoreline was 45 – 47.
Games that went over 35 points occurred 7,801 times in 100 million games, or .007801% of the time.
Games that went over 40 points occurred 191 times, or .000191% of the time.
