## Summary (Tl;DR)

Score lines worse than 6 – 13, 9 – 15, 12 – 17, and 15 – 19 are considered “winning/losing by a lot”. Consider trying to tire your opponent out or mixing it up to help you win the match rather than just the game. It’s ok to lose a battle in order to win the war.

## Introduction

As a badminton player, you already know that the scoring system has you play until you or your opponents have at least 21 points with a 2 point advantage – or hit 30 points. If you’re not familiar with this, check out our Rules post! But how much are you really winning by when the score is 21 – 15? Or how about when it’s 21 – 19? And when should you change strategies when you’re losing by a lot? What is considered losing by a lot? Read on to find out.

## Analysis

We’ll start off our analysis by considering all of the possible outcomes of scores a game of badminton may have. This can be seen in Table 1 below. It shows how many points the winner has and the number of points the other player may have. It then shows the percentage of points you won, the percentage of points you lost, and the difference – which signifies, to an extent, how much better you played than your opponent in the game.

**Table 1: Scores and their respective percentages won and lost.**

Winner | Other Player | Total Points Played | Percent of Points Won (%) | Percent of Points Lost (%) | Percent Difference with Opponent (%) |

21 | 0 | 21 | 100 | 0 | 100 |

21 | 1 | 22 | 95.5 | 4.5 | 91 |

21 | 2 | 23 | 91.3 | 8.7 | 82.6 |

21 | 3 | 24 | 87.5 | 12.5 | 75 |

21 | 4 | 25 | 84 | 16 | 68 |

21 | 5 | 26 | 80.8 | 19.2 | 61.6 |

21 | 6 | 27 | 77.8 | 22.2 | 55.6 |

21 | 7 | 28 | 75 | 25 | 50 |

21 | 8 | 29 | 72.4 | 27.6 | 44.8 |

21 | 9 | 30 | 70 | 30 | 50 |

21 | 10 | 31 | 67.7 | 32.3 | 35.4 |

21 | 11 | 32 | 65.6 | 34.4 | 31.2 |

21 | 12 | 33 | 63.6 | 36.4 | 27.2 |

21 | 13 | 34 | 61.8 | 38.2 | 23.6 |

21 | 14 | 35 | 60 | 40 | 20 |

21 | 15 | 36 | 58.3 | 41.7 | 16.6 |

21 | 16 | 37 | 56.8 | 43.2 | 13.6 |

21 | 17 | 38 | 55.3 | 44.7 | 10.6 |

21 | 18 | 39 | 53.8 | 46.2 | 7.6 |

21 | 19 | 40 | 52.5 | 47.5 | 5 |

22 | 20 | 42 | 52.4 | 47.6 | 4.8 |

23 | 21 | 44 | 52.3 | 47.7 | 4.6 |

24 | 22 | 46 | 52.2 | 47.8 | 4.4 |

25 | 23 | 48 | 52.1 | 47.9 | 4.2 |

26 | 24 | 50 | 52 | 48 | 4 |

27 | 25 | 52 | 51.9 | 48.1 | 3.8 |

28 | 26 | 54 | 51.9 | 48.1 | 3.8 |

29 | 27 | 56 | 51.8 | 48.2 | 3.6 |

30 | 28 | 58 | 51.7 | 48.3 | 3.4 |

30 | 29 | 59 | 50.8 | 49.2 | 1.6 |

Now let’s define how close of a game this is based off of percent. This can be a bit subjective but is a pretty good baseline as to how to assess your game.

**Table 2: Assessment of your game based off of the score**

Win by | Points scored by Opponent | Assessment |

Less than 2% | 29 | This means you have 30 points! This was an extremely close game and indicates that you and your opponent are evenly matched! The game may have been determined by luck (net caughts) or simple mistakes made earlier in the game. The outcome of the game could have gone either way. Congratulate your opponent on an awesome and rare game! |

2 – 10% | 18 to 28 | Very close game, likely won or lost due to a couple of unforced errors or nerves. |

11 – 20% | 14 to 17 | It’s pretty clear that you played better than your opponent this game but you don’t have too much margin for error. If you lost focus for a couple of points, your opponent would have a real chance at a comeback. |

21 – 40% | 9 to 13 | There wasn’t much of a struggle here. You could have been off the court for a third of the game and have still won. You completely outplayed your opponent or there were way too many unforced errors. |

More than 40% | 0 to 8 | No contest |

So, how do we use this information to help us? Depending on the score gap between you and your opponent, you can decide what sort of strategy to use to maximize your chances of winning the match. Yes, the match – not a particular game. Remember, the goal of a badminton match isn’t to win a game, or even the most points – it’s to win a best 2 out of 3 games to 21 with a 2 point margin (or reach the cap of 30 points). It’s important to remember this distinction as it can help you decide when you want to conserve energy or change up your play style. Furthermore, you can apply this concept to a badminton tournament as well. The goal of a badminton tournament is to win 1st place, not a particular match (although winning matches are indeed steps that are required). Using up your energy in an earlier round when it isn’t necessary is a losing strategy for winning 1st place.

For this post, we will focus on how to optimize winning a particular match rather than winning a tournament. There are several times when you may consider changing strategies during a badminton match.

- In the 1st game when you are losing by a lot
- In the 1st game when you are winning by a lot
- If you won the 1st game and you are losing by a lot in the 2nd game
- If you lost the 1st game and you are winning by a lot in the 2nd game

In other words, it’s whenever you’re winning/losing by a lot and there is still a game left to be played in the match.

Before discussing what possible strategies we can use, let’s define what “winning/losing by a lot” means. As we’ve seen in the charts above, the general cutoff for a close game is winning by 3 points or less and the cutoff for a comeback game is around a 7 point difference. So I’ll define “winning/losing by a lot” to be a 7+ point difference in the game – but we’ll refine this definition below after 2 key observations.

Our first observation is that the closer the game is to ending, the bigger of a lead the person with more points has. For example, a score of 20 to 13 is a bigger lead than a score of 7 to 0 because the player at 20 points only needs 1 more point to win and thus gives the opponent a lower chance of a comeback because there is less margin for error. In the case of the score being 20 to 13, the player with 13 points needs at least 7 points in a row before a point can be lost.

If we assume that you and your opponent are equally skilled, then that means you have a 50% of winning any particular point. With this assumption, we can calculate the probabilities of you winning the game if your opponent already has 20 points. Take a look at Table 3 below for the details.

The way the numbers were calculated was done as follows. Find the number of points you need to get to 20 points. Since you have a 50% chance per point, multiply 0.5 that many number of times. At this point, this represents the probability of reaching 20 points. Since you and your opponent are equally skilled, you have a 50% chance of winning the game at this point. Therefore, we need to multiply the probability by another 0.5 to get your chances of winning.

**Table 3: Chances of you winning when your opponent has 20 points**

You | Opponent | Chance of you winning (%) |

0 | 20 | Less than 0.1 |

1 | 20 | Less than 0.1 |

2 | 20 | Less than 0.1 |

3 | 20 | Less than 0.1 |

4 | 20 | Less than 0.1 |

5 | 20 | Less than 0.1 |

6 | 20 | Less than 0.1 |

7 | 20 | Less than 0.1 |

8 | 20 | Less than 0.1 |

9 | 20 | Less than 0.1 |

10 | 20 | Less than 0.1 |

11 | 20 | 0.1 |

12 | 20 | 0.2 |

13 | 20 | 0.4 |

14 | 20 | 0.8 |

15 | 20 | 1.6 |

16 | 20 | 3.1 |

17 | 20 | 6.3 |

18 | 20 | 12.5 |

19 | 20 | 25 |

What we can conclude here is that if your opponent already has 20 points, it’ll be pretty difficult to make a comeback if you have less than 18 points. We’ll use this number again later in the article, just keep this in mind.

Our second observation is that to win a game 21 to 19, you need 1.11 points for every 1 point your opponent scores. This is calculated by dividing 21 by 19. Take a look Table 4 below to see how many points you need to score for every possible scenario to win a game.

**Table 4: Points you need for each of your opponent’s point**

You | Opponent | Points you need per opponent’s point |

21 | 0 | N/A |

21 | 1 | 21 |

21 | 2 | 10.5 |

21 | 3 | 7 |

21 | 4 | 5.25 |

21 | 5 | 4.2 |

21 | 6 | 3.5 |

21 | 7 | 3 |

21 | 8 | 2.63 |

21 | 9 | 2.33 |

21 | 10 | 2.1 |

21 | 11 | 1.91 |

21 | 12 | 1.75 |

21 | 13 | 1.62 |

21 | 14 | 1.5 |

21 | 15 | 1.4 |

21 | 16 | 1.31 |

21 | 17 | 1.24 |

21 | 18 | 1.17 |

21 | 19 | 1.11 |

22 | 20 | 1.1 |

23 | 21 | 1.1 |

24 | 22 | 1.09 |

25 | 23 | 1.09 |

26 | 24 | 1.08 |

27 | 25 | 1.08 |

28 | 26 | 1.08 |

29 | 27 | 1.07 |

30 | 28 | 1.07 |

30 | 29 | 1.03 |

Great, so how does this help? Well, we defined that the 7 point difference is approximately where the cutoff is to where there is a chance for a comeback – so let’s take a look at what the ratio is at 21 – 14. As we can see in Table 4 above, it’s 1.5 – we need to win more than 1.5 points for every 1 point the opponent wins in order to make it difficult for a comeback. Now let’s flip it around and ask – what score lines are really difficult for the losing player to make a comeback? How can we tell in the middle of a game? What are the cutoffs?

Take a look at Table 5 below for an illustration of score lines and their respective ratios as to how many points are needed for each of your opponent’s points. We’ll say that if you can get to 18 points, you have a reasonable chance at a comeback (approximately 12.5% as seen in Table 3) so we’ll calculate the proportion by taking the number of points you need to make 18 points versus the number of points your opponent needs to make 21 points. **Any ratio with more than 1.5 indicates a pretty tough game to make a comeback from.**

**Table 5: Ratios for score lines with a 7 point gap**

You | Opponent | Points left for you to 18 | Points left for your opponent to 21 | Ratio |

0 | 7 | 18 | 14 | 1.29 |

1 | 8 | 17 | 13 | 1.31 |

2 | 9 | 16 | 12 | 1.33 |

3 | 10 | 15 | 11 | 1.36 |

4 | 11 | 14 | 10 | 1.4 |

5 | 12 | 13 | 9 | 1.44 |

6 | 13 | 12 | 8 | 1.5 |

7 | 14 | 11 | 7 | 1.57 |

8 | 15 | 10 | 6 | 1.67 |

9 | 16 | 9 | 5 | 1.8 |

10 | 17 | 8 | 4 | 2 |

11 | 18 | 7 | 3 | 2.33 |

12 | 19 | 6 | 2 | 3 |

13 | 20 | 5 | 1 | 5 |

**Table 6: Ratios for score lines with a 6 point gap**

You | Opponent | Points left for you to 18 | Points left for your opponent | Ratio |

0 | 6 | 18 | 15 | 1.2 |

1 | 7 | 17 | 14 | 1.21 |

2 | 8 | 16 | 13 | 1.23 |

3 | 9 | 15 | 12 | 1.25 |

4 | 10 | 14 | 11 | 1.27 |

5 | 11 | 13 | 10 | 1.3 |

6 | 12 | 12 | 9 | 1.33 |

7 | 13 | 11 | 8 | 1.375 |

8 | 14 | 10 | 7 | 1.43 |

9 | 15 | 9 | 6 | 1.5 |

10 | 16 | 8 | 5 | 1.6 |

11 | 17 | 7 | 4 | 1.75 |

12 | 18 | 5 | 3 | 2 |

13 | 19 | 4 | 2 | 2.5 |

14 | 20 | 3 | 1 | 4 |

**Table 7: Ratios for score lines with a 5 point gap**

You | Opponent | Points left for you to 18 | Points left for your opponent to 21 | Ratio |

0 | 5 | 18 | 16 | 1.13 |

1 | 6 | 17 | 15 | 1.13 |

2 | 7 | 16 | 14 | 1.14 |

3 | 8 | 15 | 13 | 1.15 |

4 | 9 | 14 | 12 | 1.17 |

5 | 10 | 13 | 11 | 1.18 |

6 | 11 | 12 | 10 | 1.2 |

7 | 12 | 11 | 9 | 1.22 |

8 | 13 | 10 | 8 | 1.25 |

9 | 14 | 9 | 7 | 1.29 |

10 | 15 | 8 | 6 | 1.33 |

11 | 16 | 7 | 6 | 4 |

12 | 17 | 6 | 4 | 1.5 |

13 | 18 | 5 | 3 | 1.67 |

14 | 19 | 4 | 2 | 2 |

15 | 20 | 3 | 1 | 3 |

**Table 8: Ratios for score lines with a 4 point gap**

You | Opponent | Points left for you to 18 | Points left for your opponent to 21 | Ratio |

0 | 4 | 18 | 17 | 1.06 |

1 | 5 | 17 | 16 | 1.06 |

2 | 6 | 16 | 15 | 1.07 |

3 | 7 | 15 | 14 | 1.07 |

4 | 8 | 14 | 13 | 1.08 |

5 | 9 | 13 | 12 | 1.08 |

6 | 10 | 12 | 11 | 1.09 |

7 | 11 | 11 | 10 | 1.1 |

8 | 12 | 10 | 9 | 1.11 |

9 | 13 | 9 | 8 | 1.125 |

10 | 14 | 8 | 7 | 1.14 |

11 | 15 | 7 | 6 | 1.17 |

12 | 16 | 6 | 5 | 1.2 |

13 | 17 | 5 | 4 | 1.25 |

14 | 18 | 4 | 3 | 1.33 |

15 | 19 | 3 | 2 | 1.5 |

16 | 20 | 2 | 1 | 2 |

**Table 9: Ratios for score lines with a 3 point gap**

You | Opponent | Points left for you to 18 | Points left for your opponent to 21 | Ratio |

0 | 3 | 18 | 18 | 1 |

1 | 4 | 17 | 17 | 1 |

2 | 5 | 16 | 16 | 1 |

3 | 6 | 15 | 15 | 1 |

4 | 7 | 14 | 14 | 1 |

5 | 8 | 13 | 13 | 1 |

6 | 9 | 12 | 12 | 1 |

7 | 10 | 11 | 11 | 1 |

8 | 11 | 10 | 10 | 1 |

9 | 12 | 9 | 9 | 1 |

10 | 13 | 8 | 8 | 1 |

11 | 14 | 7 | 7 | 1 |

12 | 15 | 6 | 6 | 1 |

13 | 16 | 5 | 5 | 1 |

14 | 17 | 4 | 4 | 1 |

15 | 18 | 3 | 3 | 1 |

16 | 19 | 2 | 2 | 1 |

17 | 20 | 1 | 1 | 1 |

Alright! Here are the cutoffs:

- 6 – 13
- 9 – 15
- 12 – 17
- 15 – 19

Any game with a 3 point difference is pretty close and should be contested fiercely! Any game with an 8 point difference or any score worse than the above cutoffs will be considered winning/losing by a lot and you may want to consider another strategy. What strategy though? At this point, you’re thinking about what will help you win the match rather than the game. There are 2 main things you can consider doing:

- Tire your opponent out – you want to use as little energy as possible to extract as much energy from your opponent. This can make your next game(s) more difficult for your opponent and easier for yourself. To do this, you’ll have to be consistent in your shots and not make unforced errors to make your opponent work hard to get the points.
- Try out new shots you haven’t done in the game so far. I’m not saying to try shots you have never practiced before, but to try mixing up your shots. A game usually follows a particular pattern that the players get used to. You can try breaking that pattern to see how your opponent reacts and see if you can use that to your advantage in the next game. Try to poke around to see what weaknesses and strengths your opponent has before the next game. An example is to serve to a different spot than you normally do.

These strategy changes only apply if you still have a game left after the current game – although you may still want to try something different if you’re losing by a lot in the final game as what you’ve been doing so far doesn’t seem to be working.

This model does make a couple of assumptions and of course isn’t perfect and should be taken as a guide rather than a set of rules. If you want to be more aggressive in trying to win your games, you can redefine what “winning/losing by a lot” means and change the cut-offs to be 14 – 7, 16 – 10, and 18 – 13 (Please refer back to Tables 5 to 9) . If you want to be more conservative, you can define the cut-offs as 12 – 5, 14 – 8, 16 – 11, and 18 – 14. Whatever you define it as, the point is that you should try to optimize your game play to win the match by paying attention to the score line and adapting after certain cutoffs are past. Try it out, see if it makes a difference, and let us know your thoughts in the comments section below!

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