# Are Lost Match-Points a Disadvantage?

When hearing commentary to a badminton match, you often encounter claims that lost match points are a heart-breaking moment for players. Predictions like “He was so close to winning. I wonder if he will be able to refocus again in the third game” are quite common. In these claims it is assumed that lost match points have a negative effect on players’ psychology and performance. In this post we will check if these predictions can be confirmed by the data.

## Methodology

The methodology is rather simple. As usual we use matches from the database, spanning from 2008 until today. We limit ourselves to matches played under the common scoring system of three games to 21. For the analysis we select all matches that consist of three games. We then count how many match points the loser of the second game had in the second game. As it is for the loser, these match points were obviously not converted. For most matches the number of match points will be zero, here we are mostly interested in the games where match points occurred. Finally for each number of lost match points we then count how many matches were eventually won by the players who lost the match points.

## Win Percentage after Lost Match Points

The following plot shows the percentage of matches won by the side that failed to convert the match points in the second game for different numbers of match points the loser of the second game had. The x axis shows the number of match points the loser of the second game could not convert before losing the second game. The horizontal green line indicates a winning percentage of 50%. The horizontal blue lines indicate the average winning percentage for all matches where the losing side of the second game had at least one match point.

The same data is shown in the following table.

Match Points | Matches | Won | Percentage |
---|---|---|---|

0 | 48840 | 23725 | (48.58 ± 0.23) % |

1 | 1709 | 974 | (56.99 ± 1.20) % |

2 | 1110 | 638 | (57.48 ± 1.48) % |

3 | 620 | 372 | (60.00 ± 1.97) % |

4 | 297 | 156 | (52.53 ± 2.90) % |

5 | 160 | 86 | (53.75 ± 3.94) % |

6 | 80 | 46 | (57.50 ± 5.53) % |

7 | 31 | 18 | (58.06 ± 8.86) % |

8 | 19 | 10 | (52.63 ± 11.45) % |

9 | 10 | 5 | (50.00 ± 15.81) % |

≥ 10 | 2 | 1 | (50.00 ± 35.36) % |

≥ 1 | 4038 | 2306 | (57.11 ± 0.78) % |

Most second games finished without a match point for the loser of the game, as could be expected. What might seem surprising is that players who couldn’t convert their match points in the second game go on to win about 57% of the third games. Also note that the winning percentage is rather independent of the number of lost match points.

The reason for this becomes clear when we consider the selection bias in this analysis. In order to be included this analysis the losers have to have had a match point, that means they will have had at least 20 points in the second game and then lost after extra points Most likely the first game will have been won with a larger margin than the one or two points in the second game. Thus the losers of the second game will have won more points in the first and second game together, thus it is likely that they are indeed the better players. We thus have two effects in this analysis that are pushing the winning percentages in opposite directions, the selection bias leading to higher winning percentages and the psychological disadvantage leading to lower winning percentages in the third game after losing the second game despite having match points.

Luckily there is an additional analysis we can perform to assess the influence of the selection bias.

## Win Percentage after Lost Game Points

Assuming an independent and identical distribution of outcomes
of rallies, losing game points in the first game and then winning
the second game is no different from winning the first game and
then losing match points in the second game. This difference
corresponds to switching the first and second game. Both types of
matches are then decided in the third game. The selection bias
mentioned above should be the same for both kinds of matches, the
difference is that the losing of match points in the second game
should have a higher impact than losing *just* game points
in the first game. Thus any psychological effect of lost match
points should manifest itself as a difference between the winning
percentages for the side that lost the game or match points, while
the selection bias is the same for both types of matches.

Thus we take all three game matches and count how many game points the losers of the first game had and how often this side won the match. The plot for the winning percentage depending on the number of lost game points in the first game is shown in the following plot. The average and the data for the match points are included for comparison.

The data is shown in the following table.

Game Points | Matches | Won | Percentage |
---|---|---|---|

0 | 48612 | 24402 | (50.20 ± 0.23) % |

1 | 1817 | 1030 | (56.69 ± 1.16) % |

2 | 1149 | 646 | (56.22 ± 1.46) % |

3 | 635 | 369 | (58.11 ± 1.96) % |

4 | 347 | 188 | (54.18 ± 2.67) % |

5 | 170 | 110 | (64.71 ± 3.67) % |

6 | 86 | 62 | (72.09 ± 4.84) % |

7 | 42 | 29 | (69.05 ± 7.13) % |

8 | 12 | 6 | (50.00 ± 14.43) % |

9 | 7 | 4 | (57.14 ± 18.70) % |

≥ 10 | 1 | 1 | (100.00 ± 70.71) % |

≥ 1 | 4266 | 2445 | (57.31 ± 0.76) % |

We see almost no difference. The winning percentage is again 57%, the difference is lower than the respective statistical uncertainties. Basically all properties of the previous plot are replicated.

## Conclusion

We find that lost match points have no psychological effect. The arguments for this are that

- The winning percentages are practically the same for lost game points in the first game and lost match points in the second game. Thus lost match points can not have a larger psychological effect than lost game points
- If there was at least one lost match point the winning percentage is independent of the number of lost match points. One would expect multiple lost match points to have a larger psychological effect thus decreasing the winning percentage for the players who lost many match points. We can not see any such effect in the data.

These results strongly support the assumption of rallies having independent and identically distributed outcomes. If lost match points do not have an influence, then what should have an effect?