Is Chou Tien Chen better after 11?
In his match against Anthony Sinisuka Ginting today, Chou Tien Chen came back from the mid-game interval of the first game to score seven consecutive points. Is this just a coincidence or is this a result of good coaching tips he receives in the interval. Or, if I remember correctly, Chou is known for not having a coach with him during the interval, so any difference could also be due to bad advise hist opponents receive. In today’s match he had his coach with him though.
Method
The analysis is simply to look at all games he played and then count how many rallies he won before and after the interval. We distinguish between intervals when he was in the lead and when he was trailing. The very last rally before the interval is given the index zero and is either won by Chou when he’s leading at the interval or lost when he is trailing. It is therefore not of interest for this analysis. The seven rallies before and after this rally, so effectively the eight before and the seven after the interval, are included in the analysis.
Plot
The following plot gives the percentages of rallies won by Chou in relation to the very last rally before the interval.
First of all, we see that Chou won more points before the interval when he was leading and fewer when he was trailing. This is just a selection bias, because obviously he has had won more points when he is leading at the interval. After the interval, both curves are much closer together. The curve for the games where he was in the lead is still higher, this is due to these matches being more matches where he is the stronger player, thus winning more matches. We can also see, that both curves are between the curves before the interval, this is probably just a regression toward the mean-effect. This effect occurs Chou is likely to have performed better than expectable when he is leading and performed worse when he is trailing. After the interval there is no such selection and the percentage returns to the average.
Tables
The following tables show the raw data. Negative values for the rally denote the rallies before the rally right before the interval.
When Leading at 11:
| Rally | Won | Games | Percentage |
|---|---|---|---|
| -7 | 436 | 687 | 63.46% |
| -6 | 429 | 687 | 62.45% |
| -5 | 422 | 687 | 61.43% |
| -4 | 441 | 687 | 64.19% |
| -3 | 412 | 687 | 59.97% |
| -2 | 412 | 687 | 59.97% |
| -1 | 411 | 687 | 59.83% |
| 0 | 687 | 687 | 100.00% |
| 1 | 395 | 687 | 57.50% |
| 2 | 372 | 687 | 54.15% |
| 3 | 374 | 687 | 54.44% |
| 4 | 388 | 687 | 56.48% |
| 5 | 355 | 687 | 51.67% |
| 6 | 353 | 687 | 51.38% |
| 7 | 397 | 687 | 57.79% |
When Trailing at 11:
| Rally | Won | Games | Percentage |
|---|---|---|---|
| -7 | 245 | 550 | 44.55% |
| -6 | 229 | 550 | 41.64% |
| -5 | 218 | 550 | 39.64% |
| -4 | 221 | 550 | 40.18% |
| -3 | 245 | 550 | 44.55% |
| -2 | 237 | 550 | 43.09% |
| -1 | 209 | 550 | 38.00% |
| 0 | 0 | 550 | 0.00% |
| 1 | 293 | 550 | 53.27% |
| 2 | 273 | 550 | 49.64% |
| 3 | 255 | 550 | 46.36% |
| 4 | 292 | 550 | 53.09% |
| 5 | 267 | 550 | 48.55% |
| 6 | 260 | 550 | 47.27% |
| 7 | 272 | 550 | 49.45% |
Conclusion
The data gives no evidence of different probabilites for Chou to win before or after the interval. All differences can be explained by general statistical phenomena. For a more thourogh analysis, one could do the same analysis for other players and check if the aforementioned patterns also show up for them. Also it is possible to compare the percentages of rallies won with the expected number of won rallies as predicted by the simulation.