# Bias in figure skating judging

My wife is very enthuisiastic about figure skating. She often mentions that the judging is biased, in the sense that many judges give higher scores to athletes from their own country, and lower scores to athletes from other countries.

This doesn’t sound too surprising, but I wondered if it is actually true. Can I show that there is a statistically significant bias in figure skating scoring?

## The data

To answer this question I need to have a dataset with scores of many skaters, including the nationalities of all the skaters and judges. The ISU publishes these results in PDF files on their website. Before the 2016/2017 season they randomized the order of the judges’ scores for each skater, so these seasons are not usable. Additionally they stopped publishing the nationalities of judges since the current 2019/2020 season. Therefore I downloaded all the scores of the 2016/2017 through 2018/2019 seasons from the isu websites. In a separate post I will go more into detail in how to mine PDF data like this.

A typical piece of a PDF file looks like this:

Additionally on the website we get the following information regarding the judges presented in a table like this:

## Results

This is all we need. We can now build a table comparing the scoring of a particular judge and the average of all judges together. We split this between scoring for technical elements (which should be more objective) and scoring program components (which should be more subjective). In the example above the skater is from Russia, and we see that Judge No.1 (who is from the Netherlands) gives an average GOE of $$1.003$$ for the technical elements, compared to the average of all judges of $$0.796$$. This means that her scores are $$0.287$$ above the average. This in itself doesn’t mean much, but if we observe that there is a consistent bias over many different cases where a Dutch judge is judging a Russian skater, then we have identified a bias.

Then this is what we do: for each pair of countries we collect all the cases where a judge from country A judged a skater from country B. Then we record how their scoring was compared to the average scoring of all the judges. Finally we look at the distribution of these deviations from the average. Taking the example above, in my data there were 49 cases where a Dutch judge judged a Russian skater, and the distribution looks like this:

Here we see that the distribution is roughly that of a normal distribution. Furthermore the mean is not statistically different from $$0$$; the $$p$$-value is $$0.845$$. For us to conclude that there is a statistically significant bias this value should at the least be below $$0.05$$. Since we have many pairs of countries (2586 to be precise), we might even put this criterion significantly lower (say 1/1000) to avoid false positives.

We can thus conclude that there is no statistically significant bias when it comes to Dutch judges scoring Russian skaters. But what if we look at say Russian judges scoring their own skaters? Well, then we see a very different story. We have 519 cases of this happening, and the distribution of score deviation looks like this:

We see that the far majority (82%) of the time, the Russian judges gave higher scores to Russian skaters compared to their peers. In fact the mean deviation is $$0.242$$ (which is quite significant), with a $$p$$-value of $$4.13\times 10^{-68}$$, which is most certainly statistically significant. So there you have it, Russian judges tend to score their own athletes significantly higher. But Russia is not the only country of doing this; every major figure skating country has such a bias. Out of those, the bias of Japan is the least with $$0.16$$ points, and that of France the highest with $$0.26$$. All of this is for the technical scores, but the component scores paint a very similar picture.

And we don’t just see that some countries like themselves, we also see that many countries tend to score their rivals significantly lower. If we set the barrier for statistical significance at a $$p$$-value of $$0.001$$, then we find 29 country pairs with scores significantly less than 0 (and also 29 pairs with scores more than 0). With very few exceptions all the cases where a country gives significantly lower scores to another country, then this happens between a former Warsaw pact country and a non-Warsaw pact country. One can thus see that cold war politics are still very much alive in the world of figure skating.

For reference here is a table with the pairs of countries where the $$p$$-value is less than $$0.001$$, sorted by the average deviation in GOE scores. If we increase the $$p$$-value to $$0.05$$, the number of country pairs with a negative/positive deviation increases to 100/127 respectively, but this likely also includes some false positives.

Country A Country B GOE Deviation # Samples std p-value
GEO GER -0.423535 13 0.291439 0.000292112
FIN POL -0.394558 7 0.129526 0.000298878
GEO JPN -0.391477 23 0.369426 5.66014e-05
NOR SVK -0.347513 15 0.304064 0.000767944
DEN JPN -0.287993 19 0.256627 0.000156087
GEO CAN -0.278147 23 0.321245 0.000519587
GEO FRA -0.262415 17 0.236376 0.000411082
USA POL -0.234252 37 0.319543 9.28026e-05
FIN RUS -0.223771 116 0.459913 8.11565e-07
CAN UKR -0.212031 54 0.294583 2.83725e-06
USA BLR -0.210608 54 0.30442 5.83674e-06
USA ESP -0.209474 31 0.269294 0.000185776
GEO USA -0.199728 48 0.303747 4.34335e-05
USA HUN -0.198829 32 0.301136 0.000890425
UKR CAN -0.196541 72 0.327044 3.11877e-06
ITA UKR -0.190304 27 0.249708 0.000628967
NOR RUS -0.167886 42 0.265585 0.000223648
GER RUS -0.146194 216 0.365862 1.73015e-08
BLR CAN -0.144693 57 0.273774 0.00021738
HKG RUS -0.140813 19 0.147647 0.000757625
USA RUS -0.127477 487 0.346152 3.90599e-15
RUS KOR -0.11664 69 0.246956 0.000226837
CZE USA -0.103901 131 0.327618 0.000426771
RUS JPN -0.093866 227 0.289868 2.11539e-06
KOR RUS -0.0924231 199 0.329138 0.000108097
CZE CAN -0.0915781 117 0.282166 0.000671065
RUS USA -0.088714 400 0.293915 3.75673e-09
CHN CAN -0.0817519 167 0.278467 0.000216408
RUS CAN -0.072195 313 0.268176 3.0339e-06
CZE CZE 0.10548 70 0.231123 0.000317855
FRA JPN 0.111209 102 0.285243 0.000162456
HUN RUS 0.132175 89 0.327803 0.000282576
JPN JPN 0.156523 237 0.327147 3.22684e-12
GER GER 0.163652 84 0.248169 4.80504e-08
AUT AUT 0.168284 41 0.272225 0.000348661
BLR UKR 0.172673 27 0.234309 0.000876659
RUS BLR 0.172728 48 0.261251 4.0039e-05
ITA ITA 0.191333 83 0.257742 2.20598e-09
FRA SUI 0.196021 15 0.153326 0.000291446
USA USA 0.201305 390 0.344327 1.16234e-26
CAN CAN 0.202964 309 0.328201 1.87699e-23
SLO SLO 0.220573 14 0.183307 0.00080383
CHN CHN 0.237789 126 0.27782 1.30817e-16
RUS RUS 0.242122 519 0.270732 4.12722e-68
ISR ISR 0.246661 36 0.278365 7.70606e-06
KOR KOR 0.255873 65 0.302727 4.86167e-09
FRA FRA 0.255881 149 0.334381 1.63481e-16
LTU LTU 0.264828 18 0.183077 1.53876e-05
GEO GEO 0.31548 18 0.180445 1.46255e-06
UZB UZB 0.327713 14 0.180962 1.91363e-05
ESP ESP 0.339558 27 0.278435 1.40513e-06
KAZ KAZ 0.345734 30 0.314278 1.9616e-06
MEX MEX 0.34907 15 0.247822 0.000118384
EST EST 0.369731 28 0.258569 5.41857e-08
TUR TUR 0.435335 25 0.278468 6.76828e-08
BLR BLR 0.455432 38 0.316918 1.57049e-10
HUN HUN 0.471011 34 0.344248 4.63145e-09
UKR UKR 0.505353 41 0.363255 6.7634e-11
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