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