Did Wiggins do better than Froome in the Tour?

Le Tour de France 2012 finished yesterday with the usual rounds on Champs-Élysées, and not surprisingly, it all came down to a bunch sprint, where Mark Cavendish proved to be the fastest.

Unfortunately I haven't been able to watch very much of the tour this year, but I have read a couple of times that the sky team has done incredibly well and that many people were wondering if young Chris Froome could have taken the overall first prize if his classification role in the team wasn't to help Bradley Wiggins to the victory. It looks like Wiggins settled the discussion Saturday on the last time trial of the tour, where he won with a solid margin of 1:16 to Froome.

But let's put the results to a quick test. I have collected Wiggins and Froomes time differences (in seconds) to the winning time of each stage. The source is http://www.dr.dk/Sporten/Tour_de_France/ and here is the resulting data.

Stage	Wiggins	Froome	diff
Prologue	7	16	9
1	0	85	85
2	0	0	0
3	1	1	0
4	0	0	0
5	0	0	0
6	4	4	0
7	2	0	-2
8	26	26	0
9	0	35	35
10	196	196	0
11	57	55	-2
12	474	474	0
13	0	0	0
14	1095	1095	0
15	710	710	0
16	429	429	0
17	19	19	0
18	4	4	0
19	0	76	76
20	9	9	0

The one sided paired wilcoxon signed rank test, testing for true location shift less than zero gives a p-value of 0.07056 > 0.05, which on a 95% confident measure means that Wiggins didn't do significantly better than Froome in this year's tour.

The p-value however, is so close to the rejection region, that only one more stage time difference with Wiggins being 3 seconds (or more) faster than Froome, would have made his performance significantly better (according to the test). On the contrary, if Froome wasn't caught up in the middle of the run of crashes within the last 25 kilometers of stage 1, then he probably wouldn't have gotten the 85 seconds time difference to Wiggins, and leaving out that single observation gives a more reliably p-value (0.1393).

Notice that the test only consider the observations different from zero (the ties are left out), which means that the actual number of observations for the test is down to only 6.

How predictable was EURO 2012? - Historical view

In my latest post How predictable was EURO 2012?, I introduced 2 predictability measures, and in the preceding comment I came up with a third measure of predictability for a tournament like the EUROs.

All 3 measures are based on the FIFA/Coca-Cola Zonal Ranking for the members of UEFA (FIFA ranking). The latest ranking table before the finals reflects the general expectations in the model. 

FIFA plain ranking
Pearson correlation between the final ranking and prediction based solely on the FIFA ranking, without taking group composition and tournament structure in to account. That is, the highest ranked team is expected to win the second highest ranked team is expected to become runner ups and so on.  The final ranking is a 1 to 16 list of the qualified teams, based on (in given order)
a) final position or position in group,
b) points,
c) goal difference,
d) goals scored.
If two or more teams are equal, the previous stage of the tournament is consulted, to decide who has done best. 

FIFA group dependent
Pearson correlation between the final ranking and prediction based on FIFA ranking under the constraints of the tournament structure and the group compositions. Zonal ranking has decided each round of the tournament, bases on zonal ranking difference in match or zonal ranking order in group. 

FIFA prediction score
Apply FIFA ranking to the members of each group. Give score for how many teams were predicted to qualify for the knockout stage (x_1 of 8). In the quarter finals, reapply the FIFA ranking, and give score for how many teams were predicted to qualify for the semifinals (x_2 of 4). Repeat for the semifinals (x_3 of 2) and the final (x_4 of 1). This gives a total score of (x_1 + … + x_4)/15.


In order to determine whether the 3 predictability scores for EURO 2012 were high or low, we should compare them with their historical counterparts. I have done the math, and here is the result in a nice diagram (the sources are www.fifa.com/worldranking/ and www.uefa.com).

As the diagram illustrates, EURO 2012 scored highest in 3 out of 3 measures, which indicates that EURO 2012 has been at least as predictable as the previous 4 European Championships, if not the most predictable.

The diagram is quite interesting. Beside the above conclusion, that EURO 2012 in fact was predictable compared to the previous tournaments, it gives a lot of information about the strengths and the weaknesses of the different measures.

First, the FIFA plain ranking and the FIFA group dependent are closely related (the correlation measures). That should perhaps not come as a surprise, since the teams (beside the hosts) are seeded according to the FIFA ranking. I would say that the FIFA group dependent is most valuable of the two, because the tournament structure constraints are obeyed.

Second, EURO 1996, EURO 2008 and EURO 2012 displays the same pattern, the level of the FIFA plain ranking and FIFA group dependent is 0.2-0.3 points below the FIFA prediction score. EURO 2000 has very low correlation scores. The favorites France won, but many teams surprised a lot (Netherlands, Portugal, Turkey) or didn’t live up to the expectations at all (Germany, Czech Republic, Denmark) of the FIFA ranking.

The correlation measures give more (negative) weight to great disappointments than the FIFA prediction score, and the positive effect of the overall win of the favorites is not noticeable. The FIFA prediction score, on the contrary, gives very much weight to the overall win of the favorites, since they will add to the score in each round of the tournament. In 2004 it is the exact opposite. The overall winners Greece was ranked 13 out of the 16 qualified teams, so they had great negative impact on the FIFA prediction score because they surprised in all rounds of the tournament, and had relatively little impact on the correlation measures.

How predictable was EURO 2012?

The world cup champions and reigning european champions Spain won their third conscecutive major tournament a few days ago. Many bookmakers and experts had Germany, Netherlands and Spain as favourites, and I personaly (not an expert!) had the world cup runner-ups Netherlands as favourites.

Now it's time to evaluate. How predictable was the outcome. Who surprised and who disappointed the most?

The FIFA/Coca-Cola World Ranking seems like a good measure for the expectations. A lot of different sources could be equally good or even better, like for example one of the leading bookmakers odds before the tournament, but I will make use of the FIFA ranking table from june 6th 2012 (http://www.fifa.com/worldranking/rankingtable/index.html).

Team	Final position	FIFA prediction plain ranking	Error plain ranking	FIFA prediction group dependent	Error group dep.
Spain	1	1	0	1	0
Italy	2	8	6	10	8
Portugal	3	7	4	13	10
Germany	4	2	-2	2	-2
England	5	4	-1	4	-1
Czech Republic	6	14	8	12	6
Greece	7	11	4	8	1
France	8	10	2	7	-1
Russia	9	9	0	6	-3
Croatia	10	5	-5	5	-5
Denmark	11	6	-5	9	-2
Ukraine	12	15	3	15	3
Sweden	13	12	-1	11	-2
Poland	14	16	2	16	2
Netherlands	15	3	-12	3	-12
Republic of Ireland	16	13	-3	14	-2

Above table need some explanation. Final position is based on (in given order)
a) final placement or position in group,
b) points,
c) goal difference,
d) goals scored
in each round of the tournament. FIFA prediction plain ranking is the EURO teams in the order they appear in the FIFA ranking table from june. Error is FIFA prediction minus final position. FIFA prediction group dependent is the simulated tournament where ranking has decided the outcome of each round in the tournament. The simulation is shown below. The numbers in front of each team is the FIFA zonal ranking (ranking for members of UEFA), and final position is based on
a) zonal ranking difference in match or position in group,
b) zonal ranking

Group A			Quarter final 1				Semifinal 1
Russia	9		Winner group A/Runner up group B				Winner QF 1/Winner QF 3
Greece	11		Russia	9			Spain	1
Czech Republic	16		Netherlands	3			Netherlands	3
Poland	32
			Quarter final 2				Semifinal 2
Group B			Winner group B/Runner up group A				Winner QF 2/Winner QF 4
Germany	2		Germany	2			Germany	2
Netherlands	3		Greece	11			England	4
Denmark	6
Portugal	7		Quarter final 3
			Winner group C/Runner up group D
Group C			Spain	1
Spain	1		France	10
Croatia	5
Italy	8		Quarter final 4				Final
Rep. of Ireland	13		Winner group D/Runner up group C				Winner SF 1/Winner SF 3
			England	4			Spain	1
Group D			Croatia	5			Germany	2
England	4
France	10
Sweden	12
Ukraine	28

As we can see from the table, Netherlands (-12) has disappointed most of all team in both predictive models, and Czech Republic (+8) has surprised most according to the plain ranking model, and Portugal (+10) and Italy (+8) has surprised most according to the group dependent model.

A graphical representation of above results is shown in below scatter plots.

As the figures illustrate, the FIFA prediction was better than random choosing, but far from superb. This statement is based on the fact that random choosing, on average, will have zero correlation with final position, and perfect prediction will have perfect correlation with final position, that is, correlation coefficient  1. The correlation coefficient between prediction and final position can therefore be used as measure of the goodness of the prediction, or in our case, where the FIFA ranking represent our expectations, the correlation coefficient will measure the predictability of the tournament.

The correlation between the predicted rankings and the final positions is 0.47 and 0.40 respectively.

Do goals scored correlate with yellow cards?

Last week I amused myself with the Statistical Kit for the Olympic Football Tournament in London. It is 56 pages of statistics on the Men's Olympic Football Tournament, produced by the FIFA Division Communications & Public Affairs. It can be found here: http://www.fifa.com/mensolympic/organisation/documents/index.html. Very interesting, and nice that it's public available, thumbs up.

Very well. At the last page of the report you find following diagram.

Which indicated a positive correlation between goals scored and yellow cards. Is this a coincidence or a pattern for further investigation?


I have checked the counts for the European Championships and World Cups in same period. Sources are www.uefa.com and www.fifa.com.

The Euro and World Cup graphs don't display the same pattern as the Olympics graph, so correlation between goals scored and yellow cards is unlikely. A correlation plot should support this statement, but in order to compare data from the three different tournaments in one diagram, we should divide the series by games played.