Will Germany and USA engineer a mutually beneficial draw?

Headed into the final  group stage games of the 2014 World Cup, the standings in Group G are:

Team Pld W D L GF GA GD Pts
Germany 2 1 1 0 6 2 +4 4
USA 2 1 1 0 4 3 +1 4
Ghana 2 0 1 1 3 4 -1 1
Portugal 2 0 1 1 2 6 -4 1

With the final games being Germany-USA and Ghana-Portugal, Germany and USA both have their fate in their hands, each knowing that a win or a draw would ensure qualification for the second round. A draw would mean that both teams go through, so there has been some talk about whether the two teams will play about a mutually beneficial draw.

The spectre of the 1982 World Cup rears its ugly head here. Algeria had won their final group match against Chile to give themselves a good chance of making it out of the group. However, the other final group game took place a day later, with Austria and Germany knowing that if Germany won the game between them by no more than two goals, then both teams would advance to the second round at the expense of the Algerians. Lo and behold, after Germany scored in the 10th minute what followed was 80 minutes of negative play from both sides, with players largely passing the ball around in their own half and back to the keeper (this was before the back-pass rule was implemented).  The legacy of this match is that final matches in the same group in major tournaments are now played at the same time.

However, this does leave scenarios like the one we have now which could lead to play against the spirit of the game. An oft-cited example is Sweden and Denmark playing out a 2-2 draw in Euro 2004, to put out Italy. However, had Italy beaten Bulgaria by three goals (they only won 1-0) then a Sweden-Denmark draw would’ve put Denmark out, so a draw strategy was risky for Denmark, although a high-scoring draw increased their chances of advancing on goals scored should Italy have won by two goals.

There have been some analogous examples of the Group G situation in past international tournaments (by analogous I mean a points situation of 4-4-1-1 going into the final game with the teams on 4 points playing one another, and with no chance of the team finishing 3rd advancing too). Let’s look at how those unfolded.

 

Tunisia vs Angloa, 2008 African Cup of Nations

Situation before the final group matches:

Team Pld W D L GF GA GD Pts
Tunisia 2 1 1 0 5 3 +2 4
Angola 2 1 1 0 4 2 +2 4
Senegal 2 0 1 1 3 5 -2 1
S Africa 2 0 1 1 2 4 -2 1

The results:

Tunisia 0-0 Angola

Senegal 1-1 South Africa

Here we have an example where the two teams in question did play out a draw, and an unexciting goalless draw as well. In the end it hardly mattered as Senegal-South Africa ended in a draw too meaning Tunisia and Angola would have both gone through anyway. Further, Senegal or South Africa would have needed a four-goal turnaround to progress on goal difference, which would have been a tall order.

Final group standings:

Team Pld W D L GF GA GD Pts
Tunisia 3 1 2 0 5 3 +2 5
Angola 3 1 2 0 4 2 +2 5
Senegal 3 0 2 1 4 6 -2 2
S Africa 3 0 2 1 3 5 -2 2

 

Uruguay vs Mexico, 2010 World Cup

Situation before the final group matches:

Team Pld W D L GF GA GD Pts
Uruguay 2 1 1 0 3 0 +3 4
Mexico 2 1 1 0 3 1 +2 4
France 2 0 1 1 0 2 -2 1
S Africa 2 0 1 1 1 4 -3 1

The results:

Uruguay 1-0 Mexico

France 1-2 South Africa

In this case, an imploding France had been written off before the match because surely Mexico and Uruguay would go for the draw? The BBC’s staid pundits certainly thought so, with Danny Baker treated like a madman when he came into the studio and suggested otherwise.

Well he was wrong, although his manner of being wrong was far more interesting than the manner in which any of the pundits were right for the entirety of the World Cup. He was however correct in that Mexico and Uruguay did not draw. A goal in the 43rd minute from who else but Luis Suárez led to a Uruguay win, but Mexico advanced anyway as a 5-goal deficit in goal difference proved too much for South Africa to turn around (France would have had a better shot at displacing Mexico with only a 4-goal deficit). I imagine that the Mexican players did not worry too much late on in the game as it became clear that the other scoreline was not troubling them overly.

Final group standings:

Team Pld W D L GF GA GD Pts
Uruguay 3 2 1 0 4 0 +4 7
Mexico 3 1 1 1 3 2 +1 4
S Africa 3 1 1 1 3 5 -2 4
France 3 0 1 2 1 4 -3 1

 

England vs Netherlands, Euro 96

Situation before the final group matches:

Team Pld W D L GF GA GD Pts
England 2 1 1 0 3 1 +2 4
Netherlands 2 1 1 0 2 0 +2 4
Switzerland 2 0 1 1 1 3 -2 1
Scotland 2 0 1 1 0 2 -2 1

The results:

England 4-1 Netherlands

Scotland 1-0 Switzerland

In this case England were hosts, so guaranteed advancement would be beneficial for the tournament, and a draw would mean not only that England were through but eternal rivals Scotland were out – so presumably a draw would have been a no-brainer? What transpired instead was what is generally considered to be one of England’s greatest performances, and the peak of the Shearer and Sheringham SAS partnership. Scotland, leading 1-0 against Switzerland, were headed through on goal difference until Patrick Kluivert scored a more-than-consolation goal for the Netherlands. Scotland (and England) were unable to get the extra goal that would have sent them through, and Netherlands went through on goals scored.

Final group standings:

Team Pld W D L GF GA GD Pts
England 3 2 1 0 7 2 +5 7
Netherlands 3 1 1 1 3 4 -1 4
Scotland 3 1 1 1 1 2 -1 4
Switzerland 3 0 1 2 1 4 -3 1

 

So can we expect Germany and USA to play out a draw? It’s possible and probably would be logical for both teams. However it does enter the realm of game theory – can each team trust that the other will play for the draw too? Surely, if he’s on the pitch, Miroslav Klose wouldn’t pass up a goalscoring opportunity to become the top scorer in World Cup history outright with 16 goals. Would  Thomas Müller do so, given that he has a decent shot at taking the record himself one day with 8 World Cup goals already at the age of 24? A goal for Clint Dempsey would put him level with Landon Donovan as USA’s top World Cup goalscorer. Would anyone for that matter pass up the opportunity to score in a World Cup?

Then you have goal difference as it stands. Germany are in a better position than USA, with a five-goal advantage over Ghana and eight over Portugal, while for the USA it’s five over Portugal and only two over Ghana – if USA were to lose and Ghana win with either one being by more than one goal then USA are out. USA can only go through if they lose and Ghana win if both are by one goal and USA score at worst one fewer goals against the USA than Ghana do against Portugal. So Germany might be willing to go for a win with a loss being a lower risk, while USA might be happier to settle for a draw.

The other factor coming into this is who they might face in the rest of the tournament. A winner of Germany-USA would go through as top, with a draw it would be Germany. The 2nd-placed team would play the winners of group H, which will be decided after group G, but is likely to be Belgium, while the top team will probably play Russia or Algeria, on paper an easier game. However, the bracket for the rest of the knockout stage will have been determined, so one half of the draw may appear preferable to the other, and that could be under consideration.

All-in-all, there’s no evidence that a draw is guaranteed to happen between USA and Germany, but it’s worth noting that in all of the cases seen here that the two teams in question still went through. So while Germany and USA both advancing is the most likely scenario, I wouldn’t necessarily bet the house on them doing so with a draw.

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2014 World Cup group stage final game scenarios

Here I’ll run through what each team in the 2014 World Cup needs to do in their final group game (and possibly needs other teams to do) to qualify for the 2nd round. By presenting tables and each team’s individual scenario, hopefully it’ll be clear.

 

Group A sees three teams still able to qualify (Brazil, Croatia and Mexico), while Cameroon are already eliminated.

MEX win

MEX/CRO draw

CRO win

BRA win

BRA, MEX (GD)

1. BRA 2. MEX

1. BRA 2. CRO

BRA/CMR draw

1. MEX 2. BRA

1. BRA 2. MEX

1. CRO 2. BRA

CMR win

1. MEX 2. BRA

1. MEX 2. CRO

1. CRO 2. BRA/MEX (GD)

Brazil: Will qualify with a win or draw. Can still qualify with a loss if Mexico beat Croatia, or if Croatia beat Mexico and Brazil end up with a better goal difference than Mexico (if tied on that it will go to goals scored, and if also tied on that then there will be a drawing of lots).
Mexico: Will qualify with a win or draw. Can still qualify with a loss, but only if Cameroon beat Brazil and Mexico end up with a better goal difference than Brazil (if tied on that it will go to goals scored, and if also tied on that then there will be a drawing of lots).
Croatia: Will qualify with a win. Can qualify with a draw, but only if if Cameroon beat Brazil. Cannot qualify with a loss.

 

Group B is simple: Spain and Australia are already eliminated and will contest a dead rubber. Netherlands and Chile are through with their game determining the group winners, which will be Netherlands if they win or it’s a draw, otherwise it’ll be Chile.

 

Group C has Colombia already through, with any one of Côte d’Ivoire, Japan or Greece joining them.

COL win

COL/JPN draw

JPN win

CIV win

1. COL 2. CIV

1. COL 2. CIV

COL, CIV (GD)

CIV/GRE draw

1. COL 2. CIV

1. COL 2. CIV

1. COL 2. CIV/JAP (GD)

GRE win

1. COL 2. GRE

1. COL 2. GRE

1. COL 2. GRE/JAP (GD)

Colombia: Already through.
Côte d’Ivoire: Will qualify with a win. Would qualify with a draw unless Japan beat Colombia and have a better goal difference (if tied on that it will be decided on goals scored, if also tied on that then Côte d’Ivoire qualify since they beat Japan). Cannot qualify with a loss.
Greece: Would qualify with a win unless Japan beat Colombia and have a better goal difference (if tied on that it will be decided on goals scored, if also tied on that then there will be a drawing of lots). Cannot qualify with a loss or draw.
Japan: Can qualify with a win provided Côte d’Ivoire don’t win and Japan have a better goal difference than Côte d’Ivoire if Côte d’Ivoire and Greece draw, or than Greece if Greece win (a goal difference and goals scored tie yields a drawing of lots only in the latter case, in the former case Côte d’Ivoire would qualify). Cannot qualify with a loss or draw.

 

Group D has Costa Rica (!) already qualified, while England are out (on the bright side, England fans, a win against Costa Rica means they come home from Brazil as Unofficial Football World Champions). The other qualification place is between Italy and Uruguay.

ITA win

ITA/URU draw

URU win

CRC win

1. CRC 2. ITA

1. CRC 2. ITA

1. CRC 2. URU

CRC/ENG draw

1. CRC 2. ITA

1. CRC 2. ITA

1. CRC 2. URU

ENG win

CRC, ITA (GD)

1. CRC 2. ITA

CRC, URU (GD)

Costa Rica: Are already through and will do so as group winners, unless they are beaten by England and either Uruguay or Italy wins with a better goal difference (if in this scenario they are tied on goal difference and goals scored, Costa Rica finish top having beaten Uruguay and Italy).
Italy: Will qualify with a win or a draw (with a better goal difference than Uruguay). Cannot qualify with a loss.
Uruguay: Will only qualify with a win. Cannot qualify with a draw or loss.

 

Group E has none of its teams (France, Ecuador, Switzerland and Honduras) through or out yet.

FRA win

FRA/ECU draw

ECU win

SUI win

1. FRA 2. SUI

1. FRA 2. SUI

FRA/SUI/ECU (GD)

SUI/HON draw

1. FRA 2. SUI

1. FRA 2. ECU

FRA, ECU (GD)

HON win

1. FRA 2. SUI/HON/ECU (GD)

1. FRA 2. ECU

FRA, ECU (GD)

France: Will qualify with a win or a draw. Would still qualify with a loss unless Switzerland win and they and Ecuador both have better goal differences (highly unlikely given France’s is currently +6 versus 0 and -2 for Ecuador and Switzerland, respectively).
Ecuador: Would qualify with a win unless Switzerland beat Honduras and Switzerland and France end up with better goal differences (the tie-breaker after goal difference and goals scored in this scenario will be goal difference then goals scored in the games between these three teams). Would qualify with a draw unless Switzerland win. Can only qualify with a loss if Honduras beat Switzerland and Ecuador have a better goal difference etc than Switzerland and Honduras.
Switzerland: Would qualify with a win unless Ecuador beat France and both end up with better goal differences etc. Can qualify with a draw only if France beat Ecuador. Can only qualify with a loss if France beat Ecuador and Switzerland have a better goal difference etc than Ecuador and Honduras.
Honduras: Can only qualify if they beat Switzerland and France beat Ecuador and Honduras have a better goal difference etc than Switzerland and Honduras. A draw or loss means elimination.

 

Group F has Argentina already through and Bosnia & Herzegovina already out. The other second round spot will be Iran or Nigeria.

ARG win

ARG/NGA draw

NGA win

IRN win

1. ARG 2. NGA/IRN (GD)

1. ARG 2. NGA

1. NGA 2. ARG

IRN/BIH draw

1. ARG 2. NGA

1. ARG 2. NGA

1. NGA 2. ARG

BIH win

1. NGA 2. ARG

1. NGA 2. ARG

1. NGA 2. ARG

Argentina: Are already through (and will do so as top unless they lose to Nigeria).
Nigeria: Will qualify with either a win or a draw against Argentina. If they lose to Argentina then they will need Iran to not win, otherwise they need to hope they lose to Argentina by only one goal and Iran win by only won goal but Nigeria score at least as many goals as Iran do against Bosnia & Herzegovina (if Nigeria were to score one fewer than Iran then we would have a drawing of lots).
Iran: Can only qualify if they win and Nigeria lose: if one of these is by at least two goals then Iran would qualify with a better goal difference, otherwise it would go to goals scored (Iran through if they score more than Nigeria do against Argentina) then a drawing of lots. Cannot qualify with a draw or a loss.

 

Group G has all four teams (Germany, USA, Ghana and Portugal) able to qualify.

GER win

GER/USA draw

USA win

GHA win

1. GER 2. GHA/USA (GD)

1. GER 2. USA

1. USA 2. GER/GHA (GD)

GHA/POR draw

1. GER 2. USA

1. GER 2. USA

1. GER 2. USA

POR win

1. GER 2. USA/POR (GD)

1. GER 2. USA

1. USA 2. GER/POR (GD)

Germany: Will qualify with a win or draw. Can qualify with a loss if Ghana and Portugal draw, or if they have better goal difference etc than the winner of that game.
USA: Will qualify with a win or draw. Can qualify with a loss if Ghana and Portugal draw, or if they have better goal difference etc than the winner of that game.
Ghana: Can qualify if they beat Portugal and have a better goal difference etc than a losing team in the Germany-USA game. Cannot qualify with a draw or loss.
Portugal: Can qualify if they beat Ghana and have a better goal difference etc than a losing team in the Germany-USA game. Cannot qualify with a draw or loss.

 

Group H has Belgium already through. The other spot is up for grabs between Algeria, Russia and South Korea.

BEL win

BEL/KOR draw

KOR win

ALG win

1. BEL 2. ALG

1. BEL 2. ALG

1. ALG 2. BEL

ALG/RUS draw

1. BEL 2. ALG

1. BEL 2. ALG

1. BEL 2. ALG/KOR (GD)

RUS win

1. BEL 2. RUS

1. BEL 2. RUS

1. BEL 2. RUS/KOR (GD)

Belgium: Are already through (and will do so as top unless they lose to South Korea and Algeria beat Russia).
Algeria: Will qualify with a win. Would qualify with a draw unless South Korea beat Belgium and by more than 3 goals, or by 3 goals and score 3 more goals more than Algeria do against Russia. Cannot qualify with a loss.
Russia: Can qualify with a win except if South Korea beat Belgium by two more goals than Russia beat Algeria, or by one more goal and Russia score 2 fewer than South Korea (a goals scored tie would result in a drawing of lots). Cannot qualify with a draw or loss.
South Korea: Can qualify with a win if Algeria don’t win. Need to beat Russia on goal difference etc if Russia win or Algeria if it’s a draw, in the ways described above. Cannot qualify with a draw or loss.

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Got, got, need: how much does a 2014 World Cup sticker collection cost, or why is swapping so important?

The year 2014 brings with it a World Cup, and with that an activity that is familiar to many: the collection of stickers in the attempt to complete Panini’s World Cup sticker album. The pastime has not changed much over the years since Panini’s first collection for the 1970 World Cup. The Italian company still prints the same multilingual booklet, with the pages for most, but not all, of the teams headed with the name of that country in its official language – for Belgium they split the difference and go with ‘Belgique/België’ (sorry German-speaking Belgians!), but rather than entertain a four-way tie they plump with ‘Switzerland’. The major change though is that the number of stickers to collect has increased, largely due to the World Cup itself having expanded to 32 teams in 1998. This year’s collection comprises 640 stickers: 19 for each team (17 players, the team and the logo) with the remaining stickers being the stadia, trophy, official ball etc. So how much does this cost?

The good news is that the empty album can be picked up for free, and furthermore comes with an insert of 6 stickers: Yaya Touré (Côte d’Ivoire), Cristiano Ronaldo (Portugal), Hugo Lloris (France), Gonzalo Higuaín (Argentina), Daniele  De Rossi (Italy) and Roman Shirokov (Russia). This leaves 634 stickers to buy. Stickers can be bought in packs of 5 for 50p, but you get multipacks of 5 packs for £2 in Asda. So 25 multipacks and 2 extra packs would get you 640 stickers at a cost of £51 (just buying individual packs this cost would be £63.50.)

But, of course, among these stickers are likely to be duplicates. If I were to hand you 636 randomly selected stickers the chances you’d have a complete collection would be about 1 in 10^{276}. So how much would we expect to spend before we have a complete collection. We’ll assume that each sticker is equally likely to appear (even the ones that come in the insert), so each sticker has a \frac{1}{640} probability of being Yaya Touré, or of being Wayne Rooney, or of being the Colombian logo.

So far we already have 6 of our album stickers (as stickers stuck in our album will be referred to hereon in), so when we open the first pack the first sticker we see could be one of 634 we don’t already have or one of the 6 we do, so the probability it is our 7th album sticker is \frac{634}{640}, while the probability it is a duplicate is \frac{6}{640}. If it is a duplicate then the next sticker still has a probability of \frac{634}{640} of being our 7th album sticker, and this remains the case until we find our 7th album sticker. The number of stickers we see until we have our 7th album sticker is equivalent to the number of success/failure (i.e. Bernoulli) trials until the first success. The number of Bernoulli trials of success probability p until success follows a Geometric distribution and its mean value is simply given by \frac{1}{p}. So we expect to see \frac{640}{634} stickers until we have our 7th album sticker.

Once we have our 7th album sticker, we have now 633 stickers left to collect. So the probability of a sticker being our 8th album sticker is \frac{633}{640}. After our 7th album sticker, the number of stickers we see until we have our 8th album sticker again follows a Geometric distribution, so we expect to see \frac{640}{633} more stickers until we have our 8th album sticker. We then expect to see \frac{640}{632} stickers until we see our 9th album sticker, and \frac{640}{631} until we see our 10th and so on.

So, once we have $latex i-1$ stickers, the number of stickers we expect to see before we find our ith album sticker is \frac{640}{641-i}. All told then the number of stickers we’d expect to see to complete our album of 640 stickers is

\sum_{i=7}^{640}\frac{640}{641-i}=\frac{640}{634}+\frac{640}{633}+\frac{640}{632}+\cdots+\frac{640}{2}+\frac{640}{1}=4500,

which would be 180 multipacks at a total cost of £360! (Or 900 individual packs at a cost of £450.)

The main reason for this high cost is that as you fill up your sticker album, it becomes harder and harder to add to it. Once you have 639 stickers, you’d expect to have to see 640 stickers before you get your final sticker, at a cost of £51.20 (at the 8p per sticker multipack price) or £64 (at the 10p per sticker individual pack price), which is a lot of money to get one sticker! You can see the expected number of stickers and cost at each rate for each album sticker in the spreadsheet below (the would-be cost of album stickers is included – their being free doesn’t offer a huge saving.)

Thankfully Panini have mercy and allow you a one-off order of 50 specified stickers to help you complete your collection, at the price of 14p per sticker plus £1 for postage. This works out at 16p per sticker if you order 50, which reduces to 14.6p with a 10% discount on the stickers if you order online using a code in your album. While this is more expensive than the cost of a sticker it’s still much cheaper than the cost of later album stickers, in fact from the spreadsheet we can see that even with multipacks each new album sticker is expected to cost over 14.6p when you only have 290 album stickers – not even half full! Ordering these stickers is a no-brainer and requires us then to only collect 590 album stickers beforehand, the number of stickers we’d expect to see to reach this amount is

\sum_{i=7}^{590}\frac{640}{641-i}=1619,

which requires 65 multipacks at a total cost of £130 or 324 individual packs at a total cost of £162. Add in your ordered album stickers at the reduced rate and you’re expecting to pay £137.30 with multipacks or £169.30 with individual packs, a significant reduction thanks to being able to order those last 50 otherwise incredibly expensive stickers. It is still however a good deal more than the £51 minimum cost – which is what makes the ability to make good swaps so vital, to reduce the expected cost closer towards that lower value.

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The UCI’s folly and the continuing dominance of the British track cycling team

At the 2008 Olympics the final medal table for the track cycling looked like this:

Rank Nation Gold Silver Bronze Total
1  Great Britain 7 3 2 12
2  Spain 1 1 1 3
=3  Argentina 1 0 0 1
=3  Netherlands 1 0 0 1
=5  France 0 1 1 2
=5  Germany 0 1 1 2
=5  New Zealand 0 1 1 2
=8  Australia 0 1 0 1
=8  Cuba 0 1 0 1
=8  Denmark 0 1 0 1
=11  Russia 0 0 1 1
=11  China 0 0 1 1
=11  Japan 0 0 1 1
=11  Ukraine 0 0 1 1

The governing body of cycling, the UCI, were concerned by the dominance of the British team and to try to prevent this in future, they restricted nations to one rider per event (and therefore each nation could only win one medal per event) in individual events. The medal table for the 2012 Olympics then looked like this:

Rank Nation Gold Silver Bronze Total
1  Great Britain 7 1 1 9
2  Australia 1 1 3 5
3  Germany 1 1 1 3
4  Denmark 1 0 0 1
5  France 0 3 0 3
6  China 0 2 1 3
7  United States 0 2 0 2
8  New Zealand 0 0 2 2
=9  Netherlands 0 0 1 1
=9  Hong Kong 0 0 1 1
=9  Canada 0 0 1 1

It doesn’t look like much less of a dominance by the British team, who failed to gain a medal in only one of the 10 events (the women’s team sprint, in which a strict commissaire’s ruling resulted in a disqualification depriving them of at least a silver).

It should be noted that this one-rider-per-nation rule was not the only rule change made between the two Olympics. Rightly so the UCI decided to finally ensure parity between men and women in terms of number of events (at Beijing the men had 7 to the women’s 3). The IOC demand that currently the total number of cycling events (across track, road, mountain biking and BMX) be fixed at 18. Previously, between the 2004 and 2008 games, the men’s 1km and women’s 500m time trials had been removed to introduce the BMX events for men and women (this change possibly contributed to GB’s dominance as the 1km time trial was 2004 Olympic champion Chris Hoy’s sole event and for 2008 he switched to sprinting, winning three golds in the sprint, keirin and team sprint).

To achieve parity then, men’s events would have to be taken out. The UCI decided to keep the team sprint, sprint, keirin and 4km team pursuit for the men and sprint for the women while taking out the 4km individual pursuit, points race and madison for the men and the 3km individual pursuit and points race for women. These were replaced by the omnium for the men and the team sprint, keirin, 3km team pursuit and omnium for women. These changes were not received well by many – the individual pursuits were considered by many to be the blue riband event of the track, while the omnium, a multi-discipline event including time trials, the individual pursuit and bunch races like the points race, is seen as a ‘jack of all trades, master of none’ by some.

(Side note: it’s possible that the removal of the individual pursuit also played into British success on the road as, had it stayed in for 2012, reigning champion Bradley Wiggins may have been tempted back to the track, and likely therefore not won the 2012 Tour de France.)

Ideally the UCI would not have been forced to remove men’s events to introduce ones for women, as in track & field the introduction of the 3000m steeplechase, pole vault and hammer throw for women did not come at the expense of any events. However, the UCI are to blame in that their choice of events appears to have help sustained the British medal table dominance, after all the three events which were not won by British cyclists in 2008 – the men’s and women’s points races and the men’s madison – were among those removed. These bunch races are, like road racing, more unpredictable, and cyclists can find that going into these races as favourites can work against them tactically, as Mark Cavendish and Bradley Wiggins found in the madison in 2008. The omnium can be won by a rider who dominates in the events against the clock, if they can limit their losses in the bunch races, as Laura Trott did exceptionally well to take the first women’s gold.

Retaining of the team versions of the sprint and pursuit also benefits nations that have strength in depth: one superior rider could win the individual pursuit but they need 3 other teammates of sufficient ability to win the team pursuit. A good analogy here is that George Weah may have been the greatest footballer in the world at one point, but that didn’t mean that Liberia had a great national team.

That the event changes may have played into Britain’s favour makes the UCI look particularly silly, given that the effect of the one-rider-per-nation rule (which really only applied to the sprint and keirin) was to reduce the number of British silver and bronze medals, while also depriving fans with a weakened field.

So what can the UCI do to prevent British dominance in 2016 in Rio de Janeiro? They could combat British Cycling performance director Dave Brailsford’s philosophy of ‘aggregated marginal gains’ by insisting that riders across the nations all use standard equipment. I very much doubt that they would do this, and whether this would actually make the difference is another question (the UCI’s rule deprived us the chance of comparing British riders using the same equipment).

One thing they certainly couldn’t legislate against is British Cycling’s uncanny ability to get riders to peak at the right time. Frenchman Grégory Baugé looked formidable winning the sprint at the 2009, 2010, 2011 and 2012 World Championships (albeit losing his 2011 title after missing doping tests) but he was no match for Jason Kenny come the Olympics. Likewise the Australian pursuit team had looked very strong but could not compete with a world record-breaking British quartet.

With a budget the envy of the world, there may not be a lot the UCI can do to achieve their desired goal. The medal table for 2016 may well make for familiar reading.

Note: while I was writing this, it was reported that chief UCI numpty Pat McQuaid has said they will aim to get 12 track events for 2016. I hope they’re successful – bye bye omnium? (link) 

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Heptathlon points system vs the omnium points system

The omnium is a multi-discipline track cycling event which has debuted at the Olympics this year. It is made up of six events (flying lap, points race, elimination race, individual pursuit, scratch race and time trial) and has a fairly simple point scoring system to determine overall placings: for each event the rider who places first scores 1 point, second 2 points, and so on, with the rider with the lowest total number of points across the 6 events being the winner.

In the men’s event, British rider Ed Clancy won the 1km time trial with a time of 1:00.981 (a time which would have won Olympic gold in the 1km time trial at the 2000 Olympics). This was over a second faster than all other riders in the omnium, a sizeable margin over such a short distance, but in the omnium the size of the margin is immaterial – Clancy only need have won by the smallest of measurable margins to still take just one point.

This had me wondering how the omnium might work differently if it were scored in the manner of the athletics multi-discipline events, the heptathlon and decathlon. In these events, heights, distances and times are converted into point scores according to a formula for each individual event. Basically, the faster you run/farther you throw/etc the more points you get. For the omnium, this would require the devising of a points system for each event. For the events contested against the clock (flying lap, individual pursuit, time trial) this would be feasible, but the performance of the riders in the bunch races (points race, elimination race, scratch race) is relative to one another, for example the results of the elimination race (in which the last placed rider is eliminated every 2nd lap) is simply a ranking. Thus for these races it would be difficult to devise a performance-based points system and so the ranking-based system makes sense.

However, we can apply the omnium points system to the results of the heptathlon at the 2012 Olympics. The different rankings (HR = heptathlon points system rankings, OR = omnium system rankings) are shown in this table (full spreadsheet here.)

Athlete HR OR
 Jessica Ennis (GBR) 1 1
 Lilli Schwarzkopf (GER) 2 2
 Tatyana Chernova (RUS) 3 4
 Lyudmyla Yosypenko (UKR) 4 3
 Austra Skujytė (LTU) 5 11
 Antoinette Nana Djimou Ida (FRA) 6 7
 Jessica Zelinka (CAN) 7 5
 Kristina Savitskaya (RUS) 8 6
 Laura Ikauniece (LAT) 9 10
 Hanna Melnychenko (UKR) 10 8
 Brianne Theisen (CAN) 11 9
 Dafne Schippers (NED) 12 13
 Nadine Broersen (NED) 13 16
 Jessica Samuelsson (SWE) 14 14
 Katarina Johnson-Thompson (GBR) 15 12
 Sharon Day (USA) 16 17
 Yana Maksimava (BLR) 17 19
 Eliška Klučinová (CZE) 18 20
 Ellen Sprunger (SUI) 19 18
 Olga Kurban (RUS) 20 21
 Marisa De Aniceto (FRA) 21 24
 Györgyi Farkas (HUN) 22 25
 Grit Šadeiko (EST) 23 22
 Sofia Ifadidou (GRE) 24 28
 Ivona Dadic (AUT) 25 27
 Sarah Cowley (NZL) 26 31
 Louise Hazel (GBR) 27 26
 Ida Marcussen (NOR) 28 29
 Chantae McMillan (USA) 29 23
 Jennifer Oeser (GER) 30 15
 Julia Mächtig (GER) 31 30
 Irina Karpova (KAZ) 32 32

A Spearman’s rank correlation coefficient of 0.9242 shows that the two rankings are strongly correlated as we’d expect, but for individual athletes the change of system can make quite a difference. Under the omnium system, the Russian Tatyana Chernova would lose her bronze medal to Lyudmyla Yosypenko of Ukraine. Other athletes can fall or rise a considerable number of places. Lithuanian Austra Skujytė, strong in the field events, finds the gains from her vastly superior shot putting limited as she drops 6th places. Meanwhile, for Jennifer Oeser of Germany, her considerable losses from the 800m (which she failed to finish, and so scored 0 points) are limited so much that she climbs 15 places.

It should be noted that the athletes perform in the heptathlon with knowledge of the rules and their performances will be affected accordingly. However, the heptathlon points system is probably viewed as being fairer in that greater efforts reap greater rewards irrespective of how other athletes have performed. It also enables heptathletes to contest for world records as all other track and field athletes can.

I’ve only looked at one heptathlon competition here, and one could look at more to see what effect an omnium-style points system has in those cases. It could also be applied to other multi-discipline events such as the decathlon, modern pentathlon and the individual and team all-around gymnastic events (how the system would apply in the team all-around is another question: would gymnasts be ranked individually in each event or would their scores be combined and then the teams ranked in each event?)

Note: to break ties in the individual events, where possible I have used standard tie-breaking rules for those events, i.e. looking at next best throws/jumps in the long jump/javelin/shot put and using ‘countback’ for the high jump.

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