Do England need a beautiful mind?

It is always easy to criticise in hindsight. But last night’s goal kick or line-out decision in ENG v WAL got us thinking (and we do not claim to have perfect answers).

Ever faced the following situation?  What you get from something depends on what another person does (their strategy / action); in turn, what they get depends on what you do (your strategy / action).  In a sense what you both get is interdependent. These type of situations are commonplace in life, and in sports.  They are strategic situations – a best response to a best response.

Well think of England’s decision to opt for a 5 metre line-out instead of opting to take a kick at goal last night.  The payoff to England depended on their strategy and Wales’s response to that strategy (ok they could only watch a kick).  England made a decision: go for the five points. Sounds like a strategic situation?

If you follow this reasoning, you might enjoy a branch of mathematics / decision science known as Game Theory – that helps understand strategic situations. If you think this is outlandish, think of the movie ‘A Beautiful Mind’ that immortalised Nobel prize winner John Nash (recently deceased report here).  The central idea of a Nash Equilibrium is very simple: in a strategic situation, a rational decision maker will try to do the best he / she can, given that someone else is doing the best they can.

From post-match comments , England seem to have reasoned that their probability of kick success was lower than their probability of scoring a try. But it is clear from the Welsh comments post-game, that based on past-experience, they had prepared for an English throw to the front of the line-out (and so responded with a collective counter-press).

Should England have known that Wales would have responded like this? Well maybe, there was history. So this was not a just one shot game, it was a repeated game.

In summary, game theory helps us understand sports.

Let us know on @empiricalrugby1 if you would like more on this.

Getting ready for Ireland vs Romania?

Ireland is resting a number of front-liners, so the headline gap in world rankings may be less relevant later today at Wembley (Ireland 5 vs Romania 17).

Ireland has a much smaller population than Romania, but almost 13 times the playing pool to draw on.

One unique feature: Romania has the highest proportion of arable land mass of any country in RWC 2015 (recall, in general, the close association historically between rugby and agriculture).

Ireland Romania
GDP per Capita 47539,40 5793,43
Population (mms) 6,28 20,15
Arable land % 15,42 39,08
Registered players 96880 7605
World Ranking (pre-RWC 2015) 6 17
World Ranking (current) 5 17
Affiliated players / total population % 1,54% 0,04%
Sources: World Bank, World Rugby, own calculations
Note: GDP per capita shown in constant 2005 USD.

Population definition is geographic.

Scotland vs USA: side-by-side

Only four places apart in the current rankings with Scotland at 12 and USA at 16.

USA has approx. double the number of registered players, but Scotland has 23 times the playing pool intensity.

Scotland USA
GDP per Capita 39808,69 44324,94
Population (mms) 5,30 311,72
Arable land % 25,06 16,83
Registered players 49305 110385
World Ranking (pre-RWC 2015) 10 15
World Ranking (current) 12 16
Affiliated players / total population % 0,93% 0,04%
Sources: World Bank, World Rugby, own calculations
Note: GDP per capita shown in constant 2005 USD; and is shown as a UK average for Scotland

Side-by-sides for Australia v Uruguay

Twice RWC winners Australia play Uruguay at Villa Park later today.

Current World Rank 2 meets 19.

Australia has approx 6 times the playing pool / population intensity of Uruguay.

Australia Uruguay
GDP per Capita 36504,13 7208,74
Population (mms) 22,34 3,38
Arable land % 6,21 10,10
Registered players 230663 6069
World Ranking (pre-RWC 2015) 2 19
World Ranking (current) 2 19
Affiliated players / total population % 1,03% 0,18%
Sources: World Bank, World Rugby, own calculations
Note: GDP per capita shown in constant 2005 USD

England’s historical home advantage

We had a look back at data for England vs Wales matches.

The first three entries in the tables show England home games only (all time i.e. since 1881, then since 2000 and since 2010).

England’s win percentages were (all games at home):-

  • All time – 58%
  • Since 2000 – 80%
  • Since 2010 – 67%

Then we show the data for past RWC meetings (all RWC matches held anywhere).

England’s win percentage was 50% (one win, one loss)

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England vs Wales (With England at Home)
Span Matches Won Lost Draw Win %
1881-2014 62 36 18 8 58%
2000-2014 10 8 2 0 80%
2010-2014 3 2 1 0 67%
England vs Wales in RWC
Span Matches Won Lost Draw Win %
1987-2003 2 1 1 0 50%
Source:; own calculations

What did Argentina have to do pre-2012?

According to data, Argentina had a win percentage against higher ranked teams of 50%.  Does that indicate the “bar” for emerging nations?

On 14th September 2009, it was announced that Argentina would join an expanded Tri-Nations (now Rugby Championship) in 2012.

We looked back at data for the three year period prior to the announcement. The period thus included RWC 2007 in France, in which Argentina reached the semi-final.

During that three year period, Argentina had an overall win percentage of 62.5%.  They played 24 matches, only one of which was against a nation that is not participating in RWC 2015 (Chile).

Their win percentage against (now) higher ranked opposition was 50%, i.e. they won 7 of 14 games against higher ranked teams, including wins against England, Ireland and France.

That would give a good indication of the standard emerging nations in RWC 2015 may need to achieve.

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Period   Matches Won Lost Draw
2006-2009 24 15 9 0
Opposition Ranking Matches Won Lost Win %
England 3 3 2 1 33,33%
Wales 4 1 0 1 100,00%
Ireland 5 4 3 1 25,00%
South Africa 6 2 0 2 100,00%
France 7 4 2 2 50,00%
Scotland 12 3 2 1 33,33%
Georgia 13 1 1 0 0,00%
Italy 15 4 3 1 25,00%
Namibia 20 1 1 0 0,00%
Chile 23 1 1 0 0,00%
Totals   Matches Won  Lost  Win % 
All games 24 15 9 62,50%
Vs RWC 2015 opposition 23 14 9 60,87%
vs currently higher ranked 14 7 7 50,00%
 RWC 2007 Matches Won Lost Win %
During RWC 2007 7 6 1 85,71%

Sources:, current World Rugby Rankings, Own calculations.

Springboks vs Samoa

Interesting contrasts as RSA (now ranked 7) play Samoa (now ranked 11).

RSA dominate the Registered Player numbers with 16 times as Samoa; but Samoa has the second highest ratio of Registered Players / Total Population in RWC 2015 at circa 11.1%.

Note: the population of Samoa is 190k inhabitants, the second lowest in RWC to Tonga.

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South Africa Samoa
GDP per Capita 6010,41 2752,12
Population (mms) 51,55 0,19
Arable land % 9,92 2,83
Registered players 342316 20845
World Ranking (pre-RWC 2015) 3 12
World Ranking (current) 7 11
Affiliated players / total population % 0,66% 11,12%
Sources: World Bank, World Rugby, own calculations
Note: GDP per capita in constant 2005 USD