## Decisiveness of matches in the WC group stage Russell Degnan

Watching the world cup is a complex business. There are too many games at too many odd hours to watch everything and remain gainfully employed, but it can be hard to decide whether to stay up late to watch an obscure CONCACAF side play a European superpower, or crawl out of bed for a showdown between a pair of star strikers and their traffic cones come team-mates.

If quality is all you're after then the answer is obvious, but the most interesting games are those both teams need to win. In a previous post I defined match meaning as

the total change in probability that each team will qualify for the next round based on the result of a single game.

For a knockout match between two evenly matches teams this will be 1: 2x(0.5x0.5 + 0.5x0.5). A knockout where one team is 70% likely to win will be 0.84: 2(0.7x0.3 + 0.3x0.7). For a group stage, the calculation is more complex, so a monte-carlo method was employed:

Meaning = | P(Qual) - (P(Win)xP(Qual|Win) + P(Draw)xP(Qual|Draw) + P(Loss)xP(Qual|Loss)) |

Total meaning being calculated for all four teams in the group, for each game.

Match probabilities were calculated using the Elo Ratings. Historically, draws are normally distributed around the rating difference: ~40% for evenly matched teams, with a standard deviation of 200. The win/loss probabilities are taken from the Elo formula on the site.

The results indicate that the least interesting match will be Brazil vs Cameroon, the home side being near-certainties to qualify, and the latter unlikely to overcome Croatia and Mexico. The most: Croatia vs. Mexico, being a virtual knock-out, followed by Bosnia-Herzegovina vs Nigeria, the two middle sides in a group containing Argentina and Iran. A full list of qualifying probabilities, and predicted match meaning follows:

Group A
BrazilCroatiaMexicoCameroon
98.51%39.93%49.40%12.25%
BrazilCroatia12 June0.150
MexicoCameroon13 June0.386
BrazilMexico17 June0.161
CroatiaCameroon18 June0.381
BrazilCameroon23 June0.046
CroatiaMexico23 June0.453
Group B
SpainNetherlandsChileAustralia
84.45%61.43%43.18%10.99%
ChileAustralia13 June0.341
SpainNetherlands13 June0.304
NetherlandsAustralia18 June0.352
SpainChile18 June0.363
NetherlandsChile23 June0.406
SpainAustralia23 June0.182
Group C
ColombiaGreeceIvory CoastJapan
71.18%47.41%42.65%38.51%
ColombiaGreece14 June0.375
Ivory CoastJapan14 June0.431
ColombiaIvory Coast19 June0.388
GreeceJapan19 June0.423
ColombiaJapan24 June0.386
GreeceIvory Coast24 June0.402
Group D
UruguayCosta RicaEnglandItaly
59.95%19.75%64.84%55.20%
UruguayCosta Rica14 June0.383
EnglandItaly14 June0.364
UruguayEngland19 June0.333
Costa RicaItaly20 June0.421
UruguayItaly24 June0.380
Costa RicaEngland24 June0.402
Group E
57.74%55.20%67.30%19.56%
FranceHonduras15 June0.370
SwitzerlandFrance20 June0.367
SwitzerlandHonduras25 June0.384
Group F
ArgentinaBosnia and HerzegovinaIranNigeria
89.85%43.13%31.08%36.15%
ArgentinaBosnia and Herzegovina15 June0.330
IranNigeria16 June0.396
ArgentinaIran21 June0.286
Bosnia and HerzegovinaNigeria21 June0.440
ArgentinaNigeria25 June0.321
Bosnia and HerzegovinaIran25 June0.407
Group G
GermanyPortugalGhanaUnited States
85.68%60.75%14.19%39.28%
GermanyPortugal16 June0.281
GhanaUnited States16 June0.333
GermanyGhana21 June0.197
PortugalUnited States22 June0.378
GermanyUnited States26 June0.358
PortugalGhana26 June0.395
Group H
BelgiumAlgeriaRussiaSouth Korea
72.21%21.06%72.46%34.06%
BelgiumAlgeria17 June0.369
RussiaSouth Korea17 June0.390
BelgiumRussia22 June0.268
AlgeriaSouth Korea22 June0.330
BelgiumSouth Korea26 June0.418
AlgeriaRussia26 June0.377

Football 12th June, 2014 22:48:18   [#]