If you have read the past 5 post­s, you saw it was com­ing, right? ;-)

Via Slate here's a pa­per ap­ply­ing game the­o­ry to penalties:

http://www.e­con.brown.e­du/­fac/i­pala­cios/pdf/pro­fes­sion­al­s.pdf

The con­clus­sion (and they made me re­type this, be­cause of stupid DR­M):

The im­pli­ca­tions of the Min­i­max the­o­rem are test­ed us­ing nat­u­ral da­ta. The tests use a unique da­ta set from penal­ty kicks in pro­fes­sion­al soc­cer games. In this nat­u­ral set­ting ex­perts play a one-shot two-per­son ze­ro-­sum game. The re­sults of the tests are re­mark­ably con­sis­tent with equi­lib­ri­um play in ev­ery re­spec­t: (i) win­ning prob­a­bil­i­ties are sta­tis­ti­cal­ly iden­ti­cal across strate­gies for play­er­s; (i­i) play­er­s' choic­es are se­ri­al­ly in­de­pen­den­t. The tests have sub­stan­tial pow­er to dis­tin­guish equi­lib­ri­um play from dis­e­qui­lib­ri­um al­ter­na­tives. These re­sults rep­re­sent the first time that both im­pli­ca­tions of von Neu­man­n's Min­i­max the­o­rem are sup­port­ed un­der nat­u­ral con­di­tion­s.

In hu­man:

• Play­ers are pret­­ty good at mak­ing de­­ci­­sions ac­­cord­ing to game the­o­ry

• Game the­o­rists call that good

How­ev­er (this I am mak­ing up as I go)...

• A well kicked pe­nal­­ty is a goal, be­­cause there are places the keep­­er sim­­ply can't reach in time.

• Since there is a win­n­ing strat­e­­gy, it makes no sense to ap­­ply min­i­­max: there is a glob­al max­i­­mum (yes, I know, it makes sense, you just need to con­sid­er mis­s­ing the goal as the chance of fail­ure, then it is not a win­n­ing strat­e­­gy... and I am not go­ing to read the 21-­­page pa­per to see if he thought about it).

Of course the win­ning strat­e­gy (strong kicks to the top an­gles of the goal) is im­prac­ti­cal for mere hu­man­s. All the more rea­son to con­sid­er RoboCup the most im­por­tant tour­na­ment for the fu­ture.