{ From user Lonnie, Model World_cup at 16-Jul-2018 2:15:27 PM, encoding="UTF-8" }
SoftwareVersion 5.0.17


{ System Variables with non-default values: }
SampleSize := 10K
TypeChecking := 1
Checking := 1
SaveOptions := 2
SaveValues := 0

NodeInfo FormNode: 1,0,0,1,0,0,0,,0,0,,0,0



Model World_cup
Description: How random are the outcomes of soccer (futbol or football) matches? Given that games are usually won by a single goal, it seems plausible that the inferior team may often win by chance. ~
~
This model explores this question using Poisson distributions to model the scoring of each team against the other. Inspired by the 2018 World Cup final match between France and Croatia on July 15, 2018, in which France beat Croatia 4-2 to win the World Cup.~
~
This can also serve as an introduction to the Poisson distribution, which is used here to model the actual number of goals scored by each team. The Poisson model assumes that the same goal scoring rates apply the same to every minute of play. In other words, a given team is equally likely to score in the 1st minute as in the 95th minute or in any overtime minute.
Author: Lonnie Chrisman, Ph.D.~
Lumina Decision Systems
Date: Mon, Jul 16, 2018 12:20 PM
SaveAuthor: Lonnie
SaveDate: Mon, Jul 16, 2018 2:15 PM
DiagState: 2,1,0,852,545,17
WindState: 2,486,408,720,350
FontStyle: Arial,15
FileInfo: 0,Model World_cup,2,2,0,0,C:\Users\Lonnie\Documents\Analytica\Blog models\World cup.ana

Decision Expected___goals
Title: Expected # goals
Description: The estimated(mean) number of scores made by the given team during the primary match (the 1st 95 minutes in a World Cup game), not counting any overtime.
Definition: Table(Team)(4,2)
NodeLocation: 232,64,1
NodeSize: 48,24
DefnState: 2,104,107,415,303,,DFNM
ValueState: 2,1140,34,416,303,,MIDM
Aliases: FormNode Fo1531770226

Index Team
Title: Team
Definition: ['France','Croatia']
NodeLocation: 104,64,1
NodeSize: 48,24
ValueState: 2,1113,24,416,303,,MIDM
{!40000|Att_PrevIndexValue: ['France','Croatia']}

Chance Scores_in_main_match
Title: Scores in main match
Definition: Poisson( Expected___goals )
NodeLocation: 232,136,1
NodeSize: 56,24
ValueState: 2,219,419,618,418,1,PDFP
ReformVal: [Undefined,Team,Undefined,Undefined,1]
{!40000|ProbabilityNumberFmt: 2,%,2,0,0,0,2,0,$,0,"ABBREV",0,,,0,0,15}
{!40600|Att_ClusterIndex: Team}

Function score_to_outcome(score : [Team] )
Title: score to outcome
Description: Converts the score to the name of the winning team, or to "Tie".
Definition: if score[@Team=1] = score[@Team=2] then "Tie"~
else argMax(score,Team)
NodeLocation: 104,136,1
NodeSize: 48,24
WindState: 2,254,498,720,350

Variable Pre_overtime_outcome
Title: Pre-overtime outcome
Definition: score_to_outcome( Scores_in_main_match )
NodeLocation: 368,136,1
NodeSize: 48,32
ValueState: 2,1087,215,403,214,0,PDFP,0
{!40000|ProbabilityNumberFmt: 2,%,4,4,0,0,4,0,$,0,"ABBREV",0,,,0,0,15}

Constant Overtime_length
Title: Overtime length
Units: minutes
Description: The number of minutes of overtime when a single-elimination game goes into overtime as a result of a tied score at the end of the main match.
Definition: 30
NodeLocation: 504,64,1
NodeSize: 48,24

Constant Main_play_length
Title: Main play length
Units: minutes
Description: The number of minutes in the main match when there is no overtime.
Definition: 95
NodeLocation: 616,64,1
NodeSize: 48,24

Chance Scores_during_overti
Title: Scores during overtime
Description: Models the goals scored during overtime, in the event that the game goes into overtime.
Definition: Poisson( Expected___goals * Overtime_length/Main_play_length )
NodeLocation: 504,136,1
NodeSize: 64,24
ValueState: 2,1041,486,535,360,,PDFP
ReformVal: [Undefined,Team,Undefined,Undefined,1]
{!40600|Att_ClusterIndex: Team}

Variable Score_after_overtime
Title: Score after overtime
Description: The total score of each time at the end of overtime.~
This is the game score in the case where the match does not go into overtime.
Definition: if Pre_overtime_outcome="Tie" ~
Then Scores_in_main_match+Scores_during_overti ~
Else Scores_in_main_match
NodeLocation: 504,224,1
NodeSize: 56,24
ValueState: 2,903,22,719,411,,PDFP
ReformVal: [Undefined,Team,Undefined,Undefined,1]
{!40600|Att_ClusterIndex: Team}

Variable Goal_differential
Title: Goal differential
Description: The goal differential at the end of overtime. When non-zero, this is the final goal differential. When zero, then the winner will be determined via penalty kicks.
Definition: Score_after_overtime[ @Team=1 ] - Score_after_overtime[ @Team=2 ]
NodeLocation: 648,224,1
NodeSize: 48,24
ValueState: 2,799,86,806,579,1,CDFP
{!40000|ProbabilityNumberFmt: 2,%,4,4,0,0,4,0,$,0,"ABBREV",0,,,0,0,15}

Variable Outcome_after_overti
Title: Outcome after overtime
Description: The outcome at the completion of overtime. The team name if one team has won, or "Tie" if they are still tied after overtime.
Definition: score_to_outcome( Score_after_overtime )
NodeLocation: 504,312,1
NodeSize: 64,24
ValueState: 2,941,490,464,318,0,PDFP,0
{!40000|ProbabilityNumberFmt: 2,%,4,4,0,0,4,0,$,0,"ABBREV",0,,,0,0,15}

Chance Final_outcome
Title: Final outcome
Description: Name of the winning team at the end of the game.
Definition: if Outcome_after_overti="Tie" then ChanceDist( Prob_of_winning_PKs, Team ) else Outcome_after_overti
NodeLocation: 504,384,1
NodeSize: 48,24
ValueState: 2,915,58,416,303,0,PDFP,0
{!40000|ProbabilityNumberFmt: 2,%,4,4,0,0,4,0,$,0,"ABBREV",0,,,0,0,15}

Decision Prob_of_winning_PKs
Title: Prob of winning PKs
Description: If it goes into final penalty kicks to determine the outcome of the game, this encodes the probability of each time winning during the PKs.
Definition: Table(Team)(0.6,0.4)
NodeLocation: 328,384,1
NodeSize: 48,32
Aliases: FormNode Fo1531770227
NumberFormat: 2,%,4,4,0,0,4,0,$,0,"ABBREV",0,,,0,0,15

FormNode Fo1531770226
Title: Expected # goals
Definition: 0
NodeLocation: 168,232,1
NodeSize: 120,16
Original: Expected___goals

FormNode Fo1531770227
Title: Prob of winning PKs
Definition: 0
NodeLocation: 168,272,1
NodeSize: 120,16
Original: Prob_of_winning_PKs

Close World_cup