From 9fec74c9755ca6c03e14ccaa78140097784aa281 Mon Sep 17 00:00:00 2001 From: Drew Conway Date: Wed, 9 Feb 2011 00:12:09 -0500 Subject: [PATCH] Code and images for Super Bowl pool analysis --- R/Super Bowl boxes/.RData | Bin 0 -> 6992 bytes R/Super Bowl boxes/boxes_viz.R | 28 ++++ R/Super Bowl boxes/images/q1_heatmap.png | Bin 0 -> 186555 bytes R/Super Bowl boxes/images/q2_heatmap.png | Bin 0 -> 185118 bytes R/Super Bowl boxes/images/q3_heatmap.png | Bin 0 -> 187759 bytes R/Super Bowl boxes/images/q4_heatmap.png | Bin 0 -> 183931 bytes R/Super Bowl boxes/super_bowl.R | 162 +++++++++++++++++++++++ 7 files changed, 190 insertions(+) create mode 100644 R/Super Bowl boxes/.RData create mode 100644 R/Super Bowl boxes/boxes_viz.R create mode 100644 R/Super Bowl boxes/images/q1_heatmap.png create mode 100644 R/Super Bowl boxes/images/q2_heatmap.png create mode 100644 R/Super Bowl boxes/images/q3_heatmap.png create mode 100644 R/Super Bowl boxes/images/q4_heatmap.png create mode 100644 R/Super Bowl boxes/super_bowl.R diff --git a/R/Super Bowl boxes/.RData b/R/Super Bowl boxes/.RData new file mode 100644 index 0000000000000000000000000000000000000000..01e9877293fc02dd08ab6c9fbc62db4875b60aba GIT binary patch literal 6992 zcmV-W8?WRaiwFP!000001MNNAavL|YL+WPBH^p`mCB7`fXcNkzWRa45m1D}594k?r z*jBjQxKdk;L^-ULNrj}=c5Q7PKc0tEb^hY~!1=L#-&%X;(v3@FdWNKCD3ax=0xZ%32%Pr?qz?J)Lh{pDWMzBy-yIXg@#g^3N4 zk=&p;BO69ma-&G`(2Qi!z*98vj28WHmnd$Ukt`XwOD67;iQ5J<=q%Bkk&;3BXvw5~ ztmH$y-GE6f%^4{f^pBRz4vdw2df)(>1RH&@!HiCfm3(?JUh?aP(~1w(G|L7vdNNk> z>B@M?uP-jB59LO096+Nx<0ZfTOq6^(c(&;?GMhy*8;@_- z4{ELE{LZdj?951e&W@b2<6{7ndW$Lynk4KQK8CUd#~JV z5;Dhk%iFDb!@hfK2PEcW%TpO=JR+?LJDh;BQ3Vb!mEch*8}Wgouow_-655%7`w74| zM&K|#2Ib>$KL+=H?NY{4`j8gd<}n2h`GB;YhIj(_MB5!9ea19}OF*!o-4QR=ghS=o z2!v5DIKw>h&hkdq$#X^gaZcRj#oeN~Tk`6SVm)7p&;_Vgeo;XIItiJhTd(&kh;(g1 z+=<55MB{6s@wFv!w=C|iiM#9K?uNL#iR3*#D7PvNI<*@0m-9%T!?olakDJGsUQX_m zTjlxPM%kGrMo*9LRG(MXnK}-G@pJfKXo5IyNdY+q;W(0DNr68B97Q2=!f6O+AWT8{ z0K!=a=OCPi@F9ecAbbpA8p0YON zG7x4VT!HWvge-(PFK9wNXDK#|v{e)vMcO99CXu#?VuPr*hqO6_ts!j;#kNpw3dNR? 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Only run if you have not already create data +# source(super_bowl.R) + +# Load libraries +library(ggplot2) + +# Create a data frame for boxes +positions<-do.call(rbind, lapply(0:9, function(x) cbind(0:9,x))) +boxes<-data.frame(x=positions[,1],y=positions[,2]) + +# Create a heatmap of probability of winning given different digit combinations by quarter +boxes.heatmap<-ggplot(boxes[1:10,], aes(xmin=x,xmax=x+1,ymin=y,ymax=x+1))+geom_rect(color="white") diff --git a/R/Super Bowl boxes/images/q1_heatmap.png b/R/Super Bowl boxes/images/q1_heatmap.png new file mode 100644 index 0000000000000000000000000000000000000000..aca6ad0576c9cf61b93fb3630234ab5ccb62dc4c GIT binary patch literal 186555 zcmeEuWmJ^w`Zpj58!VI%5K&NRkZuM8P&#B_Xh~_2t^stT(jwg;GIR|otx{5h3@{9- zAkBb7*T8#^d++o2d^%^X_v`uKTIvGkdG5HbUtNT1X(*qiW~L?~Avyc-!F?SPl0VFe zf2dA_|2d<6#+ihKY|ZZ8J*|iL?p@P*=3-;#XiY-mO&anD<#6c^-LbfH!2mmzp~E?( z_Z#+yu%ai5L*fKl3x_k~Y&D8+tVAA;IE$~W-Kx%g{bS}U&y*rAoAM;+s_#!LL6s0g 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z9|-_JefQ?#cPb}ETKH_m(!toXcXo@Im_CBZXe%RY$$j+{;xMI)Q&gMhW>G&#QJu$X z>G=^ga}DNzUV~;bm(|tP-*|yN@_GER(o1eOHZ~D4Lx1Bq|ICvcyB(G%Tj%=L#peG$ zOo3IpANJn!=g*H8x&PoR0_X7DXbVSBNC@?MO>M1LSEHJafV{l?0IZU?UMSyFZi5m^ z8F45e_H`&|!FIP%nzI<2^?Yr$VHaavnF1A__xtzn%e?>q(q{4XgBiRWYUA?eWR>&a z>+%#-@B1Bwa)873jhXx}(P~R5{o5+55{usEX{oM;%f0{M*M9v7_q#vNUF9oAM6?@s zN%E}f@80j`C*oBht}91HcK^4(@#`}-pF{HCN1;Zj-LjV8( literal 0 HcmV?d00001 diff --git a/R/Super Bowl boxes/super_bowl.R b/R/Super Bowl boxes/super_bowl.R new file mode 100644 index 0000000..75e36cd --- /dev/null +++ b/R/Super Bowl boxes/super_bowl.R @@ -0,0 +1,162 @@ +# File-Name: super_bowl.R +# Date: 2011-02-07 +# Author: Drew Conway +# Email: drew.conway@nyu.edu +# Purpose: Gather and manipulate historic Super Bowl score data +# Data Used: Wikipedia Super Bowl data +# Packages Used: ggplot2, RCurl, XML +# Output File: +# Data Output: +# Machine: Drew Conway's MacBook Pro + +# Copyright (c) 2011, under the Simplified BSD License. +# For more information on FreeBSD see: http://www.opensource.org/licenses/bsd-license.php +# All rights reserved. + +# Load libraries +library(ggplot2) +library(RCurl) +library(XML) + +# A function that converts a given integer into its Roman Numeral equivalent +to.RomanNumeral<-function(x) { + if(0 < x & x < 5000) { + x<-as.integer(x) + digits<-c(1000,900,500,400,100,90,50,40,10,9,5,4,1) + numerals<-c("M","CM","D","CD","C","XC","L","XL","X","IX","V","IV","I") + digits.numerals<-as.data.frame(cbind(digits,numerals), stringsAsFactors=FALSE) + numeral<-"" + for(i in 1:nrow(digits.numerals)) { + while(x >= as.numeric(digits.numerals[i,1])) { + numeral<-paste(numeral,digits.numerals[i,2],sep="") + x<-x-as.numeric(digits.numerals[i,1]) + } + } + return(numeral) + } + else { + stop(paste(x,"is invalid. Input must be an integer between 1 and 4,999")) + } +} + +# Function returns quater scores from Wikipedia Super Bown pages +get.scores<-function(numeral) { + # Base URL for Wikipedia + wp.url<-getURL(paste("http://en.wikipedia.org/wiki/Super_Bowl_",numeral,sep="")) + wp.data<-htmlTreeParse(wp.url, useInternalNodes=TRUE) + score.html<-getNodeSet(wp.data,"//table[@style='background-color:transparent;']") + score.table<-readHTMLTable(score.html[[1]]) + score.table<-transform(score.table, SB=numeral) + return(score.table) +} + +# Function returns the right-most digit of numer +last.digit<-function(x) { + digits<-strsplit(as.character(x),"")[[1]] + last.digit<-digits[length(digits)] + return(as.numeric(last.digit)) +} + +# Function takes an nxm matrix of scores and returns a nxn matrix of +# probability of winning given a combination of digits +get.probs<-function(score.df) { + digits.sums<-sum(score.df[,2:11])*10 + prob.matrix<-matrix(ncol=10,nrow=10) + for(i in 1:10) { + for(j in 1:10) { + prob.matrix[i,j]<-(score.df[1,i+1]+score.df[2,j+1])/digits.sums + } + } + prob.df<-as.data.frame(prob.matrix, row.names=0:9) + names(prob.df)<-0:9 + return(prob.df) +} + +# There have been 45 Super Bowls +bowls<-lapply(1:45, to.RomanNumeral) + +# Create data frame of all Super Bowl scores +scores.list<-lapply(bowls, get.scores) +scores.df<-data.frame(do.call(rbind, scores.list)) + +# Fix the data types +scores.df$X1<-as.numeric(as.character(scores.df$X1)) +scores.df$X2<-as.numeric(as.character(scores.df$X2)) +scores.df$X3<-as.numeric(as.character(scores.df$X3)) +scores.df$X4<-as.numeric(as.character(scores.df$X4)) +scores.df$Total<-as.numeric(as.character(scores.df$Total)) + +# Add quarter scoring data to data frame +quarters.list<-lapply(1:nrow(scores.df), function(i) c(scores.df[i,2],sum(scores.df[i,2:3]),sum(scores.df[i,2:4]))) +quarters.df<-as.data.frame(do.call(rbind, quarters.list)) + +# Final data set +super.df<-cbind(scores.df, quarters.df,rep(as.factor(c("Home","Away")),45)) +names(super.df)<-c("Team","Q1","Q2","Q3","Q4","Total","SB","Q1T","Q2T","Q3T","Type") + +# Get digit count totals in workable data frame for visualization +digits.df<-ddply(super.df,.(SB,Type), summarise, Q1D=last.digit(Q1T), Q2D=last.digit(Q2T), Q3D=last.digit(Q3T), + Q4D=last.digit(Total)) + +# Create separate data frames for each quarter +q1.counts<-ddply(digits.df,.(Type), summarise, D0=length(which(Q1D==0)), D1=length(which(Q1D==1)), D2=length(which(Q1D==2)), + D3=length(which(Q1D==3)), D4=length(which(Q1D==4)), D5=length(which(Q1D==5)), D6=length(which(Q1D==6)), D7=length(which(Q1D==7)), + D8=length(which(Q1D==8)), D9=length(which(Q1D==9))) +q1.probs<-get.probs(q1.counts) + +q2.counts<-ddply(digits.df,.(Type), summarise, D0=length(which(Q2D==0)), D1=length(which(Q2D==1)), D2=length(which(Q2D==2)), + D3=length(which(Q2D==3)), D4=length(which(Q2D==4)), D5=length(which(Q2D==5)), D6=length(which(Q2D==6)), D7=length(which(Q2D==7)), + D8=length(which(Q2D==8)), D9=length(which(Q2D==9))) +q2.probs<-get.probs(q2.counts) + +q3.counts<-ddply(digits.df,.(Type), summarise, D0=length(which(Q3D==0)), D1=length(which(Q3D==1)), D2=length(which(Q3D==2)), + D3=length(which(Q3D==3)), D4=length(which(Q3D==4)), D5=length(which(Q3D==5)), D6=length(which(Q3D==6)), D7=length(which(Q3D==7)), + D8=length(which(Q3D==8)), D9=length(which(Q3D==9))) +q3.probs<-get.probs(q3.counts) + +q4.counts<-ddply(digits.df,.(Type), summarise, D0=length(which(Q4D==0)), D1=length(which(Q4D==1)), D2=length(which(Q4D==2)), + D3=length(which(Q4D==3)), D4=length(which(Q4D==4)), D5=length(which(Q4D==5)), D6=length(which(Q4D==6)), D7=length(which(Q4D==7)), + D8=length(which(Q4D==8)), D9=length(which(Q4D==9))) +q4.probs<-get.probs(q4.counts) + +### Create visualizations + +# Create a data frame for boxes +positions<-do.call(rbind, lapply(0:9, function(x) cbind(0:9,x))) +boxes<-data.frame(x=positions[,1],y=positions[,2]) +boxes$Q1<-melt(q1.probs)$value +boxes$Q2<-melt(q2.probs)$value +boxes$Q3<-melt(q3.probs)$value +boxes$Q4<-melt(q4.probs)$value + +# Create a heatmap of probability of winning given different digit combinations by quarter +q1.heatmap<-ggplot(boxes, aes(xmin=x,xmax=x+1,ymin=y,ymax=y+1))+geom_rect(aes(color="white", fill=Q1))+ + scale_fill_gradient(limits=c(0,.047), low="lightgrey", high="darkred", name="Pr(Winning)")+ + scale_color_manual(values=c("white"="white"), legend=FALSE)+theme_bw()+ + scale_x_continuous(breaks=.5:9.5,labels=0:9)+scale_y_continuous(breaks=.5:9.5,labels=0:9)+ + xlab("Home Team")+ylab("Away Team")+opts(title="Heat Map of Win Probabilties -- First Quater") +ggsave(plot=q1.heatmap, filename="images/q1_heatmap.png", height=12, width=12) + +q2.heatmap<-ggplot(boxes, aes(xmin=x,xmax=x+1,ymin=y,ymax=y+1))+geom_rect(aes(color="white", fill=Q2))+ + scale_fill_gradient(limits=c(0,.047), low="lightgrey", high="darkred", name="Pr(Winning)")+ + scale_color_manual(values=c("white"="white"), legend=FALSE)+theme_bw()+ + scale_x_continuous(breaks=.5:9.5,labels=0:9)+scale_y_continuous(breaks=.5:9.5,labels=0:9)+ + xlab("Home Team")+ylab("Away Team")+opts(title="Heat Map of Win Probabilties -- Half Time") +ggsave(plot=q2.heatmap, filename="images/q2_heatmap.png", height=12, width=12) + +q3.heatmap<-ggplot(boxes, aes(xmin=x,xmax=x+1,ymin=y,ymax=y+1))+geom_rect(aes(color="white", fill=Q3))+ + scale_fill_gradient(limits=c(0,.047), low="lightgrey", high="darkred", name="Pr(Winning)")+ + scale_color_manual(values=c("white"="white"), legend=FALSE)+theme_bw()+ + scale_x_continuous(breaks=.5:9.5,labels=0:9)+scale_y_continuous(breaks=.5:9.5,labels=0:9)+ + xlab("Home Team")+ylab("Away Team")+opts(title="Heat Map of Win Probabilties -- Third Quarter") +ggsave(plot=q3.heatmap, filename="images/q3_heatmap.png", height=12, width=12) + +q4.heatmap<-ggplot(boxes, aes(xmin=x,xmax=x+1,ymin=y,ymax=y+1))+geom_rect(aes(color="white", fill=Q4))+ + scale_fill_gradient(limits=c(0,.047), low="lightgrey", high="darkred", name="Pr(Winning)")+ + scale_color_manual(values=c("white"="white"), legend=FALSE)+theme_bw()+ + scale_x_continuous(breaks=.5:9.5,labels=0:9)+scale_y_continuous(breaks=.5:9.5,labels=0:9)+ + xlab("Home Team")+ylab("Away Team")+opts(title="Heat Map of Win Probabilties -- Final") +ggsave(plot=q4.heatmap, filename="images/q4_heatmap.png", height=12, width=12) + + +