Monday, August 5, 2013

Returns to inequality in MLB

Take a look over here if you want to get the background for this series, otherwise read on.

Sports + Numbers Prediction: "This is anyone’s guess. The returns to inequality – after controlling for the wide distribution in overall team salary – might be strong or they might not. I don’t have a good feel for it so this will be more of a fact finding mission."

The data

To see the impact of inequality we will look at each team’s Gini coefficient against their winning percentage, controlling for team spending. The resulting equation gives us an r-squared value of 0.13 with only salary spending being significant (P-value of 0.00001) while the Gini coefficient comes in at a P-value of 0.18.

Payroll vs Winning % - MLB 2008-2012

For every million dollars in team spending the expected increase in winning percentage is 0.000654. For a team that spends $10 million more than a comparable team – all else equal – we would expect them to win an additional game.

Gini vs Winning % - MLB 2008-2012

On inequality the - insignificant - coefficient is -0.14. Within the range of Gini coefficients in baseball (0.35 to 0.66) this would mean a difference of 7 wins from the most equal to the least equal (more wins to the most equal). Not nothing but not exactly a huge impact. The gap in payroll ($19 million to $206 million) projects to a gap of nearly 20 wins.

Payroll vs Gini (color-coded by winning %) - MLB 2008-2012


Strength of the relationship over time 

The relationship stays pretty consistent for each variable. For payroll the correlation from 2008-2012 runs 0.32, 0.47, 0.37, 0.40, 0.19. Looking just at the correlation between Gini and winning percentage, the values are -0.17, 0.24, -0.04, -0.18, -0.27. The overall one-on-one correlation between Gini and winning percentage for the five year period (2008-2012) is -0.09.

Would you rather have one dollar or four quarters?

As with football it doesn't appear to matter. The graph of Gini alone looks a lot like random, normally distributed data. You'd rather have lots and lots of both. Nothing here to get my hopes up about the Indians scrappy band of equals overcoming Detroit's bloated juggernaut of Hot-N-Ready stars supported by scrap heap players.

Sports + Numbers Predictive Accuracy: High – I predicted that I didn't know where this would go and the numbers don't know it either. This turns out to be something of a known - or at least predicted - unknown.

Details

As usual there were a few salaries that escaped the view of the data. For any team with fewer than 25 players in their data set (sourced from the Lahman database) I filled in the gaps with league minimum salaries appropriate to that season. This splicing continues to upset the game warden, but he's a bit of an alarmist.


yearIDlgIDteamIDWLW%PayrollGini
2008ALBAL68930.422$64,466,246 0.52
2008ALBOS95670.586$132,190,785 0.52
2008ALCHA89740.546$120,401,832 0.52
2008ALCLE81810.500$78,579,666 0.50
2008ALDET74880.457$135,717,696 0.47
2008ALKC75870.463$57,855,500 0.54
2008ALLAA100620.617$117,628,333 0.55
2008ALMIN88750.540$56,932,766 0.50
2008ALNYA89730.549$205,938,839 0.52
2008ALOAK75860.466$46,792,126 0.55
2008ALSEA611010.377$117,276,482 0.55
2008ALTBA97650.599$41,850,597 0.47
2008ALTEX79830.488$66,147,326 0.54
2008ALTOR86760.531$97,009,600 0.55
2008NLARI82800.506$65,026,712 0.58
2008NLATL72900.444$100,415,683 0.62
2008NLCHN97640.602$117,561,833 0.53
2008NLCIN74880.457$72,945,195 0.52
2008NLCOL74880.457$68,265,500 0.55
2008NLMIA84770.522$18,691,500 0.35
2008NLHOU86750.534$88,150,414 0.59
2008NLLAN84780.519$117,027,536 0.56
2008NLMIL90720.556$79,359,999 0.48
2008NLNYN89730.549$135,782,876 0.49
2008NLPHI92700.568$96,702,380 0.50
2008NLPIT67950.414$48,299,783 0.57
2008NLSDN63990.389$71,335,166 0.54
2008NLSFN72900.444$75,034,500 0.58
2008NLSLN86760.531$96,484,949 0.50
2008NLWAS591020.366$53,366,500 0.45
2009ALBAL64980.395$66,701,666 0.50
2009ALBOS95670.586$119,731,999 0.48
2009ALCHA79830.488$95,668,500 0.58
2009ALCLE65970.401$80,775,366 0.51
2009ALDET86770.528$113,885,145 0.52
2009ALKC65970.401$70,114,333 0.50
2009ALLAA97650.599$112,505,000 0.53
2009ALMIN87760.534$63,664,766 0.59
2009ALNYA103590.636$201,049,189 0.53
2009ALOAK75870.463$61,110,000 0.59
2009ALSEA85770.525$97,704,166 0.60
2009ALTBA84780.519$61,670,034 0.47
2009ALTEX87750.537$66,572,068 0.62
2009ALTOR75870.463$79,334,600 0.58
2009NLARI70920.432$72,715,666 0.51
2009NLATL86760.531$95,121,166 0.56
2009NLCHN83780.516$134,809,000 0.56
2009NLCIN78840.481$74,358,500 0.60
2009NLCOL92700.568$74,399,000 0.58
2009NLMIA87750.537$35,634,000 0.48
2009NLHOU74880.457$102,143,914 0.58
2009NLLAN95670.586$100,414,592 0.62
2009NLMIL80820.494$79,782,502 0.51
2009NLNYN70920.432$148,166,987 0.48
2009NLPHI93690.574$112,199,046 0.48
2009NLPIT62990.385$48,293,000 0.49
2009NLSDN75870.463$42,533,700 0.58
2009NLSFN88740.543$81,825,450 0.60
2009NLSLN91710.562$87,728,409 0.57
2009NLWAS591030.364$58,728,000 0.52
2010ALBAL66960.407$81,212,500 0.52
2010ALBOS89730.549$160,734,833 0.41
2010ALCHA88740.543$105,130,000 0.51
2010ALCLE69930.426$59,601,266 0.62
2010ALDET81810.500$122,064,928 0.57
2010ALKC67950.414$70,598,500 0.51
2010ALLAA80820.494$103,359,666 0.48
2010ALMIN94680.580$96,346,666 0.51
2010ALNYA95670.586$206,333,389 0.56
2010ALOAK81810.500$52,424,900 0.60
2010ALSEA611010.377$85,309,000 0.57
2010ALTBA96660.593$71,117,071 0.49
2010ALTEX90720.556$53,640,814 0.56
2010ALTOR85770.525$60,214,200 0.54
2010NLARI65970.401$60,318,166 0.48
2010NLATL91710.562$83,623,666 0.57
2010NLCHN75870.463$145,808,000 0.56
2010NLCIN91710.562$71,361,542 0.61
2010NLCOL83790.512$82,613,000 0.52
2010NLMIA80820.494$56,225,219 0.56
2010NLHOU76860.469$91,155,500 0.58
2010NLLAN80820.494$94,553,516 0.55
2010NLMIL77850.475$79,489,778 0.51
2010NLNYN79830.488$133,206,942 0.54
2010NLPHI97650.599$140,722,379 0.48
2010NLPIT571050.352$34,141,500 0.49
2010NLSDN90720.556$37,398,000 0.52
2010NLSFN92700.568$97,435,333 0.56
2010NLSLN86760.531$93,540,751 0.61
2010NLWAS69930.426$59,399,000 0.56
2011ALBAL69930.426$84,887,038 0.49
2011ALBOS90720.556$160,895,475 0.45
2011ALCHA79830.488$126,950,000 0.48
2011ALCLE80820.494$47,114,466 0.59
2011ALDET95670.586$104,868,231 0.59
2011ALKC71910.438$35,298,000 0.41
2011ALLAA86760.531$136,059,166 0.54
2011ALMIN63990.389$112,737,000 0.56
2011ALNYA97650.599$200,547,428 0.54
2011ALOAK74880.457$65,282,500 0.42
2011ALSEA67950.414$84,454,100 0.60
2011ALTBA91710.562$40,638,671 0.47
2011ALTEX96660.593$90,628,264 0.53
2011ALTOR81810.500$60,010,300 0.41
2011NLARI94680.580$52,808,833 0.45
2011NLATL89730.549$86,588,692 0.58
2011NLCHN71910.438$125,047,329 0.59
2011NLCIN79830.488$73,869,634 0.55
2011NLCOL73890.451$87,733,071 0.54
2011NLMIA72900.444$56,530,000 0.57
2011NLHOU561060.346$69,027,000 0.61
2011NLLAN82790.509$102,093,499 0.46
2011NLMIL96660.593$83,394,333 0.54
2011NLNYN77850.475$118,019,309 0.64
2011NLPHI102600.630$170,906,379 0.48
2011NLPIT72900.444$43,388,500 0.52
2011NLSDN71910.438$43,379,300 0.51
2011NLSFN86760.531$117,365,833 0.51
2011NLSLN90720.556$104,605,572 0.58
2011NLWAS80810.497$62,198,928 0.52
2012ALBAL93690.574$75,907,999 0.52
2012ALBOS69930.426$168,475,117 0.49
2012ALCHA85770.525$96,919,500 0.59
2012ALCLE68940.420$76,503,200 0.55
2012ALDET88740.543$130,375,000 0.59
2012ALKC72900.444$58,499,300 0.49
2012ALLAA89730.549$152,555,166 0.51
2012ALMIN66960.407$93,125,000 0.60
2012ALNYA95670.586$194,548,864 0.53
2012ALOAK94680.580$52,972,500 0.51
2012ALSEA75870.463$80,537,400 0.64
2012ALTBA90720.556$62,731,300 0.47
2012ALTEX93690.574$120,030,974 0.48
2012ALTOR73890.451$74,045,000 0.45
2012NLARI81810.500$72,841,833 0.46
2012NLATL94680.580$80,909,942 0.59
2012NLCHN611010.377$87,717,033 0.58
2012NLCIN97650.599$80,763,616 0.52
2012NLCOL64980.395$76,149,571 0.54
2012NLHOU551070.340$60,171,000 0.66
2012NLLAN86760.531$92,736,575 0.51
2012NLMIA69930.426$117,118,000 0.55
2012NLMIL83790.512$97,172,944 0.51
2012NLNYN74880.457$92,393,103 0.64
2012NLPHI81810.500$172,127,438 0.52
2012NLPIT79830.488$61,507,999 0.51
2012NLSDN76860.469$53,797,000 0.46
2012NLSFN94680.580$115,219,683 0.56
2012NLSLN88740.543$108,860,862 0.56
2012NLWAS98640.605$78,442,143 0.55

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