# SOCR EduMaterials Activities BaseballSalaryWins

## Summary

Baseball Salary and Success

This activity will center around investigating how a MLB team's payroll correlates with success. The first step is to use simple regression to compare wins to payroll each year and overall. To do this, go to the mapping tab and select each year's payroll as the independent variable with the corresponding year's wins as the dependent variable.

## Goals

The aims of this activity are to:

• investigate whether baseball salaries and team wins or losses are correlated.
• demonstrate the use of several SOCR exploratory and quantitative data analysis tools (e.g., SOCR analyses, SOCR charts).
• explore the relations between multiple variables.

## Data

These data are collected from the following resources: Baseball Payroll, 2008, 2009, and 2010 standings.

TeamLeague2010Wins2010Losses2010W-L%2010Runs2010RunsAgainst2010Rundiff2010Payroll2009Wins2009Losses2009W-L%2009Runs2009RunsAgainst2009Rundiff2009Payroll2008Wins2008Losses2008W-L%2008Runs2008RunsAgainst2008Rundiff2008PayrollTotalWinsTotalPayroll
PHINL97650.5994.840.814192738193690.5745.14.40.711300404892700.5684.94.20.798269880282353201309
TBRAL96660.593540.97192347184780.51954.70.36331303597650.5994.84.10.643820597277179057103
NYYAL95670.5865.34.31206333389103590.6365.64.6120144928989730.5494.94.50.4209081577287616864255
MINAL94680.584.84.10.79755916787760.53454.70.36529926788750.545.14.60.556932766269219791200
SFGNL92700.5684.33.60.79782883388740.5434.13.80.38216145072900.44444.7-0.776594500252256584783
CINNL91710.5624.94.20.67238654478840.4814.24.5-0.37096850074880.4574.34.9-0.674117695243217472739
ATLNL91710.5624.63.90.78442366786760.5314.540.69672616772900.4444.64.8-0.2102365683249283515517
TEXAL90720.5564.94.20.65525054587750.5374.84.60.36864602379830.4885.66-0.467712326256191608894
SDPNL90720.5564.13.60.53779930075870.4633.94.7-0.84279670063990.3893.94.7-0.873677616228154273616
BOSAL89730.54954.60.516274733395670.5865.44.50.812269600095670.5865.24.30.9133390035279418833368
CHWAL88740.5434.64.30.310827319779830.4884.54.509606850089740.54654.50.5121189332256325531029
STLNL86760.5314.540.69354075391710.5624.540.68852841186760.5314.84.50.399624449263281693613
TORAL85770.5254.74.50.26268935775870.4634.94.80.28099365786760.5314.43.80.697793900246241476914
COLNL83790.5124.84.40.38422700092700.56854.40.57520100074880.4574.65.1-0.568655500249228083500
OAKAL81810.54.13.90.25165490075870.4634.74.706231000075860.46644.3-0.347967126231161932026
DETAL81810.54.64.6012286492986770.5284.64.6011508514574880.4575.15.3-0.2137685196241375635270
FLANL80820.4944.44.405564150087750.5374.84.703681400084770.5224.84.8021811500251114267000
LAAAL80820.4944.24.3-0.110501366797650.5995.54.70.8113709000100620.6174.74.30.4119216333277337939000
NYMNL79830.48844013270144570920.4324.14.7-0.513577398889730.5494.94.40.5137793376238406268809
MILNL77850.4754.65-0.38110827980820.4944.85-0.28025750290720.5564.64.30.480937499247242303280
HOUNL76860.4693.84.5-0.79235550074880.45744.8-0.810299641586750.5344.44.6-0.288930414236284282329
CHCNL75870.4634.24.7-0.514685900083780.5164.44.20.213505000097640.6025.34.21.1118345833255400254833
CLEAL69930.42644.6-0.76120396765970.4014.85.3-0.68162556781810.554.70.378970066215221799600
WSNNL69930.42644.6-0.561425000591030.3644.45.4-159328000591020.36645.1-1.154961000187175714000
KCRAL67950.4144.25.2-17226771065970.4014.25.2-17090833375870.4634.34.8-0.658245500207201421543
BALAL66960.4073.84.8-1.18161250064980.3954.65.4-0.86710166768930.4224.95.4-0.567196246198215910413
ARINL65970.4014.45.2-0.86071816770920.4324.44.8-0.47357166782800.5064.44.40.166202712217200492546
SEAAL611010.3773.24.3-1.19837666785770.52544.3-0.398904167611010.3774.15-0.9117666482207314947316
PITNL571050.3523.65.3-1.73494300062990.38544.8-0.84874300067950.4144.55.5-0.948689783186132375783

## Data Analysis

### Exploratory data analysis (EDA)

The correlations between payroll and team success for 2008, 2009, 2010, and overall are 0.327, 0.501, 0.349, and 0.520, respectfully. This indicates that the strength of the relationship varies from year to year.

### Quantitative data analysis (QDA)

#### ANOVA

The next step is to compare the average payroll each year in the American League and National League. To do this, use ANOVA and select league as the independent variable and each year's payroll as the dependent variable. The p-value for each year is 0.328 for 2008, 0.442 for 2009, 0.434 for 2010 and 0.381 overall. This suggests that there is no significant difference between the two leagues.

#### T-Test

Another thing to check is how the average payroll changed from year to year. To do this, select the Two-paired sample T test and choose 2008 and 2009 as the variables, then repeat with 2009 and 2010 as the variables. The test for 2008 and 2009 has a p-value of .315. The test for 2009 and 2010 has a p-value of .167. This means there isn't evidence of a significant increase in payroll each year.

#### Multiple linear regression

As a team's record is heavily influenced by the number of runs they score and the number of runs they allow, it would be interesting to check the relationship between each of those and wins as well as the relationship between them and payroll. To do this, first use multiple regression with wins each year as the dependent variable and runs and runs against the independent variables.

### Conclusion

• For 2008, the slope estimates are 17.421 for runs and -16.904 for runs against. For 2009, the slope estimates are 15.715 for runs and -19.459 for runs against. For 2010, the slope estimates are 15.538 for runs and -14.809 for runs against. This suggests that scoring more runs was slightly more important in 2008 and 2010 while allowing fewer runs was more important in 2009. Next, use simple regression to compare the correlation and plot the relationship between payroll and runs and between payroll and runs against each year.

• In 2008, the correlation between payroll and runs was .281, and the correlation between payroll and runs against was -.261. For 2009 they were .372 and -.290 respectively. For 2010 they were .364 and -.111 respectively. This suggests that it is easier to use payroll spending improve hitting than it is to improve pitching. This suggests that the ability to still get good pitching is what allows some teams with lower payrolls to remain competitive.