Introduction

• How many rbi (Runs Batted In) can a player earn in a regular season?

• Which position in the line up could the player fit better in order to help the team to produce more runs? Which means more chance to win

I will be analyzing from my observational data set that I have collected over time from MLB regular seasons 2000-2016. In order to improve my data analysis I excluded pitchers, and players with less than 1000 at bat, also I chose the line up position with the most recurrent position in the past 16 seasons. The line up position is crucial for predicting. It is well known that players from 3 to 6 find more runners in score position than any other line up position.

The result will help scouts and team members to relocate players and predict rbi.

Knowing the data set

Variables	Description
player_id	Player id
player_name	Player name
at_bat	Number of at bat
rbi_average	Total rbi divided by at bat
hit_average	Total hits divided by at bat
line_average	Total lines divided by at bat
ground_average	Total grounds divided by at bat
fly_average	Total flies divided by at bat
strikeout_average	Total strike outs divided by at bat
lineup_position	Most recurrent line up position

path <- "https://raw.githubusercontent.com/luije87/Big-Data-Analysis/master/project.csv"
data <- read.csv(path)
mlb_data <- data[ , c("rbi_average", "hit_average", "line_average", "ground_average", "lineup_position")]

attach(mlb_data)

pairs(mlb_data, pch=16, col="blue")

This pairs graph show us the correlation between variables. What I expected :

• line_average and hit_average to have an strong correletation, meaning the line drive is hardest to catch (more hits) , than grounds and flies in this order.

• lineup_position and rbi_average shows us positions 3, 4, 5 run batters in more than any other line up position.

Our model will use the following relation:

Rbi = (\(\beta_0\) + \(\beta_1\) * hit_average + \(\beta_2\) * line_average + \(\beta_3\) * ground_average + \(\beta_4\) * lineup_position) * AtBat

mlb_model <- lm(rbi_average ~ hit_average + line_average + ground_average + format(lineup_position), data = mlb_data)

summary(mlb_data)

##   rbi_average      hit_average      line_average    ground_average  
##  Min.   :0.0584   Min.   :0.1947   Min.   :0.1161   Min.   :0.1943  
##  1st Qu.:0.1022   1st Qu.:0.2488   1st Qu.:0.1643   1st Qu.:0.3208  
##  Median :0.1219   Median :0.2621   Median :0.1809   Median :0.3575  
##  Mean   :0.1231   Mean   :0.2635   Mean   :0.1814   Mean   :0.3639  
##  3rd Qu.:0.1412   3rd Qu.:0.2797   3rd Qu.:0.1971   3rd Qu.:0.4056  
##  Max.   :0.2092   Max.   :0.3209   Max.   :0.2533   Max.   :0.5813  
##  lineup_position
##  Min.   :1.000  
##  1st Qu.:2.000  
##  Median :3.000  
##  Mean   :4.071  
##  3rd Qu.:6.000  
##  Max.   :9.000

summary(mlb_model)

## 
## Call:
## lm(formula = rbi_average ~ hit_average + line_average + ground_average + 
##     format(lineup_position), data = mlb_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.029749 -0.008996 -0.001147  0.007998  0.047274 
## 
## Coefficients:
##                           Estimate Std. Error t value Pr(>|t|)    
## (Intercept)               0.065343   0.012480   5.236 3.04e-07 ***
## hit_average               0.660817   0.060822  10.865  < 2e-16 ***
## line_average             -0.219223   0.034286  -6.394 5.94e-10 ***
## ground_average           -0.261231   0.016442 -15.888  < 2e-16 ***
## format(lineup_position)2  0.014618   0.002614   5.591 4.94e-08 ***
## format(lineup_position)3  0.032195   0.003063  10.510  < 2e-16 ***
## format(lineup_position)4  0.042626   0.003268  13.044  < 2e-16 ***
## format(lineup_position)5  0.030952   0.002977  10.398  < 2e-16 ***
## format(lineup_position)6  0.015821   0.003328   4.754 3.06e-06 ***
## format(lineup_position)7  0.021401   0.004046   5.290 2.32e-07 ***
## format(lineup_position)8  0.017106   0.003018   5.669 3.29e-08 ***
## format(lineup_position)9  0.005194   0.004172   1.245    0.214    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01373 on 310 degrees of freedom
## Multiple R-squared:  0.7828, Adjusted R-squared:  0.7751 
## F-statistic: 101.6 on 11 and 310 DF,  p-value: < 2.2e-16

The p-values for the selected variables are significants and Adjust R Square is 77%, meaning the model explain 77% the variability of the response around its means.

par(mfrow=c(2,2))
plot(mlb_model, which = 1:4)

Residual vs Fitted

Observed values are not far away from 0, which means the model fitted well:

residual = observed y - model-predicted y, values should be around 0.

We have three residuals that are away from 0; 67, 83 and 117

Lets predict one of those data points (67), Wilson Ramos, 35 RBI in 2017:

predict(mlb_model, list(line_average = 0.14903, ground_average = 0.4735, hit_average = 0.25961, lineup_position = 7)) * 280

##        1 
## 28.54172

The prediction for 2017 season is not that close.

Normal Q-Q

Observations lie well along the 45-degree line, so we can asume that normality holds here.

Season (2017)

I picked 4 players with different positions in the line up and applied the model:

Conclusion

The predictions for players selected were close to their RBI in 2017. The model works as expected. The baseball game has a lot of stats that can influence our results. I learned we cannot exclude variables we know are important like lineup_position in this case which improved my predictions notably.

I will keep working on this model to improve it to help coaches to find the perfect fit in their line up.

References

Fan Graph - https://www.fangraphs.com

ESPN - http://www.espn.com/

Retrosheet - http://www.retrosheet.org/

Baseball Reference - https://www.baseball-reference.com/