Warren_Butler

Comparing TJ Warren and Jimmy Butler

Shooting

## Summarise df into totals
warren_butler_total_df = warren_butler_df %>% group_by(Player) %>%
  summarise(tot_3p = sum(X3P),
            tot_2p = sum(X2P),
            tot_3fga = sum(X3PA),
            tot_2fga = sum(X2PA)) %>% mutate(tot_fga = tot_2fga + tot_3fga,
                                             efg = (tot_3p*1.5+tot_2p)/tot_fga,
                                             tot_fgm = round(tot_3p*1.5+tot_2p))

## `summarise()` ungrouping output (override with `.groups` argument)

## Warren's numbers
warren_succ = (warren_butler_total_df %>% filter(Player == "Warren") %>% select(tot_fgm))$tot_fgm
warren_n    = (warren_butler_total_df %>% filter(Player == "Warren") %>% select(tot_fga))$tot_fga

## Butler's numbers
butler_succ = (warren_butler_total_df %>% filter(Player == "Butler") %>% select(tot_fgm))$tot_fgm
butler_n    = (warren_butler_total_df %>% filter(Player == "Butler") %>% select(tot_fga))$tot_fga

## Frequentist 2 Proportion Z test
prop.test(x = c(warren_succ, butler_succ), n = c(warren_n, butler_n))

## 
##  2-sample test for equality of proportions with continuity correction
## 
## data:  c(warren_succ, butler_succ) out of c(warren_n, butler_n)
## X-squared = 18.536, df = 1, p-value = 1.667e-05
## alternative hypothesis: two.sided
## 95 percent confidence interval:
##  0.02322830 0.06234542
## sample estimates:
##    prop 1    prop 2 
## 0.5324028 0.4896159

## Bayesian Approach
p <- seq(from=0.4, to=0.6, by=0.01) ## EFG for these players ranges from 0.4 to 0.6.  Assume uniform prior.
prior <- rep(1/length(p), length(p))
war_likelihood <- dbinom(warren_succ, size = warren_n, prob = p)
but_likelihood <- dbinom(butler_succ, size = butler_n, prob = p)

# posterior
war_numerator <- prior * war_likelihood
but_numerator <- prior * but_likelihood
war_denominator <- sum(war_numerator)
but_denominator <- sum(but_numerator)
war_posterior <- war_numerator / war_denominator
but_posterior <- but_numerator / but_denominator

#par(mfrow = c(2,3), bg = NA)
#barplot(prior, names.arg = p, las = 2, main = "Prior")
#barplot(war_likelihood, names.arg = p, las = 2, main = "Likelihood")
#barplot(war_posterior, names.arg = p, las = 2, main = "Posterior")
#
#barplot(prior, names.arg = p, las = 2, main = "Prior")
#barplot(but_likelihood, names.arg = p, las = 2, main = "Likelihood")
#barplot(but_posterior, names.arg = p, las = 2, main = "Posterior")

### Put Posteriors in a data.frame to visualize in ggplot
efg_posterior_df <- data.frame(Player = c(rep("Warren", 21), rep("Butler", 21)),
                               EFG = c(seq(from=0.4, to=0.6, by=0.01), seq(from=0.4, to=0.6, by=0.01)),
                               probs = c(war_posterior, but_posterior))

### Overlapping bar chart visualization in ggplot
#par(mfrow = c(1,1))
ggplot(efg_posterior_df, aes(x=EFG,y=probs,fill=Player)) + 
        geom_bar(stat="identity", position = "identity", alpha=.3) +
        labs(x = "\neFG%", y = "Probability\n", title = "Butler vs. Warren: Posterior eFG% Distributions")

Turnovers

## `summarise()` ungrouping output (override with `.groups` argument)

## 
##  2-sample test for equality of proportions with continuity correction
## 
## data:  c(warren_succ, butler_succ) out of c(warren_n, butler_n)
## X-squared = 21.293, df = 1, p-value = 3.942e-06
## alternative hypothesis: two.sided
## 95 percent confidence interval:
##  -0.03273163 -0.01368205
## sample estimates:
##     prop 1     prop 2 
## 0.07018290 0.09338974

Rebounding

## `summarise()` ungrouping output (override with `.groups` argument)

## 
##  2-sample test for equality of proportions with continuity correction
## 
## data:  c(warren_succ, butler_succ) out of c(warren_n, butler_n)
## X-squared = 6.6377, df = 1, p-value = 0.009984
## alternative hypothesis: two.sided
## 95 percent confidence interval:
##  -0.011728240 -0.001655699
## sample estimates:
##     prop 1     prop 2 
## 0.07801418 0.08470615

## [1] 0.001535069

Free Throws

## `summarise()` ungrouping output (override with `.groups` argument)

## 
##  2-sample test for equality of proportions with continuity correction
## 
## data:  c(warren_succ, butler_succ) out of c(warren_n, butler_n)
## X-squared = 805.95, df = 1, p-value < 2.2e-16
## alternative hypothesis: two.sided
## 95 percent confidence interval:
##  -0.2790561 -0.2465065
## sample estimates:
##    prop 1    prop 2 
## 0.1552841 0.4180654