Kobe Probability
Michele Bradley
9/8/2017
#DATA606::startLab('Lab2')
load("/Users/Michele/Lab2/more/kobe.RData")
head(kobe)## vs game quarter time
## 1 ORL 1 1 9:47
## 2 ORL 1 1 9:07
## 3 ORL 1 1 8:11
## 4 ORL 1 1 7:41
## 5 ORL 1 1 7:03
## 6 ORL 1 1 6:01
## description basket
## 1 Kobe Bryant makes 4-foot two point shot H
## 2 Kobe Bryant misses jumper M
## 3 Kobe Bryant misses 7-foot jumper M
## 4 Kobe Bryant makes 16-foot jumper (Derek Fisher assists) H
## 5 Kobe Bryant makes driving layup H
## 6 Kobe Bryant misses jumper MQuestion 1
What does a streak length of 1 mean, i.e. how many hits and misses are in a streak of 1? What about a streak length of 0?
I believe, that a streak length of 1 would mean that Kobe made one basket and did not make any before or after that basket. A streak length of 0 would mean that Kobe missed a basket.
kobe_streak <- calc_streak(kobe$basket)
barplot(table(kobe_streak))
Question 2
Describe the distribution of Kobe’s streak lengths from the 2009 NBA finals. What was his typical streak length? How long was his longest streak of baskets?
His most typical streak was 0, which would be an instance where he missed a basket. His longest streak was 4 baskets in a row.
Question 3
outcomes <- c("heads", "tails")
sim_fair_coin <- sample(outcomes, size = 100, replace = TRUE)
table(sim_fair_coin)## sim_fair_coin
## heads tails
## 39 61In your simulation of flipping the unfair coin 100 times, how many flips came up heads?
sim_unfair_coin <- sample(outcomes, size = 100, replace = TRUE, prob = c(0.2, 0.8))
table(sim_unfair_coin)## sim_unfair_coin
## heads tails
## 19 81Question 4
What change needs to be made to the sample function so that it reflects a shooting percentage of 45%? Make this adjustment, then run a simulation to sample 133 shots. Assign the output of this simulation to a new object called sim_basket.
outcomes <- c("H", "M")
sim_basket <- sample(outcomes, size = 133, replace = TRUE, prob = c(0.45, 0.55))
sim_basket## [1] "M" "M" "M" "H" "H" "M" "M" "H" "M" "H" "H" "H" "H" "M" "H" "M" "M"
## [18] "H" "M" "H" "H" "M" "M" "M" "M" "M" "M" "M" "M" "H" "H" "H" "H" "H"
## [35] "H" "M" "H" "H" "M" "M" "M" "M" "M" "H" "M" "H" "M" "H" "M" "M" "H"
## [52] "H" "M" "M" "H" "H" "M" "H" "H" "M" "H" "H" "M" "M" "M" "H" "M" "H"
## [69] "M" "M" "M" "H" "H" "H" "M" "H" "M" "M" "H" "M" "H" "H" "H" "H" "M"
## [86] "M" "H" "M" "M" "H" "H" "M" "H" "M" "M" "H" "M" "M" "M" "M" "M" "M"
## [103] "M" "M" "H" "M" "M" "H" "H" "M" "H" "M" "H" "M" "M" "H" "M" "M" "H"
## [120] "M" "H" "M" "M" "H" "M" "H" "M" "M" "M" "M" "M" "M" "H"table(sim_basket)## sim_basket
## H M
## 57 76table(kobe$basket)##
## H M
## 58 75On Your Own
Using calc_streak, compute the streak lengths of sim_basket.
simulation_kobe <- calc_streak(sim_basket)
barplot(table(simulation_kobe))
- Describe the distribution of streak lengths. What is the typical streak length for this simulated independent shooter with a 45% shooting percentage? How long is the player’s longest streak of baskets in 133 shots?
The typical streak length is still at 0, but the longest streak has increased to five as opposed to four.
- If you were to run the simulation of the independent shooter a second time, how would you expect its streak distribution to compare to the distribution from the question above? Exactly the same? Somewhat similar? Totally different? Explain your reasoning.
This would depend on how the simulation is run – sometimes one needs a simulation buffer to ensure it is running properly. However, I would assume it would be similar, because the simulation has a large sample size.
- How does Kobe Bryant’s distribution of streak lengths compare to the distribution of streak lengths for the simulated shooter? Using this comparison, do you have evidence that the hot hand model fits Kobe’s shooting patterns? Explain.
Kobe’s distribution demonstrates that he is very likely to geta basket, but is more likely to get only one streak as opposed to multiple. It appears as though our independent shooter is more likely to get multiple shots in than Kobe is.