Revolutions

Mariano Rivera’s baseball prowess, illustrated with R

Kevin Quealy, graphics editor at the New York Times, has published another fascinating behind-the-scenes look at how the Times creates data visualizations for print and online. In his latest post, he looks at how a visualization of the Yankee's Mariano Rivera performance compared to other Major League Baseball pitchers was created. (Detail below, click for the full image.) 

The infographic began its life as a hand-drawn sketch, that begat a line-chart created using R (based on data scraped from the Web). The R chart was was then cleaned up and annotated using Adobe Illustrator for publication. One interesting detail of the process: the source R graph is deliberately created using garish colours (purples, greens, etc.) to make the color-selection process easier in Illustrator.

Check out the ChartsNThings archive for other great studies of the process of data journalism. Many of the case studies involve the use of R code, such as these visualizations of visitors to the White House, Santorum's primary support, Santorum/Romney exit poll data, NFL players mentioned on ESPN, the defense budget and the richest 1%.

ChartsNThings: Sketches: How Mariano Rivera Compares to Baseball’s Best Closers

What makes a hockey Hall-of-Famer?

At the JSM conference last week, I stopped by a great poster by Steve Salaga and Brian Mills, graduate students at University of Michigan's Department of Sport Management. The guys were clearly hockey fans, and had channelled their enthusiasm for a sport into an interesting statistical analysis of game and player data from the NHL. One analysis, based on a random forest model implemented in the R statistical language, looked at the characteristics of players selected for the NHL Hall of Fame:

We are attempting to gauge how well each player aligns with the views of the Hall of Fame Voting Committee and whether or not they were 'snubbed' based on how the committee would be predicted to vote. 

According to their criteria, the key criteria for forwards and defensemen selected for the Hall of Fame are All-Star game appearances, assists, goals and (to a lesser extent) plus/minus and Stanley Cup wins. (Factors that appear not to much influence the committee's decision included shot percentage, and whether the player was French-speaking or not. Goalies were not included in the analysis.) On this basis, players that appear to have been "snubbed" by the selection committee include Kevin Lowe, Alexander Mogilny, Dave Taylor and Theoren Fleury. 

Steve and Brian will be publishing their analysis in a paper soon, but in the meantime you can see more details in their poster (PDF. 3.1Mb) or at their blog post below.

The Prince of Slides: More on JSM

The Luck and Skill of Scrabble

Scrabble is a game that involves both skill and luck. There's skill in knowing the words you can play and — especially — the most advantageous ways to play them. But there's also luck in the tiles you draw randomly from the bag: get saddled with a rack containing four I's and there's usually not much you can do. That's why professional Scrabble tournaments are decided by playing multiple games between each pair of players. Tournaments do this to average out the variability in tile draws between players, to make the deciding factor skill rather than luck.

But how much does luck affect a typical Scrabble game? Andrew C Thomas, a professor in Statistics at Carnegie Mellon University, came up with an ingenious idea to test this. (Thomas's research will soon be published in a paper, a draft of which is now available on Arxiv.org.) What if we could observe a game between a couple of equally-matched players, where we "fix" the luck factor by determining the tiles each player gets in advance? Then, we can eliminate the "skill" factor by having those players re-play the fixed game many times: they'll get the same letters, but might make different strategic plays during the game. Each player's scores will vary over the series of games, but on average, the player with the better "luck" — in other words, the better pre-determined sequence of letters — will have the higher average score.

There are two problems with this approach. First of all, it's not practical to get expert players to play the same game over and over with consistent results. Thomas solves this by using open-source Scrabble AI software instead. (To avoid the robot players making exactly the same moves each time, ha adds a small random factor to the AI decision-making process, by weighting the future value of any given move up or down a point or two.)

The second problem is more of a mechanical one: how can you guarantee that each robot player will get the same sequence of letters each time? In Scrabble, each player may play anywhere between one and seven tiles each move (with a 50-point "bingo" bonus for all seven), or play none at all and exchange some tiles for a new set randomly selected from the pool. The scheme Thomas comes up with to address this is very clever: rather than have each player draw from the same sequence, he pre-generates one sequence of tiles and has each player draw from opposite ends, as shown in this diagram from his paper:

In this diagram, Player 1 drew seven tiles from the left of the sequence to create the rack; Player 2 drew from the right. This way, each player gets the same sequence of tiles in the repeated games, regardless of the number of tiles played each move. Or nearly so: if Player 1 plays many long words in a game, he may access a tile toward the right of the sequence he doesn't usually get. And tile exchanges, which are mixed in with the reserve sequence, add more variability. But in general, the more a letter is towards the left of the sequence, the more likely Player 1 will get to play it, and vice versa.

Again, in a real Scrabble game it would be impractical to lay out the tiles in a pre-determined sequence like this (especially without the players seeing them!). Thomas solves this problem by simulating the games in software: code in the R programming language simulates the sequence of tiles, hands new tiles to the AI players, and then observes their final score. 100 simulated matches are played for each sequence: the average score difference between Player 1 and Player 2 is then a measure of how "lucky" that sequence is for Player 1. And Thomas repeats this process for 10,000 different random sequences, which allows him to do statistical analysis in R on how the tile sequence (or "luck") affects Scrabble games on average. For example, Thomas noted that most sequences where the Q was towards the left led to a point advantage for Player 2, and so in that sense Q is an "unlucky" tile to get. 

Thomas takes this analysis even further: when you get a high-value "power tile" like a Q or a Z also makes a difference. Getting a Q early in the game when there are few options to play it is bad; getting it later in the game when the board has more options is better; letting your opponent draw it is best. These options are reflected in where in the initial sequence (used by both players) the Q falls: towards the left, in the middle, or on the right. Using this method, Thomas maps average player's scores for Q, J, X, and Z depending on where in the sequence they fall:

To the left of the chart, Player 1 has each tile early in the game; towards the right, Player 2 has it. In contrast to the Q, the X is generally beneficial to the player who draws it. Using these techniques, Thomas finds the following conclusions about tiles:

• The blank is worth about 30 points to a good player, mainly by making 50-point "bingo" plays possible.
• Each S is worth about 10 points to the player who draws it.
• The Q is a burden to whichever player receives it, effectively serving as a 5 point penalty for having to deal with it due to its effect in reducing bingo opportunities, needing either a U or a blank for a chance at a bingo and a 50-point bonus.
• The J is essentially neutral pointwise.
• The X and the Z are each worth about 3-5 extra points to the player who receives them. Their difficulty in playing in bingoes is mitigated by their usefulness in other short words.

(Of course, all of these conclusions will depend on exactly which Scrabble dictionary you're using: there are a lot more words available to play from the OED Chambers-based SOWPODS dictionary, and I presume this is based on the official TWL dictionary used in American Scrabble game. I'd love to see the effect on this chart of using British rules.)

Thomas also finds that the player who goes first generally has an advantage, to the tune of about 14 points. So if you're a gracious Scrabble player, let your opponent go first.

AC Thomas: Statistics and Scrabble, Together At Last

Where Ichiro Hits

Google research scientist Peter Hauck used Weka and k-means cluster analysis to describe where Mariners right-fielder Ichiro favours hitting the baseball. He then used R to visualize the 6 clusters the k-means analysis identified:

I sometimes find K-means clusting tough to explain as a statistical technique, but this makes for a great example: if you're a fielder facing Ichiro, it might be a good idea to keep an eye on those six spots when he hits. See the full ananlysis on the Infochimps blog at the link below.

Infochimps blog: Clustering Baseball Data with Weka

Baseball, T-tests and statistical surprises

Are MLB players better hitters now than they were 20 years ago? Revolution Analytics' Joseph Rickert uses R to take a look at the data, and offers an instructive lesson in checking your assumptions for statistical tests in the process -- Ed.

Data are everywhere – but, even for simple things, I still seem to spend a too much time surfing the web to find an appropriate data set. Many times a data set will come my way for some reason and then end up being interesting for some entirely different reason. If I only had a good way to cross reference all of these data sets: you know, a list of every data set I ever came across annotated with what it is good for and with a link to where I put it. Of course, if I had this list I would have to keep it in my list of all my other lists; and then, to make sure I could remember where it was, I would have to keep  it in a special place and ….

Anyway, baseball season is here and few things in the world do data better than baseball. From opening day (3/31/11) to the end of October the ballparks of this country will generate more data than I can keep up with. Fortunately, there are others who can. Take a look, for example, at Baseball Prospectus  for comprehensive baseball statistics organized by year in csv files that are easy to download or at Sean Lahman’s website for a comprehensive data base going back to 1871.

Given that today is the first day of the baseball season, I have the perfect excuse and data set to illustrates how important it is to check the assumptions before doing a t-test. Let's look at the batting averages (AVG) for both major leagues for the years 1990 and 2010. Except for the apparent increase in variability for 2010, the box plots for the two distributions look pretty similar.

So it might seem reasonable to do a simple t-test to see if there is any significant difference. In R this is one line of code that produces the result:

> t.test(AVG ~ YEAR,data=bdat,var.equal=T)

Two Sample t-test
data:  AVG by YEAR
 
t = 1.4098, df = 1682, p-value = 0.1588
 
alternative hypothesis: true difference in means is not equal to 0
 
95 percent confidence interval:
 -0.003395079  0.020751550
 
sample estimates:
mean in group 1990   mean in group 2010
         0.2034081          0.1947299

Created by Pretty R at inside-R.org

Because the confidence interval contains 0 there is no reason to reject the null hypothesis that the means of the two distributions are indeed the same; so it appears that both there is no change in batting average between 1990 and last season. However, is the t-test the right test to use? Forget about the fact that I blew off the apparent increase in variability as irrelevant; are the two distributions even approximately Normal?

 

Good thing I checked! The kernel density plots indicate that these distributions have two, or maybe three, modes – not even close to Normal! These plots are pretty interesting on their own: when I watch hitters this season I’ll we wondering under which bump they belong. But getting back to a formal test to look for a difference in the means of the batting averages for the 1990 and 2010 seasons, it appears that the Wilcoxon Rank Sum Test (also known as the Mann-Whitney test, and which doesn't assume the distributions are Normal) is the way to go.

> wilcox.test(AVG ~ YEAR, data=bdat,conf.int=TRUE)
 
Wilcoxon rank sum test with continuity correction
data:  AVG by YEAR
 
W = 370070.5, p-value = 0.03541
 
alternative hypothesis: true location shift is not equal to 0
 
95 percent confidence interval:
 6.849543e-06 1.302933e-02
 
sample estimates:
difference in location
           0.004991099

Created by Pretty R at inside-R.org

The Willcoxon indicates that there is a significance difference, at the 5% level anyway. (The R code for the charts and analysis appears after the jump.) This was a surprise to me; maybe I’m easily surprised but isn’t life more fun that way. I am looking forward to quite a few surprises from 2011 Baseball. Enjoy the season!

Learning R through baseball: sab-R-metrics

The words "statistics" and "baseball" are often found near each other, but there's a lot more to statistics than dividing the number of hits by the number of swings to get a batting average. And there's a lot more to sabermetrics -- the statistical analysis of baseball -- than averages, too. Many baseball fans are also stats geeks (and vice versa) and have done deep statistical analysis of baseball data, oftentimes with R. 

Dave Allen of the Baseball Analysts website regularly uses R to visualize PitchFX data, as does his stablemate Jeremy Greenhouse (for example, in this analysis of optimal swing rates). ESPN's the Sports Guy inspired a detailed analysis in R by Ryan Elmore. Ricky Zanker of the Hardball Times has published a guide on reading baseball data into R. Mike Driscoll created an interactive R application to visualize data from PitchFX. Even the widely-read New York Times election analyst Nate Silver got his statistical start with sabermetrics.

If you're a baseball fan and you'd like to do some sabermetrics of your own, but haven't made the leap to learn R yet, Millsy is here to help. He's a graduate student in Sport Management at the University of Michigan, and has created a series of tutorials to help you learn R by analyzing baseball data. The tutorials take the new R user and baseball fan step-by-step through your first R commands, reading in data, manipulating objects, and even creating charts and doing simple analysis. Good practical advice is scattered throughout, such as advice "to use color to help portray the information you are trying to communicate, rather than just to make things bright", with this awesome example of what not to do:

There are five parts to the series so far, and I'm looking forward to seeing more in this great series.

The Prince of Slides: sab-R-metrics

Baseball games: getting longer?

ESPN's Bill Simmons (aka The Sports Guy) recently suggested that the primary cause of dwindling interest in Red Sox games by fans is that baseball games these days are too long. "It's not that fun to spend 30-45 minutes driving to a game, paying for parking, parking, waiting in line to get in, finding your seat ... and then, spend the next three-plus hours watching people play baseball", he says. But this is a relatively new phenomenon: are the games really any longer today than they used to be?

Inspired by the column and having recently learned about the power of R's ggplot2 package to visualize data, R user (and baseball fan) Ryan Elmore decided to find out. He wrote code to scrape from the Web data on the lengths of all MLB games since 1970, and then created some lovely visualizations using ggplot 2 and R. For example, here's a scatterplot of the lengths of games from all teams over time, with a smooth trend indicating a clear lengthening of the game, at least through the turn of the century:

The peak average game length comes during the "Steroids Era" of Baseball, which Ryan delineates on the chart with the dashed red lines. Beyond that peak, there appears to be a slow but steady decline in the length of the games (although still more than 20 minutes longer than games in the 70's). So how does this explain the disaffectation of Red Sox fans suggested by The Sports Guy? Ryan takes it one step further, and break out Red Sox games separately:

So it does seem that Boston games are indeed getting longer, lending credence to the Sports Guy's claim. However: I'm no baseball expert, but I'm pretty sure there have been more than 3 Red Sox games since 2004, and the apparent increase may just be a fluke. Given that Ryan has posted his code in R to create the chart, maybe someone with access to more data can verify the result? If you do, let us know in the comments. 

The Log Cabin: Are MLB games getting longer?

Charting the World Cup

Now that Spain has won the World Cup, it's interesting to go back and look at some metrics from the matches and see if we can tease out what characteristics made for a winning Cup team this time around. Fortunately, the Guardian's Data Blog has made a wealth of World Cup statistics available, with data on every player of every team (position, shots at goal, passes, tackles made, and saves), plus aggregate statistics for each team (goals, % shots on target, fouls, and much more). The data are ripe for analysis in R, especially given that you can download the data directly from the cloud as an R object with the following commands:

players <- read.csv("http://spreadsheets.google.com/pub?key=tOM2qREmPUbv76waumrEEYg&single=true&gid=1&range=A1%3AH596&output=csv")

teams <- read.csv("http://spreadsheets.google.com/pub?key=tOM2qREmPUbv76waumrEEYg&single=true&gid=0&range=A1%3AAG15&output=csv")

The method I've described before for accessing a Google Spreadsheet from R didn't quite apply here, as those instructions assume you own the document (and have access to the Publish menu). But some experimentation and tweaking of the spreadsheet URL made it work: the key parameters seem to be the "&gid=" (sheet number) and "%range=" (cell ranges, use %3A to encode the colon) and "&output=csv" to download in CSV format. It would be nice if Google published the specs to form URLs like these, but as far as I know they don't. 

Anyway, a couple of bloggers have used these data to great effect to express the results of the World Cup visually using R graphics. For example, the R Charts blog used ggplot2 to look at the number of fouls committed by each team during the tournament:

 

(Personally, I would have sorted the rows by descending number of fouls, rather than alphabetically.) Interesting to see that Cup champions Spain are in the middle of the pack on fouls, whereas runners-up Netherlands lead this table (boosted heavily by their performance in the final).

Blogger Jason Priem also took a look at the data, this time with a scatterplot of goals per game by fouls per game, related to how far each team advanced in the competition:

 

(Download Jason's code for this chart here.) Again it's interesting to see the positions of the two finalists here, with Netherlands on the extreme frontier for both fouls and goals, while spain is moderate on goals per game and near the lowest on fouls per games.

It's a rich dataset and I'm sure other Revolutions readers could come up with some equally interesting visualizations. If you do, tell us about it in the comments.

Guardian Data Blog: World Cup 2010 statistics: every match and every player in data

Analyzing competitive nordic skiing with R

Here's another great example of R being used to analyze sports data. Statistician and skier Joran Elias has started a project to analyze and visualize international cross country ski racing results, and he publishes his analysis at the blog Statistical Skier. All of the analyses are done using R (and for data, SQLite via the RSQLite package). As much as I love to ski, I'm not so familiar with the intricacies of ski racing as a sport, but it looks like there's a rich source of data ripe for analysis, and Joran is pulling out some interesting results. For example, here's the recent history of one recently-retired five-time Olympian Sabina Valbusa:

 

I can only assume a low "FIS Points" is better: Joran notes "best season overall might have been 2002-2003". A great use of ggplot2 and smoothing to visualize these data. Check out the blog for some other analyses -- especially if you're a ski junkie.

Statistical Skier: Data based analysis and commentary on nordic skiing

Winning the first game in a baseball series: a harbinger, or not?

For those not familiar with the major-league baseball in the US (and despite living here for more than 10 years, I still include myself in that category), the games usually played in series: team A visits the home of team B, and the two teams play two or more games against each other on successive days. It's common wisdom that if team A wins on the first day, they're more likely to be the victors on the second day, too. (Folks "knowledgeable in baseball and the mathematics of forecasting" give the probability of a second-day win given winning the first game at 65% to 70%.) But is that assertion borne out by the data?

Decision Science News has analyzed data from all major league baseball games played between 1970 and 2009, and used R to analyze the likelihood of winning the second game in a consecutive pair of games, given the result of the first. (All of the R code and data are provided, if you want to try and replicate the analysis yourself.) You can see various analyses in DSN's post, but the most revealing one for me was this chart on the frequency of successive wins with respect to the margin of victory (excess runs) in the first game:

So moderate and even significant wins by several runs don't in the first game don't appear to confer much benefit in the second. As DSN points out:

The equation of the robust regression line is: Probability(Win_Second_Game) = .498 + .004*First_Game_Margin which suggests that even if you win the first game by an obscene 20 points, your chance of winning the second game is only 57.8%

In fact, any second-game advantage from the first win that may exist is far overshadowed by the home-team advantage: "When it comes to winning the second game, it’s better to be the home team who just lost than the visitor who just won." See the full article at Decision Science News for the details of the analysis.

Decision Science News: You won, but how much was luck and how much was skill?