In comments, Rick Schoenberg wrote: One thing I tried to say as politely as I could in [the book, “Probability with Texas Holdem Applications”] on p146 is that there’s a huge error in Chen and Ankenman’s “The Mathematics of Poker” which renders all the calculations and formulas in the whole last chapter wrong or meaningless […]

**Sports**category.

## Luck vs. skill in poker

The thread of our recent discussion of quantifying luck vs. skill in sports turned to poker, motivating the present post. 1. Can good poker players really “read” my cards and figure out what’s in my hand? For a couple years in grad school a group of us had a regular Thursday-night poker game, nickel-dime-quarter with […]

## Understanding the hot hand, and the myth of the hot hand, and the myth of the myth of the hot hand, and the myth of the myth of the myth of the hot hand, all at the same time

Josh Miller writes: I came across your paper in the Journal of Management on unreplicable research, and in it you illustrate a point about the null hypothesis via the hot hand literature. I am writing you because I’d like to move your current prior (even if our work uses a classical approach). I am also […]

## NFL players keep getting bigger and bigger

Aleks points us to this beautiful dynamic graph by Noah Veltman showing the heights and weights of NFL players over time. The color is pretty but I think I’d prefer something simpler, just one dot per player (with some jittering to handle the discrete reporting of heights and weights). In any case, it’s a great […]

## Stan World Cup update

The other day I fit a simple model to estimate team abilities from World Cup outcomes. I fit the model to the signed square roots of the score differentials, using the square root on the theory that when the game is less close, it becomes more variable. 0. Background As you might recall, the estimated […]

## Stan goes to the World Cup

I thought it would be fun to fit a simple model in Stan to estimate the abilities of the teams in the World Cup, then I could post everything here on the blog, the whole story of the analysis from beginning to end, showing the results of spending a couple hours on a data analysis. […]

## D&D 5e: Probabilities for Advantage and Disadvantage

The new rules for D&D 5e (formerly known as D&D Next) are finally here: Dungeons & Dragons, 5th Edition: Basic Rules D&D 5e introduces a new game mechanic, advantage and disadvantage. Basic d20 Rules Usually, players roll a 20-sided die (d20) to resolve everyting from attempts at diplomacy to hitting someone with a sword. Each […]

## Visualizing sampling error and dynamic graphics

Robert Grant writes: What do you think of this visualisation from the NYT [in an article by Neil Irwin and Kevin Quealy but I’m not sure if they’re the designers of the visualization]? I’m pretty impressed as a method of showing sampling error to a general audience! I agree. P.S. In related news, Antony Unwin […]

## Dimensionless analysis as applied to swimming!

We have no fireworks-related posts for July 4th but at least we have an item that’s appropriate for the summer weather. It comes from Daniel Lakeland, who writes: Recently in one of your blog posts (“priors I don’t believe”) there was a discussion in which I was advocating the use of dimensional analysis and dimensionless […]

## “Who’s bigger”—the new book that ranks every human on Wikipedia—is more like Bill Simmons than Bill James

I received a copy of “Who’s Bigger?: Where Historical Figures Really Rank,” by Steven Skiena, a computer scientist at Stony Brook University, and Charles Ward, an engineer at Google. Here’s the blurb I gave the publisher: Skiena and Ward provide a numerical ranking for the every Wikipedia resident who’s ever lived. What a great idea! […]

## Quantifying luck vs. skill in sports

Trey Causey writes: If you’ll permit a bit of a diversion, I was wondering if you’d mind sharing your thoughts on how sabermetrics approaches the measurement of luck vs. skill. Phil Birnbaum and Tom Tango use the following method (which I’ve quoted below). It seems to embody the innovative but often non-intuitive way that sabermetrics […]

## What’s the algorithm, Kenneth?

I can’t figure out what’s the deal with the bars for Corners. The bar labeled “7” is much less than 7 times the bar labeled “1.” At first I was guessing that maybe they’re not counting the numbered part in the bar width (which would be a pretty weird choice) but that wouldn’t work for […]

## World Cup pseudo-science

Lee Sechrest pointed me to this news article by Vitomir Miles Raguz, “Brazil Won’t Win the World Cup. A European team will win again thanks to training and statistical analysis.” Hmmm . . . “statistical analysis.” This Raguz character better coordinate stories with Nate; it seems that the statistical experts are disagreeing . . . […]

## How much can we learn about individual-level causal claims from state-level correlations?

Hey, we all know the answer: “correlation does not imply causation”—but of course life is more complicated than that. As philosophers, economists, statisticians, and others have repeatedly noted, most of our information about the world is observational not experimental, yet we manage to draw causal conclusions all the time. Sure, some of these conclusions are […]

## Is a steal really worth 9 points?

Theodore Vasiloudis writes: I’d like to bring your attention to this article by Benjamin Morris discussing the value of steals for the NBA. The author argues that a steal should be a highly sought after statistic as it equates to higher chances of victory and is very hard to replace when a player is injured. […]

## Win probabilities during a sporting event

Todd Schneider writes:

## The myth of the myth of the myth of the hot hand

Phil pointed me to this paper so I thought I probably better repeat what I wrote a couple years ago: 1. The effects are certainly not zero. We are not machines, and anything that can affect our expectations (for example, our success in previous tries) should affect our performance. 2. The effects I’ve seen are […]

## What is it with Americans in Olympic ski teams from tropical countries?

Every time I hear this sort of story: Morrone—listed at 48 years old, which would have made her the oldest Olympic cross-country skier of all time by seven years—didn’t even show up for the 10K women’s classic on Feb. 13, claiming injury. (She was the only one of the race’s 76 entrants who didn’t start.) […]

## Econometrics, political science, epidemiology, etc.: Don’t model the probability of a discrete outcome, model the underlying continuous variable

This is an echo of yesterday’s post, Basketball Stats: Don’t model the probability of win, model the expected score differential. As with basketball, so with baseball: as the great Bill James wrote, if you want to predict a pitcher’s win-loss record, it’s better to use last year’s ERA than last year’s W-L. As with basketball […]

## Basketball Stats: Don’t model the probability of win, model the expected score differential.

Someone who wants to remain anonymous writes: I am working to create a more accurate in-game win probability model for basketball games. My idea is for each timestep in a game (a second, 5 seconds, etc), use the Vegas line, the current score differential, who has the ball, and the number of possessions played already […]