Super Bowl XLVIII Game Probability

The game probability for Super Bowl XLVIII is now available at the New York Times. This week I take a look at why the efficiency model may differ from some other models and the public consensus.

...Some other analytical models, along with the consensus odds, give Denver a small advantage. I suspect the disagreement can be attributed to two factors. First, I doubt the strength-of-schedule effect is fully appreciated by wider audiences. And second, recent outcomes are often overweighted both by quantitative models (by design) and by fans and analysts (often unwittingly). Focusing on recent games would tend to favor Denver, which has appeared to be winning in easier fashion lately...

Podcast Episode 18 - Brian Burke

Brian Burke returns to the show for the final podcast of the season. He and Dave kick off the episode with a NFL rules brainstorming session. They discuss some of Brian's (and readers') ideas for creative rule changes the league could implement to make the game more interesting and fun.

Brian then dives into an explanation of his latest article on the value of a time out. He describes his process for analyzing the win probability ramifications of "burning" time outs, and why sometimes it's better for a team to make any choice rather than use a valuable resource debating the optimum choice.

Dave and Brian discuss Brian's win prediction model for the Superbowl, and why it looks to be a very close match-up. To wrap up the episode they use the Franchise Season Visualization tool to take a look back at the 2013 season.

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Thomas Bayes Would Approve of Seattle's Defensive Tactics

The following is a guest article by Gary Montry, a professional applied mathematician. Editor's note: Gary uses net yardage as the measure of utility, and we might prefer something like EP or WP, I think the general point of the article stands, and its strength is in the construction and solution to the problem. It's also a great refresher on conditional probabilities and Bayes' theorem.   

Last week a WSJ article about the Seahawks' defensive backs claimed that they "obstruct and foul opposing receivers on practically every play."  I took a deeper look in to the numbers and found that as long as referees are reluctant to throw flags on the defense in pass coverage (as claimed in the article), holding the receiver is a very efficient defensive strategy despite the risk of being penalized.

The following is an analysis using the concepts of expected utility, expected cost, and bayesian statistics.

The reason defensive holding is an optimal strategy comes down to one word. Economics. The referee's reluctance to call penalties on the defensive secondary is analogous to a market inefficiency. The variance in talent on NFL rosters, coaching staffs, and front offices between the best and worst teams in the league is probably very small. Successful teams win within a small margin. Seattle has found a way to exploit a relaxation in marginal constraints within the way the game is called that their competitors have not, and turned it into a competitive advantage.

If you think about committing a penalty in the same way as committing a crime, the expected utility is essentially the same. The expected utility (EU) for defensive holding is (opponent loss of down due to incomplete pass - probability of being penalized x cost of penalty). In other words, EU is the benefit of an incomplete pass minus the cost of the penalty times the probability of getting caught.

Advanced Stat Breakdown for Super Bowl 48

Instead of reading a bunch of words about the Super Bowl matchup, where each phase is trying its hardest to express some sort of numerical evaluation, wouldn't you prefer to see the numbers themselves collected into one giant eye chart? Well, if that appeals to you, you'll enjoy the SEA-DEN Matchup page.

NFL Overtime Modeled as a Markov Chain

by Ben Zauzmer. Ben is a junior majoring in Applied Math at Harvard University and is a member of the Harvard Sports Analysis Collective. This article was originally published at harvardsportsanalysis.org.

In 2012, the NFL created new overtime rules designed to make the game fairer. The league switched from a sudden death setup to an arrangement that allows both teams to have a chance at scoring, unless the first team to receive scores a touchdown. Even with this change, it would seem that a coach should still always elect to receive if he wins the coin toss at the start of overtime, since an opening touchdown drive wins the game.

However, earlier this year, for the first time under the new rules, a coach made exactly the opposite decision. Bill Belichick, the three-time Super Bowl-winning coach of the New England Patriots, made the gutsy call to kick at the start of overtime. Many considered the main factor behind this decision to be the heavy winds at Gillette Stadium (if a team defers the choice of kicking or receiving, it may choose which direction to face). However, kicking first may also give a team better field position on offense and may actually benefit teams with strong defenses.

To calculate which strategy coaches should prefer, we will model NFL overtime as a Markov Chain. We will define our states as the set of possible point differentials, from the perspective of the team that receives the opening kickoff, in overtime: -6, -3, -2, 0, 2, 3, 6. This model inherently assumes that state-to-state probabilities are not conditional, and that the probability of the score differential being 5 or 9 – both technically possible under the new rules – is negligible.

We will let be the transition matrix for the receiving team’s first offensive possession, be the receiving team’s first defensive possession, be every subsequent receiving team offensive drive, and be every subsequent receiving team defensive drive. The first row/column of each matrix represents the receiving team at a -6 scoring difference, and so on until the last row/column is the receiving team at a +6 scoring difference.

The matrices have the following forms:

Momentum Part 5 - Series Level Analysis

This is the final part of my series on momentum in a football game. Is momentum a causative property that a team can gain or lose, or is it only something our minds project to explain streaks of outcomes that don't alternate as much as we expect? It's been a couple months since I began this series, so as a refresher, here is what I've looked at so far:

Part 1 examined the possibility that momentum exists by measuring whether teams that obtain the ball in momentum-swinging ways go on to score more frequently than teams that obtained the ball by regular means.

Part 2 looked at whether teams that gained possession following momentous plays went on to win more often than we would otherwise expect.

Part 3 focused on drive success following a turnover on downs, which is often cited by coaches and analysts as a reason not to go by the numbers when making strategic decisions.

Part 4 applied a different method of examining momentum by using the runs test so see the degree to which team performance is streakier than random, independent trials.

In this part, I'll apply the runs test at the series level, to see if teams convert first downs (or fail to convert them) more consecutively than random independence would suggest. But first, I'll tie up some loose ends left hanging from part 4. Specifically, I'll redo the play-level runs test to eliminate potential confusion caused by a team with disparate performance from their offensive and defensive squads.

Franchise Season Plots Updated

Check out how your favorite team's fortunes have evolved over the past 14 seasons. The Franchise Season visualization has been updated with 2013's data. It's a fun snapshot of each team's "identity" from year to year, plotting Expected Points Added per Game.

You can examine how SEA has completed its circle of life with its 2013 campaign, covering all possible combinations of good&bad offense&defense. See how DEN's offensive production changed with the arrival of Peyton Manning (or check out IND's 2011 year in the wilderness).

The reigning champions are always the default selections for all our charts and tables at ANS, so this is will be the last week as the default for my hometown team. To me it's interesting to see that they've spent most of their franchise's existence along one axis, ranging from all-world defense/terrible offense to above-average offense/average defense, and won the Lombardi Trophy on both extremes of the axis.

It's rare for a team to sustain above-average production on both sides of the ball for beyond a season or two at a time, even for perennial contenders like NE and IND. PIT might be the best counter-example, with seasons that cluster in the upper-right quadrant consistently through the recent era. Even their "down" years were decent. For example, 2013 saw the Steelers finish 8-8, falling perfectly at the average/average intersection in the plot.

CHI's plot is a really interesting one. They should feature it on Sesame Street. One of these years is not like the other...

It's interesting to see how the average line can appear to be something like the sound barrier to some squads. ATL just can't seem to put together an above average defense, and BUF can barely break the average-barrier on offense.

A smaller version is included below, but the permanent full-size version is available via the Tools | Visualizations menu.

As always, up and to the right is good. Down and to the left is bad. My thanks to Chase Stuart who suggested the idea for this a couple years ago.

Podcast Episode 17 - Kevin Quealy

Kevin Quealy, graphics editor at the New York Times, comes on the show to discuss data visualizations. An expert in using data to tell visual stories, Kevin walks Dave through the process he and the graphics department use to tell news-worthy stories with data and graphics. 

Kevin describes some of his recent sports work, including a graph of longest QB start streaks, the 4th Down Bot and his NFL draft success chart. He talks about how he and his team begin their work process by looking for interesting stories and data-sets, and how those stories go through a variety of iterations before they are turned into visually striking charts. Kevin explains his criteria for what makes for a great visualization and provides some helpful tips for aspiring information designers.

If you're interested in learning more about data visualizations, check out the rest of Kevin's work here and his post about the process of creating the QB streak graphic. While you're at it, take a look at Jennifer Daniel's terrific 4th down Bot sketches.

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