Interactive 2015 NFL Forecasts

As promised in my last post, I’ve now built and deployed a web app that lets you poke through my preseason forecasts for the 2015 NFL regular season:

2015 NFL Forecasts

I learned several new tricks in the course of generating these forecasts and building this app, so the exercise served its didactic purpose. (You can find the code for the app here, on GitHub.) I also got lucky with the release of a new R package that solved a crucial problem I was having when I started to work on this project a couple of weeks ago. Open source software can be a wonderful thing.

The forecasts posted right now are based on results of the pairwise wiki survey through the morning of Monday, August 17. At that point, the survey had already logged upwards of 12,000 votes, triple the number cast in last year’s edition. This time around, I posted a link to the survey on the r/nfl subreddit, and that post produced a brief torrent of activity from what I hope was a relatively well-informed crowd.

The regular season doesn’t start until September, and I will update these forecasts at least once more before that happens. With so many votes already cast, though, the results will only change significantly if a) a large number of new votes are cast and b) those votes differ substantially from the ones already cast, and those conditions are highly unlikely to intersect.

One thing these forecasts help to illustrate is how noisy a game professional football is. By noisy, I mean hard to predict with precision. Even in games where one team is much stronger than the other, we still see tremendous variance in the simulated net scores and the associated outcomes. Heavy underdogs will win big every once in a while, and games we’d consider close when watching can produce a wide range of net scores.

Take, for example, the week 1 match-up between the Bears and Packers. Even though Chicago’s the home team, the simulation results (below) favor Green Bay by more than eight points. At the same time, those simulations also include a smattering of outcomes in which the Bears win by multiple touchdowns, and the peak of the distribution of simulations is pretty broad and flat. Some of that variance results from the many imperfections of the model and survey scores, but a lot of it is baked into the game, and plots of the predictive simulations nicely illustrate that noisiness.


The big thing that’s still missing from these forecasts is updating during the season. The statistical model that generates the predictive simulations takes just two inputs for each game — the difference between the two teams’ strength scores and the name of the home team — and, barring catastrophe, only one of those inputs can change as the season passes. I could leave the wiki survey running throughout the season, but the model that turns survey votes into scores doesn’t differentiate between recent and older votes, so updating the forecasts with the latest survey scores is unlikely to move the needle by much.*

I’m now hoping to use this problem as an entry point to learning about Bayesian updating and how to program it in R. Instead of updating the actual survey scores, we could treat the preseason scores as priors and then use observed game scores or outcomes to sequentially update estimates of them. I haven’t figured out how to implement this idea yet, but I’m working on it and will report back if I do.

* The pairwise wiki survey runs on open source software, and I can imagine modifying the instrument to give more weight to recent votes than older ones. Right now, I don’t have the programming skills to make those modifications, but I’m still hoping to find someone who might want to work with me, or just take it upon himself or herself, to do this.


Deriving a Fuzzy-Set Measure of Democracy from Several Dichotomous Data Sets

In a recent post, I described an ongoing project in which Shahryar Minhas, Mike Ward, and I are using text mining and machine learning to produce fuzzy-set measures of various political regime types for all countries of the world. As part of the NSF-funded MADCOW project,* our ultimate goal is to devise a process that routinely updates those data in near-real time at low cost. We’re not there yet, but our preliminary results are promising, and we plan to keep tinkering.

One of crucial choices we had to make in our initial analysis was how to measure each regime type for the machine-learning phase of the process. This choice is important because our models are only going to be as good as the data from which they’re derived. If the targets in that machine-learning process don’t reliably represent the concepts we have in mind, then the resulting models will be looking for the wrong things.

For our first cut, we decided to use dichotomous measures of several regime types, and to base those dichotomous measures on stringent criteria. So, for example, we identified as democracies only those cases with a score of 10, the maximum, on Polity’s scalar measure of democracy. For military rule, we only coded as 1 those cases where two major data sets agreed that a regime was authoritarian and only military-led, with no hybrids or modifiers. Even though the targets of our machine-learning process were crisply bivalent, we could get fuzzy-set measures from our classifiers by looking at the probabilities of class membership they produce.

In future iterations, though, I’m hoping we’ll get a chance to experiment with targets that are themselves fuzzy or that just take advantage of a larger information set. Bayesian measurement error models offer a great way to generate those targets.

Imagine that you have a set of cases that may or may not belong in some category of interest—say, democracy. Now imagine that you’ve got a set of experts who vote yes (1) or no (0) on the status of each of those cases and don’t always agree. We can get a simple estimate of the probability that a given case is a democracy by averaging the experts’ votes, and that’s not necessarily a bad idea. If, however, we suspect that some experts are more error prone than others, and that the nature of those errors follows certain patterns, then we can do better with a model that gleans those patterns from the data and adjusts the averaging accordingly. That’s exactly what a Bayesian measurement error model does. Instead of an unweighted average of the experts’ votes, we get an inverse-error-rate-weighted average, which should be more reliable than the unweighted version if the assumption about predictable patterns in those errors is largely correct.

I’m not trained in Bayesian data analysis and don’t know my way around the software used to estimate these models, so I sought and received generous help on this task from Sean J. Taylor. I compiled yes/no measures of democracy from five country-year data sets that ostensibly use similar definitions and coding criteria:

  • Cheibub, Gandhi, and Vreeland’s Democracy and Dictatorship (DD) data set, 1946–2008 (here);
  • Boix, Miller, and Rosato’s dichotomous coding of democracy, 1800–2007 (here);
  • A binary indicator of democracy derived from Polity IV using the Political Instability Task Force’s coding rules, 1800–2013;
  • The lists of electoral democracies in Freedom House’s annual Freedom in the World reports, 1989–2013; and
  • My own Democracy/Autocracy data set, 1955–2010 (here).

Sean took those five columns of zeroes and ones and used them to estimate a model with no prior assumptions about the five sources’ relative reliability. James Melton, Stephen Meserve, and Daniel Pemstein use the same technique to produce the terrific Unified Democracy Scores. What we’re doing is a little different, though. Where their approach treats democracy as a scalar concept and estimates a composite index from several measures, we’re accepting the binary conceptualization underlying our five sources and estimating the probability that a country qualifies as a democracy. In fuzzy-set terms, this probability represents a case’s degree of membership in the democracy set, not how democratic it is.

The distinction between a country’s degree of membership in that set and its degree of democracy is subtle but potentially meaningful, and the former will sometimes be a better fit for an analytic task than the latter. For example, if you’re looking to distinguish categorically between democracies and autocracies in order to estimate the difference in some other quantity across the two sets, it makes more sense to base that split on a probabilistic measure of set membership than an arbitrarily chosen cut point on a scalar measure of democracy-ness. You would still need to choose a threshold, but “greater than 0.5” has a natural interpretation (“probably a democracy”) that suits the task in a way that an arbitrary cut point on an index doesn’t. And, of course, you could still perform a sensitivity analysis by moving the cut point around and seeing how much that choice affects your results.

So that’s the theory, anyway. What about the implementation?

I’m excited to report that the estimates from our initial measurement model of democracy look great to me. As someone who has spent a lot of hours wringing my hands over the need to make binary calls on many ambiguous regimes (Russia in the late 1990s? Venezuela under Hugo Chavez? Bangladesh between coups?), I think these estimates are accurately distinguishing the hazy cases from the rest and even doing a good job estimating the extent of that uncertainty.

As a first check, let’s take a look at the distribution of the estimated probabilities. The histogram below shows the estimates for the period 1989–2007, the only years for which we have inputs from all five of the source data sets. Voilà, the distribution has the expected shape. Most countries most of the time are readily identified as democracies or non-democracies, but the membership status of a sizable subset of country-years is more uncertain.

Estimated Probabilities of Democracy for All Countries Worldwide, 1989-2007

Estimated Probabilities of Democracy for All Countries Worldwide, 1989-2007

Of course, we can and should also look at the estimates for specific cases. I know a little more about countries that emerged from the collapse of the Soviet Union than I do about the rest of the world, so I like to start there when eyeballing regime data. The chart below compares scores for several of those countries that have exhibited more variation over the past 20+ years. Most of the rest of the post-Soviet states are slammed up against 1 (Estonia, Latvia, and Lithuania) or 0 (e.g., Uzbekistan, Turkmenistan, Tajikistan), so I left them off the chart. I also limited the range of years to the ones for which data are available from all five sources. By drawing strength from other years and countries, the model can produce estimates for cases with fewer or even no inputs. Still, the estimates will be less reliable for those cases, so I thought I would focus for now on the estimates based on a common set of “votes.”

Estimated Probability of Democracy for Selected Soviet Successor States, 1991-2007

Estimated Probability of Democracy for Selected Soviet Successor States, 1991-2007

Those estimates look about right to me. For example, Georgia’s status is ambiguous and trending less likely until the Rose Revolution of 2003, after which point it’s probably but not certainly a democracy, and the trend bends down again soon thereafter. Meanwhile, Russia is fairly confidently identified as a democracy after the constitutional crisis of 1993, but its status becomes uncertain around the passage of power from Yeltsin to Putin and then solidifies as most likely authoritarian by the mid-2000s. Finally, Armenia was one of the cases I found most difficult to code when building the Democracy/Autocracy data set for the Political Instability Task Force, so I’m gratified to see its probability of democracy oscillating around 0.5 throughout.

One nice feature of a Bayesian measurement error model is that, in addition to estimating the scores, we can also estimate confidence intervals to help quantify our uncertainty about those scores. The plot below shows Armenia’s trend line with the upper and lower bounds of a 90-percent confidence interval. Here, it’s even easier to see just how unclear this country’s democracy status has been since it regained independence. From 1991 until at least 2007, its 90-percent confidence interval straddled the toss-up line. How’s that for uncertain?

Armenia's Estimated Probability of Democracy with 90% Confidence Interval

Armenia’s Estimated Probability of Democracy with 90% Confidence Interval

Sean and I are still talking about ways to tweak this process, but I think the data it’s producing are already useful and interesting. I’m considering using these estimates in a predictive model of coup attempts and seeing if and how the results differ from ones based on the Polity index and the Unified Democracy Scores. Meanwhile, the rest of the MADCOW crew and I are now talking about applying the same process to dichotomous indicators of military rule, one-party rule, personal rule, and monarchy and then experimenting with machine-learning processes that use the results as their targets. There are lots of moving parts in our regime data-making process, and this one isn’t necessarily the highest priority, but it would be great to get to follow this path and see where it leads.

* NSF Award 1259190, Collaborative Research: Automated Real-time Production of Political Indicators

Hello?!? Not All Forecasters Are Strict Positivists

International relations is the most predictively oriented subfield of political science…Yet even in the other empirical subfields, the positivist notion that everything must ultimately be reducible to (knowable) universal laws displays its hold in excrescences such as quadrennial attempts to derive formulae for predicting the next presidential election outcome, usually on the basis of ‘‘real’’ (economic) factors. Even if one follows Milton Friedman (1953) in insisting that the factors expressed by such formulae are not supposed to be actually causing electoral outcomes, but are merely variables that (for some unknown reason) allow us to make good behavioral predictions, in practice one usually wants to know what is actually causing the behavior, and it is all too easy to assume that whatever is causing it—since it seems to be responsible for a behavioral regularity—must be some universal human disposition.

That’s from a 2012 paper by Jeffrey Friedman on Robert Jervis’ 1997 System Effects and the “problem of prediction.” I actually enjoyed the paper on the whole, but this passage encapsulates what drives me nuts about what many people—including many social “scientists”—think it means to try to make forecasts about politics.

Contrary to the assertions of some haters, political scientists almost never make explicit forecasts about the things they study—at least not in print or out loud. Some of that reticence presumably results from the fact that there’s no clear professional benefit to making predictions, and there is some professional risk in doing so and then being wrong.

Some of that reticence, though, also seems to flow from this silly but apparently widely-held idea that the very act of forecasting implies that the forecaster accepts the strict positivist premise that “everything must ultimately be reducible to (knowable) universal laws.” To that, I say…

charlie brown aaugh

Probability is a mathematical representation of uncertainty, and a probabilistic forecast explicitly acknowledges that we don’t know for sure what’s going to happen. Instead, it’s an educated guess—or, in Bayesian terms, an informed belief.

Forecasters generally use evidence from the past to educate those guesses, but that act of empiricism in itself does not imply that we presume there are universal laws driving political processes lurking beneath that history. Instead, it’s really just a practical solution to the problem of wanting better information—sometimes to help us plan for the future, and sometimes to try to adjudicate between different ideas about the forces shaping those processes now and in the past.

Empiricism is a practical solution because it works—not perfectly, of course, but, for many problems of interest, a lot better than casting bones or reading entrails or consulting oracles. The handful of forecasters I know all embrace the premises that their efforts are only approximations, and that the world can always change in ways that will render the models we find helpful today less helpful in the future. In the meantime, though, we figure we can nibble away at our ignorance by making structured guesses about that future and seeing which ones turn out to be more reliable than the others. Physicists still aren’t entirely sure how planes manage to fly, but millions of us make a prediction every day that the plane we’re about to board is somehow going to manage that feat. We don’t need to be certain of the underlying law to find that prediction useful.

Finally, I can’t resist: there’s real irony in Freidman’s choice of examples of misguided forecasting projects. To have called efforts to predict the outcome of U.S. presidential elections “excrescences” in the year those excrescences had a kind of popular coming out, well, that’s just unfortunate. I guess Friedman didn’t see that one coming.

Some Suggested Readings for Political Forecasters

A few people have recently asked me to recommend readings on political forecasting for people who aren’t already immersed in the subject. Since the question keeps coming up, I thought I’d answer with a blog post. Here, in no particular order, are books (and one article) I’d suggest to anyone interested in the subject.

Thinking, Fast and Slow, by Daniel Kahneman. A really engaging read on how we think, with special attention to cognitive biases and heuristics. I think forecasters should read it in hopes of finding ways to mitigate the effects of these biases on their own work, and of getting better at spotting them in the thinking of others.

Numbers Rule Your World, by Kaiser Fung. Even if you aren’t going to use statistical models to forecast, it helps to think statistically, and Fung’s book is the most engaging treatment of that topic that I’ve read so far.

The Signal and the Noise, by Nate Silver. A guided tour of how forecasters in a variety of fields do their work, with some useful general lessons on the value of updating and being an omnivorous consumer of relevant information.

The Theory that Would Not Die, by Sharon Bertsch McGrayne. A history of Bayesian statistics in the real world, including successful applications to some really hard prediction problems, like the risk of accidents with atomic bombs and nuclear power plants.

The Black Swan, by Nicholas Nassim Taleb. If you can get past the derisive tone—and I’ll admit, I initially found that hard to do—this book does a great job explaining why we should be humble about our ability to anticipate rare events in complex systems, and how forgetting that fact can hurt us badly.

Expert Political Judgment: How Good Is It? How Can We Know?, by Philip Tetlock. The definitive study to date on the limits of expertise in political forecasting and the cognitive styles that help some experts do a bit better than others.

Counterfactual Thought Experiments in World Politics, edited by Philip Tetlock and Aaron Belkin. The introductory chapter is the crucial one. It’s ostensibly about the importance of careful counterfactual reasoning to learning from history, but it applies just as well to thinking about plausible futures, an important skill for forecasting.

The Foundation Trilogy, by Isaac Asimov. A great fictional exploration of the Modernist notion of social control through predictive science. These books were written half a century ago, and it’s been more than 25 years since I read them, but they’re probably more relevant than ever, what with all the talk of Big Data and the Quantified Self and such.

The Perils of Policy by P-Value: Predicting Civil Conflicts,” by Michael Ward, Brian Greenhill, and Kristin Bakke. This one’s really for practicing social scientists, but still. The point is that the statistical models we typically construct for hypothesis testing often won’t be very useful for forecasting, so proceed with caution when switching between tasks. (The fact that they often aren’t very good for hypothesis testing, either, is another matter. On that and many other things, see Phil Schrodt’s “Seven Deadly Sins of Contemporary Quantitative Political Analysis.“)

I’m sure I’ve missed a lot of good stuff and would love to hear more suggestions from readers.

And just to be absolutely clear: I don’t make any money if you click through to those books or buy them or anything like that. The closest thing I have to a material interest in this list are ongoing professional collaborations with three of the authors listed here: Phil Tetlock, Phil Schrodt, and Mike Ward.

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