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The Philadelphia Eagles are 2-0, but they’re living dangerously. The Eagles fell behind 17-0 against Jacksonville on opening day before hanging 34 unanswered points on the Jaguars defense. And Philadelphia was at it again in Monday night’s victory over the Indianapolis Colts. Trailing 20-6 at one point in the third quarter, the Eagles came back to win on a Cody Parkey field goal as time expired.

Philadelphia has an average points-per-game margin of +10 so far this season, which ties it for fifth-best in the NFL. If you look at how the Eagles’ games have developed, though, you’d never guess they’d have such a positive scoring margin. To measure this phenomenon, FiveThirtyEight contributor Chase Stuart has created a metric called Game Scripts, which attempts to more accurately measure how the totality of a game played out beyond the final score line. A team’s Game Script in a given game (or season) is its average point margin at any given moment.

Against Indianapolis, the Eagles had a Game Script of -4.8, meaning they trailed by nearly five points at any given moment in the game. Needless to say, teams that post a Game Script of -4.8 tend to lose. Historically, only about 17 percent of teams with that particular Game Script win the game in question. But that’s nothing compared with Philadelphia’s game vs. Jacksonville — the Eagles won despite a -7.1 Game Script. Teams with such a negative Game Script tend to win only 9 percent of the time.

Adding those two winning percentages up, we’d expect the Eagles to have won just 0.26 games so far this year, based on the degree to which they’ve trailed and the amount of time they’ve spent trailing. That represents a huge difference from their actual win total (two). Through two games, it’s the biggest difference between actual wins and Game Script-predicted wins of any team since 1978 (when the league expanded to a 16-game schedule in 1978).

But that gap is probably unsustainable. After all, impressive late-game comebacks aren’t necessarily very predictive of how a team will play in the future. However, I decided to test which statistic was a better descriptor of a team like the Eagles: two actual wins in two games, or 0.26 Game Script-predicted wins?

For both metrics, I looked at teams’ two-game starts to the season (excluding strike-shortened campaigns) and their records over the remainder of the season. For example, the average 2-0 team ended up winning eight games out of its next 14. So just from Philadelphia’s record alone, we’d expect them to finish the season 10-6. But the average team with 0.26 Game Script-predicted wins through two games won only 5.9 of their next 14 games, which would yield a predicted record of about 8-8 for the Eagles despite the 2-0 start.

I then tested which mixture of actual and Game Script-predicted wins yielded the best prediction about how a team would finish the year. The result? Both variables carry almost exactly the same weight. Accuracy is maximized when predicting a team’s rest-of-season record by giving 50.7 percent weight to that which would be predicted from its actual record, and 49.3 percent to that which would be predicted from its Game Script. (And both variables are statistically significant.)

For the Eagles, this means they aren’t quite the team we’d expect from their 2-0 record. But they also shouldn’t have their big average deficits completely held against them. Combining the two metrics, we’d expect them to finish with almost exactly seven wins in their final 14 games, which would yield a record of 9-7.

You’re the general manager of an NBA team, and come 2016, one of your star players wants to try out for Team USA. The squad just dominated the FIBA World Cup, he says, and he wants in on the next gold medal.

What do you decide?

One school of thought says that playing for Team USA will help a player’s NBA performance. Grantland’s Bill Simmons has cited Kevin Durant’s 2010 FIBA experience as a turning point in Durant’s career. Players have said they were “getting better while facing the best players in the world.” And others have described a confidence boost simply in being selected.

On the other hand, some analysts, owners and players have expressed concern about giving up scarce summer rest to put on additional basketball miles, particularly for veterans coming off grueling June playoff runs. And what about injuries?

The NBA first sent its players to compete in international play with the 1992 Olympic Dream Team. NBA players have since competed in 10 biennial international tournaments (the NBA did not send pros to the 1998 FIBA World Championships due to a lockout). Let’s look at how those players performed in win shares (WS), win shares per 48 minutes (WS/48) and player efficiency rating (PER) in the NBA season following their overseas experience (relative to their age-adjusted Simple Projection System estimates).

The average change among all players was +1.6 percent in WS, +3.0 percent in WS/48 and -1.6 percent in PER. The results don’t seem to confirm nor deny the arguments for or against international participation.

Breaking the results down by year, however, shows that some tournaments may have provided a larger performance boost than others.

So, what happened to the gold-winning 2010 squad that competed in Turkey? Tyson Chandler had a monster 2010-11 year for a championship-winning team after coming off an injury-plagued previous two seasons. Stephen Curry, Eric Gordon, Kevin Love and Lamar Odom also made huge strides. Meanwhile, Russell Westbrook emerged as an All-Star, and Derrick Rose broke out to win the league MVP. (Durant was one of only two players from the 2010 squad to have a lesser-than-expected 2010-11 season.)

What has caused the recent post-Team USA boost? Well, it could just be noise. But it’s worth noting that Mike Krzyzewski took over as coach in 2006, and his training may have helped spur the rate of improvement. Interestingly, the only years Team USA failed to take gold (2002, 2004 and 2006) are the years players performed worse in the following NBA season (excluding the original 1992 squad). This may be due to Team USA management selecting more of an “All-Star team” during those years, with many perennial All-Stars already at their peaks.

When Jerry Colangelo took over as director of USA Basketball in 2005, he demanded more long-term commitments from players (but this requirement didn’t make the team younger; although older players largely made up the 1990s Dream Teams, the average age of Team USA declined in the early 2000s and has remained fairly constant between 24 and 26 since then).

Assuming the average boost continues after the 2014 FIBA World Cup, here’s how Team USA players are expected to perform in the next NBA season.

Of course, there are a few limitations to this analysis. First, Team USA members aren’t randomly selected, and it may be that the coaching staff now picks players they deem to be on the rise. It’s also worth noting that the Simple Projection System is a metric designed for use on the average NBA player, so it may need tweaking when applied to the stars of Team USA. Also, the system is probably too conservative about adjusting for a player’s age.

Still, it appears instruction from Coach K and training and playing with peers atop the basketball universe may have positive, long-lasting effects. That may be reason for NBA teams to think twice before holding players out from international competitions.

The income of the median U.S. household was $51,900 in 2013, the Census Bureau reported Tuesday. That’s essentially unchanged from 2012, after adjusting for inflation, and is 8 percent lower than in 2007, before the recession began. Median income hasn’t shown a statistically significant increase since the recession ended in 2009. Median income is an imperfect measure of financial well-being. The government’s official measure ignores noncash benefits, such as food stamps, and after-tax benefits, such as the Earned Income Tax Credit. Moreover, it doesn’t account for demographic changes, such as the aging of the population and the shrinking of the typical household. Adjusting for those changes would probably show at least some improvement in income, especially over the longer term. Still, Tuesday’s report makes clear how little progress the American middle class has made — not just over the past few years, but over recent decades. Median household income was lower in 2013 than in 1989 and is 8.7 percent below its 1999 peak. The pain hasn’t been shared equally. The average income of the bottom fifth of earners has fallen 16 percent since 1999, compared to 2 percent for the richest fifth. The top 20 percent of earners accounted for 51 percent of all income in 2013, unchanged from 2012 and up slightly from 49.4 percent in 1999. The “gini index,” a measure of income inequality in which 0 represents perfect equality and 1 represents perfect inequality, was essentially unchanged in 2013 at 0.476. But it remains high by historical standards. Tuesday’s report did have glimmers of progress. The official poverty rate fell to 14.5 percent from 15 percent, and the child poverty rate fell for the first time since 2000. More people, and especially more men, worked full time in 2013. And fewer people went without health insurance. Here are a few other interesting data points from Tuesday’s report: Young, old see gains: The weak recovery has hit young people especially hard; the unemployment rate for Americans younger than 25 is still 13 percent, more than double the 6.1 percent for the population as a whole. But the “lost generation” may at last be seeing some gains. Americans ages 15 to 24 saw their household income rise 10.5 percent in 2013, the biggest increase for any group, though they are still earning 4 percent less than before the recession. Those 65 and older, meanwhile, saw their incomes rise 3.7 percent. No other age group saw statistically significant income gains. But young people’s gains come with an important caveat: Household income figures are based on the age of the “householder.” So-called boomerang children, 20-somethings living in their parents’ basements because they can’t find good jobs don’t count as their own households and thus are left out of those numbers. (Their income still counts, but it’s part of their parents’ household income.) Still, even looking at individual income, rather than household income, young people saw modest progress; their median individual income rose 2.7 percent, faster than any other age group. Pay gap narrows: Women working full time, year-round earned 78 cents for every dollar men made in 2013. The Census Bureau’s measure of the gender pay gap is crude, ignoring differences in hours worked, education, industry and numerous other factors. (Even adjusting for those factors, however, the pay gap is larger than zero by almost every calculation.) Still, while the exact number may not be meaningful, the trend is significant. The pay gap, which had been stuck at 77 cents on the dollar for nearly a decade, narrowed by a penny in 2013, the first change since 2004. The shift was due to rising earnings for women, not falling earnings for men. Big racial gaps remain: The median income of an African-American household was$34,600 in 2013, more than 40 percent less than the median non-Hispanic white household. The race gap has been little changed in recent years. It peaked at about 45 percent in the 1980s and narrowed to 35 percent in 2000, but has since lost much of that ground. More than a quarter of blacks live below the official poverty line, compared to 10 percent of whites.

Hispanics, however, saw modest income gains in 2013, though their $41,000 median household income is still about 39 percent less than whites’ and their poverty rate, at 23.5 percent, is far higher. Asians had the highest median income of any racial group, at$67,000.

An imperfect poverty measure: Tuesday’s report included data on Americans living beneath the official poverty line, which in 2013 was about $15,162 for a family of two. But economists widely regard the official poverty rate as misleading. It ignores benefits that keep millions of people out of poverty and fails to account for regional variations in the cost of living, among other significant weaknesses. An alternative measure, which is seen as more accurate, won’t be released until next month. Last year’s alternative measure showed overall poverty was higher than the official measure indicated, but lower among children. Lots more data: The Census Bureau released far more data Tuesday than it included in its main report. Dozens of tables break down income by age, sex, education, marital status and other factors, and a separate widget allows users to create their own tables. And there’s more to come: On Thursday, the Census Bureau will release results from the 2013 American Community Survey, which will provide a detailed look at demographics and earnings by state and local area. We’ll have more for you as we dig through it all. ### Comments Add Comment I was troubled by a survey released Monday by Mitchell Research in Michigan. It wasn’t that the results — which showed Democratic Rep. Gary Peters leading Republican Terri Lynn Land by 2 percentage points in the U.S. Senate race and Republican Gov. Rick Snyder leading Democrat Mark Schauer by 5 points in the governor’s race — were necessarily wrong. It was how Mitchell said it arrived at them that bothered me. From the Mitchell release: Mitchell Research had intended to release a survey today that we conducted on Wednesday, Sept. 10th, prior to President Obama’s speech to the nation regarding the conflict in the Mid-East. That poll showed Snyder leading by only 1 point, and Peters up by 8 points. However, because of changing poll data nationally, we decided to conduct a survey last night (September 14) to see if those events coupled with the increased television advertising by Snyder and Land might have changed the races in Michigan. Here’s one way to read this: Mitchell Research conducted a poll, thought the results looked wrong and decided to conduct another survey to get results it thought made more sense. That would be fine if Mitchell released the full data from the first poll. But it didn’t. A pollster should release its work regardless of whether it thinks the results are right. Outliers happen even to the best pollsters. They are supposed to happen. And, of course, a pollster has no way of knowing whether a result is an outlier. Sometimes when a poll appears to be an outlier, it’s the first survey to pick up real movement in a race. And sometimes when a poll fits neatly into previous surveys, all the surveys end up being wrong. Squashing results, however, suggests a pollster is looking at other pollsters’ work (beyond its weighting mechanism) to determine whether data is worthy of publication. Such decisions can lead us down a bad path. When a pollster holds back some data, we can’t be sure what other results it might be holding back or changing. What might have happened if Mitchell Research’s second poll didn’t seem to match what it thought it should be? Would it have conducted a third poll? What happens when there are other results Mitchell Research doesn’t like? And though it’s beside the point, I should note that Mitchell’s explanation for the change in results has no backing from the majority of other polls. President Obama’s approval rating is the same as it was a week ago, according to the aggregate of polling information. There hasn’t been a big swing to Republicans in the majority of other Senate races. The FiveThirtyEight estimate actually gives Democrats a better shot at holding on to the Senate than they had a week ago. But not releasing all results that were meant for public consumption is sketchy, even if it’s thought that those results might be wrong. ### Comments Add Comment Scottish residents will go to the polls Thursday to decide whether they want to split from the United Kingdom. On many public policy questions, Scotland is already divided from much of Britain, which is part of the rationale behind the independence movement. But just how much of an ideological outlier is Scotland? Each year, London-based NatCen Social Research gets more than 3,000 people to take the British Social Attitudes survey (the poll covers Britain but not all of the U.K.; Northern Ireland is excluded). Responses are available on the British Social Attitudes Information System website, which is free with registration. I downloaded data for 23 questions on policy. I chose questions that cover broad areas of concern for Britain but don’t directly ask about Scotland or Scottish independence. The questions covered public benefits, the European Union, nuclear weapons, immigration, the death penalty, pollution and income redistribution (20 of the 23 can be found in the tables below). I then compared the data across the six regions the BSA uses to define Britain: Scotland, Wales and four part of England — Greater London, the South, the Midlands and the North. This isn’t a definitive study of how Scots differ from fellow Britons. It doesn’t cover demographics, culture or history, such as the Battle of Bannockburn, part of an England-Scotland war whose 700th anniversary coincides — perhaps not coincidentally — with this week’s referendum (some have already cast their ballots). It also relies on a survey that only 284 Scots answered for many questions, and fewer for others that aren’t asked of the whole panel. Others might also choose different questions than I did. And the survey doesn’t extend north of the Caledonian Canal, which omits the northernmost reaches of Scotland. Nonetheless, the BSA was about as good a tool as I could find to see how much Scots diverge from other Brits, and how that compares to division among the rest of Britain. For each question in each region and for Britain as a whole, I defined a net score. For example, for a question asking whether respondents would want to see more or less government spending on benefits for single parents, I added the percentage of people who said they’d want to see “much more spending,” and of those who said they wanted to see “more spending.” Then I subtracted the percentage of respondents who chose “less” or “much less.” Scotland’s net score was 28.9 percentage points. In Britain overall, it was 11.9 points. For each question, I calculated the absolute value of the difference between Scotland’s net score and every other region’s. Then I averaged that gap for each pair of regions, over all 23 questions. I found that Scotland differed, on average, by about 8 percentage points from Greater London, 9 points from Northern England, 11 from Wales, 12 from the Midlands and 13 from the South. I then calculated the same gaps for every pair of regions: How much do Greater London and Wales differ, for instance? How about the South and the North? Nearly every other region’s most distant ideological neighbor was Scotland. The gap was largest for the South, which was 13 percentage points apart from Scotland, on average, but placed within 9 points or fewer relative to every other region. The one exception was Greater London, which was closer to Scotland than to the South and the Midlands — the two regions that are closest to Greater London. Scotland is generally more liberal than the rest of Britain, but the regions don’t split along obvious ideological lines. For example, Scottish and Welsh respondents were in close agreement on benefits: They wanted to expand them. But they were sharply divided on pollution and cars (Scots were much more supportive of road-use savings for drivers of cars that are better for the environment), immigrant rights (Scots were much quicker to grant immigrants benefits and voting rights) and the death penalty (the Welsh favored it as a punishment in at least some cases much more strongly). For each question, I also evaluated what the Scottish answer was — whether the net score for Scottish respondents was above or below the net score for all British respondents. Then for respondents from each of the other five regions, I counted the number of questions for which they gave answers in the same direction as the Scottish answer. For instance, Scots were more anti-nuke than average, and so were the Welsh and Londoners, but everyone else was more pro-nuke than average. By this measure, Greater London was the most Scottish part of Great Britain. The South lined up with Scotland on just two questions, and the Midlands on just six. The North agreed on 11, and the Welsh on 12 — just over half. But Greater London agreed on 21 of 23 questions. So, why was the average divergence between Londoners and Scots not much smaller than the ones between Scotland and the other regions? In part because Londoners were more of an outlier than the Scots. Geography and history militate a breakaway Scotland-London republic as much as, say, a California-New York one. And London is hardly the only capital that is far more liberal than the rest of the country. But on policy preferences, Scotland and the home of the government it might reject Thursday have more in common than many other regions between them. ### Comments Add Comment When we officially launched our forecast model two weeks ago, it had Republicans with a 64 percent chance of taking over the Senate after this fall’s elections. Now Republican chances are about 55 percent instead. We’ve never quite settled on the semantics of when to call an election a “tossup.” A sports bettor or poker player would grimace and probably take a 55-45 edge. But this Senate race is pretty darned close. What’s happened? The chart below lists the change in our forecast in each state between Sept. 3 (when our model launched) and our current (Sept. 15) update. As you can see, there hasn’t been an across-the-board shift. Republicans’ odds have improved in several important races since the launch of our model. Democrats’ odds have improved in several others. But the two states with the largest shifts have been Colorado and North Carolina — in both cases, the movement has been in Democrats’ direction. That accounts for most of the difference in the forecast. It might help to break the states down into several groups: • Republican defenses (Georgia, Kansas, Kentucky). These are the three Republican-held seats where Democrats have some chance for a pickup. Democrats got good news in Kansas two weeks ago when their own candidate, Chad Taylor, ceased his campaign in the state — improving the odds for the center-left independent candidate, Greg Orman. Orman, however, is a slight underdog against the Republican incumbent Pat Roberts, and Orman isn’t certain to caucus with Democrats if he wins. Meanwhile, Democrats’ odds have declined somewhat in Georgia and Kentucky. Taken as a group then, these states have not produced much change in the overall forecast. • Republican path of least resistance states (Alaska, Arkansas, Louisiana, Montana, South Dakota, West Virginia). These are the six Democratic-held seats in deeply red states. If the GOP wins each one — while holding all their own seats — they’ll win the Senate. Republicans remain favored in each of these six races, and their odds haven’t changed much since we launched our forecast. (They’re doing a tiny bit better in Alaska and a tiny bit worse in Louisiana, but these changes cancel out.) • Highly competitive purple states (Colorado, Iowa, Michigan, New Hampshire, North Carolina). These are the five competitive Senate races — all seats are currently held by Democrats — in states generally considered presidential swing states. It’s here where Democrats have gained ground. There have been numerous recent polls in North Carolina, including two released on Monday, showing Democratic Sen. Kay Hagan ahead. Her odds of holding her seat have improved to 68 percent from 46 percent when the model launched. Colorado has followed a similar path, with Democratic Sen. Mark Udall’s chances of keeping his seat improving to 69 percent from 47 percent. Democrats have also made smaller gains in Iowa and Michigan. New Hampshire has been an exception. The model isn’t buying that the race is tied, as a CNN poll implied Monday, but it does have Democratic Sen. Jeanne Shaheen’s chances falling from 81 percent to 75 percent. • Republican reaches (Illinois, Minnesota, New Jersey, Virginia). These states are only on the fringe of being competitive and haven’t received much attention from the news media or from pollsters. But each has been polled at least twice since our model launched. Those polls haven’t shown Democrats gaining or losing any ground — but they have confirmed Democrats are ahead, often by double-digit margins. Our model shows more confidence as the volume of polling increases, so these polls have also slightly helped Democrats. Most of the Democrats’ gains, however, have come from the purple states. What’s perplexing is that this has happened right as Democrats’ position on the generic congressional ballot — probably the best indicator of the national mood — has deteriorated. Historically, the generic ballot and state-by-state Senate polls — while not perfectly correlated — have moved in tandem more often than not. On average since 1990, a one-percentage-point change in the generic ballot has translated to a half-point change (in the same party’s direction) in the average Senate race. Might Democrats be benefiting from strong voter outreach in these states — perhaps the residue of President Obama’s “ground game” in 2012? You could make that case in North Carolina, where two polls released on Monday showed a smaller gap between registered and likely voters than most other states that have been polled this year. But this story isn’t so consistent. By contrast, CNN’s poll of New Hampshire on Monday had a conspicuously large turnout gap. And in 2010, presidential swing states showed an especially large turnout drop-off for Democrats. Money could be a more important factor. Consider the states with the largest polling movement: In North Carolina, Hagan had$8.7 million in cash on hand as of June 30 as compared with just $1.5 million for her Republican opponent, Thom Tillis. In Colorado, Udall had$5.7 million as compared with \$3.4 million for Republican Cory Gardner.

These totals do not account for outside spending. But in stark contrast to 2010, liberal and Democratic “super PACs” have spent slightly more money so far than conservative and Republican ones, according to the the Center for Responsive Politics. (One caveat for Democrats is that when money is spent on advertising, it can sometimes have short-lived effects.)

Whatever the reason, the GOP’s path to a Senate majority is less robust than before. They still look pretty good in the “path of least resistance” states. But while West Virginia, Montana and South Dakota are extremely likely pickups, Alaska, Arkansas and Louisiana are not sure things. Meanwhile, Republicans have fewer top-tier backup options, as states like North Carolina and Colorado have trended away from them. Republicans may need to decide whether to consolidate their resources. It won’t help them if they lose each of Colorado, Iowa, New Hampshire and North Carolina by a couple of percentage points — and in the process blow a state like Arkansas.

New Yorkers may be proud that Kira Kazantsev brought home the title of Miss America on Sunday, giving the Empire State the crown for the third consecutive year. But singers across the country probably don’t feel the same amount of delight (they probably weren’t tuning in), despite the fact that Kazantsev’s talent was a vocal performance of Pharrell Williams’s “Happy.”

Unlike New Yorkers, who can only claim six Miss America titles, this was the 46th win for a vocalist (there was no talent portion for eight years of the 88-year pageant). In fact, despite the competition’s historical reputation of less serious plate-spinning and baton-twirling, musical performances — singing, dancing and playing an instrument — dominate.

The 1945 to 1964 period is notable, however. Of its winners, nine performed dramatic recitations as their talent.

These days, such recitations are few and far between. Since 2010, there have been only three that could (with a stretched definition) fit into that category: two comedic monologues (Miss Montana in 2013 and this year’s Miss Maine) and one act of ventriloquism (this year’s Miss Ohio). Of the 318 performances since 2010, just 10 do not explicitly fit into the singing, dancing or musical instrument categories. (A quick note: There were two winners in 1984 because Vanessa Williams stepped down.)

Musicality wins. Why stray from the tried-and-true when no one has won the title by doing so since 1979 (in which the nonconformist was Miss Virginia, with a gymnastics routine)?

But in a competition to be “Miss America,” it’s worth asking how well these women actually represent America. Is a plethora of musical performances indicative of a particularly musical people? Data on how many recreational singers, dancers, instrument-players, comics and ventriloquists we have in the United States is hard to come by, but the Census does give us a way to approximate an answer.

The 2010 Census asked people whether they had participated in various leisure activities within the past year, and although nearly half of the respondents ate out in that period, the numbers aren’t as high for singing, dancing and playing an instrument.

Every Monday, the National Bureau of Economic Research, a nonprofit organization made up of some of North America’s most respected economists, releases its latest batch of working papers. The papers aren’t peer-reviewed, so their conclusions are preliminary (and occasionally flat-out wrong). But they offer an early peek into some of the research that will shape economic thinking in the years ahead. Here are a few of this week’s most interesting papers:

Authors: Alex Edmans, Luis Goncalves-Pinto, Yanbo Wang, Moqi Xu

What they found: CEOs release more discretionary company news during months when their stock holdings or stock options vest.

Why it matters: For many CEOs, their compensation includes stock (or “equity”) grants, but these grants do not vest, or become salable, often until many years in the future. As part of their job, these executives interact with the public by releasing company news, some of it mandatory and some at their discretion. The authors of this paper find that CEOs are strategic in unveiling discretionary company news so that it coincides with months when their stock holdings or options vest. Because these stock grants were made contractually several years prior to the vesting date, it is “exogenous” to the state of the company’s news. Yet, compared with non-vesting months, CEOs release 2 percent more discretionary news — that is, news not required by regulation, such as quarterly filings to investors — while the amount of nondiscretionary news is unchanged. The discretionary news is often positive in nature, temporarily boosting the stock price exactly when the CEO can cash in.

Key quote: “Discretionary disclosures are significantly higher in months in which equity is scheduled to vest, and significantly lower in the months before and after vesting. They are associated with favorable media coverage, suggesting that they are positive in tone. The news releases lead to temporary increases in the stock price and trading volume, consistent with an attention story. CEOs exploit these temporary effects: the median CEO sells all his vesting equity within 7 days of a discretionary news release in a vesting month.”

Data they used: Data on months when CEO equity is vested, from the Equilar data set (2006-11) and data from proxy statements and SEC Form 4 filings (1994-2005); news events from Capital IQ’s Key Developments database

Authors: Casey Ichniowski, Anne Preston

What they found: A professional soccer player’s performance improves faster after playing on an elite team rather than on a lower-level team.

Why it matters: There is a vast economic literature documenting how worker productivity is especially influenced by high-performing peers. To explore these “peer effects,” the authors study professional soccer players to see whether playing with other elite players accelerates their performance gains. Given that better players get invited to play on better teams, the researchers had to disentangle this selection effect to isolate their performance gains. To do this, they used two novel comparisons: 1) how players perform on their national-level teams before and after joining an elite professional team and 2) how foreign players performed after the 1995 Bosman ruling, which banned restrictions of foreign players on European club teams. Using these controls, the authors find significant and lasting effects on player performance after stints with other elite players. This analysis was bolstered by a separate study using individual player tracking data.

Key quote: “An increase of one or two players on a national team joining an elite club can lead to substantial improvement in national team play that can change the world ranking of the team by several spots.”

Data they used: A national team data set covering 101 countries, as well as data on elite professional European club teams, from 1990 to 2010; player-level data from Opta

Authors: Alberto Basso, Howard Bodenhorn, David Cuberes

What they found: The hypothesis that individuals have more children as insurance for themselves in old-age seems to be born out (zing!) in the data.

Why it matters: Economists in the 1970s proposed a theory — called the old-age security hypothesis — that individuals would have more children as a means to transfer income back to themselves later in life, the implication being that fertility levels and financial development (like banking, insurance, etc.) should be inversely correlated. Using county-level data from 1850, the authors seek to test this theory. They find that the presence of a bank in a county, after controlling for other demographic and economic variables, leads to a reduction in the child-woman ratio of about 3 percentage points.

Key quote: “We find a robust negative correlation between financial development and fertility, which strongly supporting the old-age security hypothesis. We do not argue that the old-age security motive is the main — nor even the most important — factor. … Our results are rather interpreted as highlighting the importance of financial development as a mechanism reducing parents’ incentives to have a large number of offspring.”

Data they used: County-level data from the Northeastern United States from 1850.

Senator Mark Begich, Democrat of Alaska.

Bill Clark / CQ Roll Call

The Senate race in Alaska is as important as any in the country. As we’ve described previously, Republicans can win a Senate majority by winning the race there along with those in five other deeply red states: Arkansas, Louisiana, Montana, South Dakota and West Virginia. But Alaska is probably the toughest “get” of the six for the GOP.

Unfortunately, Alaska has received very little polling — and just about every poll we do have from the state has been either an Internet poll, an automated poll or a partisan poll. The stronger pollsters seem to be avoiding the state — perhaps for good reason.

A new, partisan poll of Alaska came out over the weekend. The survey, conducted for Senate Majority PAC by Harstad Strategic Research, shows the Democratic incumbent Mark Begich leading his Republican opponent Dan Sullivan 45 percent to 40 percent. That contradicts the last two nonpartisan polls of the state, which had shown Sullivan ahead.

Senate Majority PAC’s goals are pretty clear; its mission is to “protect and expand the Democratic majority in the U.S. Senate.” Longtime readers will know that we’re not fans of partisan polls, which tend to be inaccurate and biased.

But defining a partisan poll can be tricky. Many pollsters release some polls on behalf of campaigns, while publishing other results under their own names. Some polls have ties to interest groups that aren’t well disclosed: For instance, the polling firm We Ask America is a subsidiary of the Illinois’ Manufacturers Association. Explicitly partisan blogs and websites have been commissioning more of their own polls in recent years (of course, many people would claim that traditional media outlets like Fox News and the New York Times have their own biases).

We’ve experimented a lot with different definitions of what constitutes a partisan poll over the years and decided we’re not inclined to play “poll police” in borderline cases. So since 2012, we’ve been excluding only polls conducted directly on behalf of campaigns or party groups like the Democratic Senatorial Campaign Committee and the Republican National Committee. Everything else gets included in the FiveThirtyEight model — including this weekend’s Alaska poll.

But the model has a defense mechanism: its house effects adjustment, which evaluates polls for signs of a partisan lean and adjusts them accordingly. In this case, the model detects a significant Democratic house effect in Harstad’s polls, and it treats the Alaska survey as showing the equivalent of a 1 or 2 percentage-point lead for Begich, instead of a 5-point advantage. The poll still helps Begich some — his chances of winning the race jumped from 31 percent to 38 percent — but not nearly as much as if a nonpartisan pollster had shown the same result.

But there’s another reason to be suspicious of the poll — and others that purport to show Begich ahead in Alaska. As other commentators have noted, Alaska is a hard state to poll accurately. What we haven’t seen remarked upon is how those misses have come in one direction, almost always overestimating the performance of Democrats.

The table below lists Alaska results from our pollster ratings database, which covers polls conducted in the last three weeks of campaigns since 1998. (We’ll be publicly releasing this database soon.) For each race, I’ve compared the polling average against the actual margin, excluding the 2010 Senate campaign where the top two finishers were both Republicans, Joe Miller and Sen. Lisa Murkowski (who ran as a write-in candidate after losing her primary).

In every single race, the polls have shown a Democratic bias. In 2008, for instance, Begich was favored by almost 10 percentage points in the polls against the Republican incumbent Ted Stevens, but won by barely more than a percentage point. Also that year, the polls favored the Democrat Ethan Berkowitz to win the state’s at-large House district from the Republican incumbent Don Young, but Young prevailed instead. In 2004, the polls had the Democrat Tony Knowles, the state’s former governor, tied in his race against Murkowski, but Murkowski won by three points. In 2010, the Republican gubernatorial candidate Sean Parnell by a margin much larger than the polls anticipated. On average since 1998, polls of Alaska have had a 7-point bias toward Democrats.

The FiveThirtyEight model does not account for this property, but it’s something to keep in mind as you peruse polls of the state. The model does, however, include a “state fundamentals” estimate for each state, based on factors like fundraising and state partisanship, and includes it along with the polls.

The state fundamentals estimate does not receive very much weight in the model — it represents only about 15 percent of the projection in Alaska, for example, and as little as 5 percent in some other key states with more abundant polling.

Still, it can be interesting to look at. In Alaska, while our adjusted polling average puts Sullivan ahead by just one percentage point, the fundamentals estimate has him as an 8- or 9-point favorite instead. That gap of about seven points is right in line with the historical Democratic bias in Alaska polls.

Overall — also accounting for new polls in Louisiana and Georgia — the FiveThirtyEight forecast is not much changed. It shows Republicans with a 58 percent chance of winning the Senate majority, down just slightly from 59 percent Friday.