Scott Van Pelt believes a playoff berth is no longer a dream for the Raiders, but something that is bound to happen this season. (2:20)

Luck is a dirty word in football circles, at least outside of Indianapolis. After putting in hours upon hours of mental and physical preparation week after week, no successful football team wants to believe that it is winning games because it has been lucky. The struggling teams might want to believe that they're unlucky, but once they turn things around, you better believe they'll be pointing toward hard work, resilience and improved play, not good bounces and the vagaries of randomness.

Yet, taking a step back, we know luck can play a huge role in determining football games. Luck tends to even out over a larger sample, which naturally means that luck matters more when fewer games have been played. It matters more and plays a bigger part in a half-season, as an example, than it does over a full campaign. It's with that exact argument in mind that we're going to take a look at how luck has influenced the first half of the NFL season today.

Luck is shorthand here for a number of concepts; a better word would be randomness or variance, but luck will do. If you've been reading my work for the past few years, you'll be familiar with many of these concepts (although I did not invent many of them). If not, you can read about many of them here. I last wrote about them before the season in suggesting that the Panthers and Broncos would decline, while the Cowboys and Chargers would improve. So far, so good.

Pythagorean expectation

Point differential is a better predictor of future win-loss record than current win-loss record. It's true in baseball, and research (by Rockets general manager Daryl Morey during his time at STATS) has reiterated the accuracy of that statement for football as well. We can generate an expected win total for each team by running their point totals through the Pythagorean expectation formula -- Points For2.37 / (Points For2.37 + Points Against2.37) -- and multiplying it by the number of games each team has played.

We're already seeing the impact of last year's Pythagorean expectation in 2016.

The five teams who outperformed their point differential most significantly last year were Carolina, Denver, Indianapolis, Minnesota and San Francisco. They've underperformed their point differential this year by 1.9 combined wins.

The five teams who most underperformed their point differential last year, meanwhile, were San Diego, Tennessee, Seattle, the New York Giants and Jacksonville. They're still underperforming their expected win totals in 2016, but only by a combined 0.4 wins.

Looking at 2016 performance, there are two teams who stand out as well ahead of their point differentials, and several who are likely to improve comfortably in the coming two months:

Best, Worst Pythagorean Differential (2016) Team Record Pyth Wins Diff Team Record Pyth Wins Diff Raiders 7-2 5.0 2.0 Browns 0-9 2.2 -2.2 Texans 5-3 3.1 1.9 Cardinals 3-4-1 5.1 -1.6 Giants 5-3 3.9 1.1 Eagles 4-4 5.5 -1.5 Chiefs 6-2 4.9 1.1 49ers 1-7 2.1 -1.1 Cowboys 7-1 6.0 1.0 Bills 4-5 5.0 -1.0

The Raiders and Texans have produced better records than their point differentials (and underlying level of play) would suggest. The good news for the Raiders is that it shouldn't really matter; even if they play like the just-above-.500 team their point differential suggests over the rest of the way, they've already banked enough wins to make it into the postseason. Indeed, ESPN's Football Power Index gives them an 80.9 percent chance of making it into January. The Texans are down at 64.5 percent, and even that is only because the rest of their division is so dreadful. They're playing like a 6-10 team this year.

Derek Carr's late-game work has helped the Raiders sneak past their expected win total based on scoring differential. Ezra Shaw/Getty Images

Things should improve for the Browns, but their second-half performance won't really matter for entirely different reasons. This is more tangible information for fans of the Cardinals and Eagles. (I'm counting the tie as a half-win for Arizona.) While Arizona has been disappointing this season, the dramatic shift in its win-loss record overstates the drop-off. Point differential suggest that the 13-3 Cards were a 11.9-win team last year and would have them on pace to be a 10.2-win team this season.

The Eagles, sadly, might have sunk their own chances. They've surrounded statement wins over likely playoff teams in Pittsburgh and Minnesota with narrow losses to the Lions and the three other teams in the NFC East, all by one score or less. Likewise, the Bills turned around their season after an 0-2 start by winning four straight, but three consecutive losses -- including one-score defeats at the hands of the Dolphins and Seahawks -- might doom their playoff hopes.

Record in close games

Where gaps in Pythagorean expectation reside, unlikely good or bad luck in close games tends to follow. Performances in one-score games are generally inconsistent from year to year, and we're already seeing that with the standouts from last year. Last year, the five best teams in the league in games decided by one touchdown or less were the Panthers, Cardinals, Broncos, Vikings and 49ers. They were a combined 27-9 (.750) in one-score games last year; this season, they're 3-8-1 (.292) in those same contests.

Meanwhile, the dregs of the league have improved. The five worst teams in close games last year were the Browns, Cowboys, Giants, Titans and Chargers. (Well, some of them have improved.) They were a combined 11-33 (.250) in one-touchdown games last season, and in 2016, they're 11-13 (.458). Regression toward the mean is a strong concept here.

Five teams have gone winless in close games in 2016, with the Cardinals having a mere tie to their name as the sixth:

Best, Worst Record In Close Games (2016) Team Close Games Team Close Games Texans 4-0 1.000 Bills 0-4 0.000 Patriots 2-0 1.000 Browns 0-4 0.000 Raiders 5-1 0.833 Eagles 0-4 0.000 Bengals 1-0-1 0.750 49ers 0-1 0.000 Cowboys/Chiefs 3-1 0.750 Steelers 0-1 0.000

The Bills, Browns and Eagles all reappear on this list thanks to their combined 0-12 record in one-score contests. The Texans and Raiders show up on the other side of the coin. The 5-2 Giants lurk just behind the Cowboys and Chiefs in terms of teams riding their luck in close games; the only game they have played that wasn't decided by seven points or fewer was their 14-point defeat at the hands of the Vikings in Week 4.

Fumble recovery rate

Forcing fumbles is a skill, and giving away fumbles is a legitimate liability. What happens once the ball hits the ground is mostly randomness. No team has exhibited a steady ability to recover a disproportionately high percentage of the fumbles in their games. Not even that team you know who runs fumble recovery drills in practice and makes it a priority. (All teams do that.)

Who recovers this fumble is almost entirely random. Thus far in 2016, the Giants' "fumble luck" has been poor. Michael Reaves/Getty Images

If we know the rate at which fumbling teams recover the football, we can estimate how many fumbles each team "should" have recovered. Last year, that was 53.7 percent. (This year, as Chase Stuart noted last week, it's closer to 57 percent.) The teams who outperformed their expected fumble recovery rates the most in 2015 were the Raiders, Texans, Giants, Bills and Jaguars. Those teams have actually recovered two fewer fumbles than league average given their combined opportunities this season. Again: It's random, folks, not a symptom of aggression or lack thereof. The Giants and Jags each ranked among the five "best" teams in the league in terms of fumble recovery rate last year; in 2016, they're the first and third worst in terms of rate.

On the other hand, the Cowboys, Patriots, Lions, Titans and Colts were the five worst teams in terms of fumble recoveries below expectation last season. This year, they've combined to recover 0.9 fumbles more than a typical team, basically leaving them at league average. Where are the outliers in 2016?

Fumble Recovery Rate (2016) Team Fum Rec ExpRec Diff Team Fum Rec ExpRec Diff Eagles 29 17 14.4 2.6 Giants 21 5 10.7 -5.7 Steelers 23 14 11.4 2.6 Panthers 14 3 7.0 -4.0 Rams 21 13 10.4 2.6 Jaguars 19 6 9.7 -3.7 Buccaneers 23 14 11.6 2.4 Dolphins 23 9 11.3 -2.3 Saints 20 12 9.6 2.4 Falcons 17 6 8.0 -2.0

The big one is Big Blue.

The Giants have lost eight of their 12 fumbles on offense, but even more distressingly, they've forced nine fumbles on defense and recovered just one of them for an 11 percent rate. Those rates can't continue. The Panthers are just behind them, having lost all seven of their fumbles on offense this year when we would expect them to recover four of the seven lost footballs. The Jags, just 2-for-8 in recovering fumbles on defense, lurk just behind. The grouping on the other side isn't quite as extreme.