In light of the San Francisco 49ers’ narrow 19-13 defeat to the Arizona Cardinals at Levi’s Stadium last week — which stood in stark contrast to the 40-point beatdown that took place in Glendale back in September — there has been a good amount of discussion this week on the disparity in performance of Jim Tomsula’s team at home versus on the road.

On one hand, this obviously makes sense; over a large enough sample every NFL team plays better at home than they do on the road. But has that gap been larger for the 49ers in 2015 than we would expect from your average team? And if so, is there any reason why that’s been the case?

I’m typically less inclined to pay much attention to the official NFL rankings many will use for this type of thing, which are based on total yardage and can be skewed by the game script (e.g., good teams will often allow more passing yardage because their opponents are frequently trailing and trying to catch up). So I wanted to take a quick look at some different home/road splits that should add a bit more context.

Point Differential

Let’s start with the most basic measure. Point differential is a better indicator of performance than straight win-loss record because of sample size. Theoretically, teams can score, or be scored on, on any given play, whereas teams only have 16 chances to win or lose a game over the course of the season. Here are the five teams with the largest deviation in point differential when they’re at home as opposed to on the road in 2015:

The 49ers are getting outscored by an average of three touchdowns per game on the road this season, comfortably the worst margin in football with Washington’s 15.2 points per game figure as the next closest. Over their five road games, San Francisco has only managed to finish within one score of their opponent once, a three-point loss to the Giants in Week 5.

San Francisco doesn’t suddenly become good at home — they’re still getting outscored by 2.3 points per game — but they do become more competitive. However, even that figure is propped up a healthy amount by their now-bizarre season-opening win over the Vikings. Remove that game and the 49ers have been outscored by an average of 6.2 points per game at home, which would be the league’s sixth-worst figure and would bring their home/road point differential down to 14.8, dropping them below the Saints in our table above. Regardless, we’re talking about at least a two-touchdown improvement when San Francisco stays at Levi’s.

DVOA

It’s clear that, at least in 2015, the 49ers receive a larger boost by playing at home than the average NFL team. But is there one unit more responsible for that boost? Football Outsiders offers home/road splits for offensive and defensive performance in their premium database, which should give us a good indication of how much better San Francisco’s individual units are at home relative to the rest of the league. Let’s start with the defense, which is where most people have attributed the 49ers’ improved home performance.

A couple of quick reminders about DVOA for those who are unfamiliar. DVOA is adjusted for opponent, game situation, and other factors, which gives us a more accurate representation of team or unit performance than yardage. Negative numbers are better for the defense, positive numbers are better for offense, and 0.0 percent is average.

As you can see, the 49ers defense has the league’s largest upward swing in performance when at home, going from a figure that ranks them as one of the worst defenses in football to roughly average performance. That’s a massive swing, and you’d have to go back to the 2011 Chargers and Ravens to find a defense that benefitted more from playing at home, according to DVOA.

That might not be terribly surprising for many of you, as many have suggested the 49ers defense has been much better at home this season. More surprising, perhaps, is that San Francisco’s offense has seen a similar bump.

It’s not quite as drastic as the leap in defensive performance, but the 49ers offense still sees one of the league’s biggest jumps when at home, once again approaching mediocrity from bottom-dweller performance on the road.

If you were looking closely at the last two tables, you might have noticed that the 49ers are the only team to show up on both lists. In fact, the Chiefs are the only other team to see even one of the 10-largest jumps in performance at home, let alone top-five, on both offense and defense, finishing ninth and 10th, respectively.

Schedule

My initial reaction to the data above was that the 49ers’ schedule had to be a bit friendlier at home, which would help explain why they’ve seen such significant splits this season, but that doesn’t appear to be the case.

Football Outsiders doesn’t have strength of schedule home/road splits publicly available anywhere, but using the average rank should suffice here. And as you can see, there’s been virtually no difference between the quality of competition the 49ers are facing at home compared to on the road. That holds true even if we look strictly at out-of-division games, where home opponents would have an average DVOA rank of 14.5 and away opponents would land at 14.7.

Looking ahead to San Francisco’s remaining five games, these numbers don’t bode well for the 49ers adding many more victories this season.

In a vacuum, four of those remaining five contests would qualify as winnable, with the Bengals as the clear exception (obviously, "Any Given Sunday" and all that, but c’mon). Three of the other four are road games, and the one home game is against the Rams, who I would probably put as the best of the bunch at his point, though the Bears, Lions, and Rams are all pretty close.

So to summarize, three-quarters of San Francisco’s remaining winnable games come on the road, where they’ve pretty comfortably been the worst team in football, and their two remaining home games, where they’ve played at roughly a league-average level, come against the two toughest opponents left on the schedule. I guess depending on your motivations for the rest of this season, that could be either a really good or really bad thing.

♦♦♦

While it’s clear the 49ers have been a much better team at home, I’m hesitant to search for too many more reasons why. As I mentioned at the top of the article, every team is better at home over a meaningful sample. Since 2002, when the current schedule and division structure was established, there’s not a single team that doesn’t have a better point differential at home than on the road.

San Francisco has seen a larger increase in performance at home in 2015 than we would typically expect from an average team, but we can likely chalk that up to random variation; every year there will be teams with more drastic home/road splits than others. I went back and looked at numerous seasons worth of data, and if there’s any correlation from one season to the next, it would take someone much smarter than me to find it.

As an example, in 2012, the 49ers had the fourth-largest jump in offensive performance at home. But then, with the same coaching staff and core of players, they had an identical level of performance at home and on the road (9.1 percent DVOA for both) in 2013 before going on to be a markedly better road offense in 2014.

Yes, the 49ers switched stadiums in that time, but when you look at the majority of teams, the point remains. Due to a number of factors, this stuff just isn’t sticky from year to year, and the reasons often given for these extreme splits — new coaching staff, young roster, West Coast team, etc. — are likely nothing more than empty explainers.