Data Analysis: How Quick Have Formula 1 Rivals Closed Gap to Mercedes?

Just four races into the 2014 Formula One season, Mercedes has already opened a 97-point gap to its nearest rival, Red Bull, in the Constructors' Championship.
Powered by the best engine in the field, Lewis Hamilton and Nico Rosberg have combined to win all four of those races, with no other team coming within 23 seconds of the lead Mercedes in any race. In fact, the margins between the top Mercedes and top non-Mercedes finishers have remained remarkably consistent all season:
Australia | Malaysia | Bahrain | China |
---|---|---|---|
24.525s | 24.534s | 24.067s | 23.604s |
But does that mean the other teams are not closing the gap to Mercedes at all?
To answer that, we need to examine some of the other numbers available. Of course, we do not have access to the teams' advanced telemetry, but Rosberg finished second in China without it, so we should be OK.
The main reason that the overall gap between the Silver Arrows and the rest of the field is not a reliable indicator for our purposes is that Mercedes has generally not needed to push their cars to the maximum during the races. Also, safety cars in Australia and Bahrain artificially closed the gaps.

While we can safely assume that the other teams are going as fast as they can, keeping in mind tyre and fuel management, Mercedes is not. Once they have built a comfortable lead in the races, they have been able to back off and manage the gap without stressing their cars.
So, what data can we use to see whether the other teams are getting closer to Mercedes? Two sets of numbers that should demonstrate the cars at, or near, the limits of their performance are the times from Q3, as well as the drivers' fastest laps from the races.
The following charts compare the gaps between the lead Mercedes and the lead car for Red Bull, Force India and Ferrari—the next three teams in the championship. Each of those teams also represent one of the three engine manufacturers this year: Renault, Mercedes and Ferrari, respectively.
A straight comparison of the differences between the Q3 and fastest lap times at the various grands prix does not work, though. A one-second gap is more significant in a one-and-a-half-minute lap at Sakhir than it is in a two-minute lap at Sepang.
Therefore, for our comparison, the times have been converted to a percentage of the lead Mercedes' time, just like for the 107 percent rule in qualifying.
Here are the Q3 results, based on data from the FIA, from each grand prix ("100" on the vertical axis represents Mercedes' time, so the closer the other teams' times are to 100, the closer they are to Mercedes):

The qualifying pace of all three teams has been up and down, depending in part, on which circuits favour certain cars. Both Ferrari and Red Bull were closest to Mercedes, relatively, in Malaysia, while Force India's best performance was in Bahrain. (Not surprisingly, Sergio Perez scored the team's first podium since 2009 in that race.)
Overall, at least according to the Q3 times, the other teams are not closing the gap to Mercedes, though. And that makes sense. Sure, the teams are developing their cars as quickly as they can, but so is Mercedes.
Also, Mercedes' biggest advantage is their power units. With the ban on in-season engine development, there is only so much Renault and Ferrari can do in terms of matching the Mercs' power.
Here are the comparisons of the fastest laps for the teams at each grand prix, again, using the FIA's timing data:

In race trim, the individual results look somewhat different, but the overall point is the same. No one is really catching Mercedes. If they were, we would see a downward trend for at least one team on the graphs, but that is not the case.

It should also be noted that the worst race for Ferrari and Red Bull (and second-worst for Force India) relative to Mercedes was Bahrain. This is significant because Bahrain was the one race where the Mercedes drivers were pushing their cars for most of the race, as they fought a close battle with each other right to the finish.
That is not good news for the rest of the field. When they want (or need) to be, the Mercedes cars can be much quicker than we have seen on a regular basis this year.
In fact, Rosberg indicated at the FIA post-race press conference last weekend that Mercedes' goal is to pull even further ahead at the Spanish Grand Prix. "We want to go to Barcelona with the biggest step, that’s our ambition," he said. "Barcelona is a chance for us to extend the advantage that we have and that’s the approach that we have going to Barcelona."
Another Mercedes 1-2 in Spain will put them at least 113 points ahead of the second-place team. Red Bull's lead after five races last season—when they eventually won the Constructors' Championship by 236 points—was 14 points.