If you don't believe me, watch the game tapes from the matches where Kompany played and compare them to the game tapes from the matches where Kompany was sidelined with injury.
Note here that I am not just saying "City are unbeaten when Kompany starts." Though that statement is true, it does not do nearly full justice to the difference in the way City play when Kompany is on the pitch as against when he is not.
Putting aside the Newcastle blasting on opening day, City were without Kompany for three Premier League matches (at Cardiff City, Hull City, at Stoke City.) Those three matches featured in no particular order: one win, one draw, one loss and shockingly awful centre-back play from Javi Garcia.
Granted, it was not Garcia's fault that neither Kompany nor Matija Nastasic were fit to play at Cardiff City. Even alongside Nastasic at Stoke City, though, Garcia was all at sea.
Kompany came back for City's Champions League opener against Viktoria Plzen and, in hostile territory with prior European failures fresh in their heads, City and Kompany restored order.
From there, City comprehensively throttled Manchester United in the season's first derby and, with Kompany safely tucked away, battered Wigan Athletic in a Capital One Cup match that City might just as soon have been better off losing.
Everyone who has a passing knowledge of Manchester City football these past few seasons knows how heavily Roberto Mancini relied on Kompany.
The Belgian international played 26 Premier League matches in 2012/2013 when City were busy losing the Premier League title—and 31 matches in 2011-/2012 when the Sky Blues were busy winning it.
Before that, Kompany played an absurd 37 of 38 possible Premier League matches in 2010/2011. Current City manager Manuel Pellegrini projects to have enough squad depth to ever need to have that happen again.
A weekend football fan watching a City match out of the corner of his eye while filling out a crossword will surely notice Kompany's physically imposing defensive style.
There is a reason why Manchester United's only Premier League derby win in five tries came with Kompany leaving the pitch after 20 minutes.
What casual football fans might not see in Kompany's game, though, is the transformative effect he has on City's offense.
Kompany is the rare centre-back who is comfortable with the ball in the mad traffic that Joe Hart's goal mouth often features. Kompany is an adept passer, and he can dribble out of trouble over short distances when the need arises.
And while he is not a prolific goal-scorer, the ones he does score tend to carry weight.
Kompany allows Pellegrini's hyper-aggressive offensive tactics to flourish safe in the knowledge that, if Jesus Navas or Samir Nasri get dispossessed in midfield, he and his cohort (Nastasic, Gael Clichy, Pablo Zabaleta et al) can calmly stifle the resulting counter-attack.
Kompany's value to City was eloquently set forth at length in a worthy post from Simon Curtis on ESPNFC.com. There are too many verbal bouquets tossed at Kompany to recite them all—just read the piece, it's really good—but this description of Kompany's hand in the final City goal of the recent derby is a great example:
Kompany once again stuck out an imperious limb and nicked the ball cleanly from one of United's rare counters upfield. Instead of stopping to admire his handiwork and play a Marouane Fellaini-esque sideways ball to Matija Nastasic, he stayed on his feet, looked up and began a surge of his own...as Nasri patted it home, there was Kompany on his knees by the near post, a picture of delight mirroring the gleaming faces in the rows before him.
This action by Kompany came with his team already up 3-0 in the derby in the 50th minute. Kompany had been dealing with Wayne Rooney and his mostly hapless teammates for nearly an hour and his side had a commanding lead.
Human nature would suggest that Kompany might have conserved energy and let Navas et al make the play without him. Except, that is not the way Kompany plays football.
As a result, there he was, at the end of, as Curtis noted, a "lung-busting run from one box to the other" to support of a possible fourth goal with his team already well ahead.
City can stare into the distance of their seemingly endless schedule and see that the coming onslaught is pretty fearsome. In their next six matches, City have to deal with Bayern Munich, Everton, CSKA Moscow and Chelsea.
So, yeah, City got Kompany back just in time.
And they had better hope he sticks around for awhile.