It is true that Sampras faced tougher players in the later rounds of grand slams. However, he still had a lot of easy matches in the early rounds, and the majority of his matches in grand slams were against players similar level to the ones Karlovic faced. By my calculation, just 29.0% (70/241) of Sampras matches were played in the quarterfinals or later. The majority of his grand slam matches were still played against mediocre competition.
Again I don't think the competition factor is as great as it's made out to be, but since we're almost quibbling with a 2-3% difference it's not something that can be dismissed wholesale. And remember, we're not just talking about pure Xs and Os. Holding serve in the 3rd round of a 500 series event is a whole world removed from having to serve from two break points down in the 5th set of a major final or even SF. And I don't think I'm alone in doubting that even Ivo and Isner would be unfazed by the pressure, especially given their career TB and 5-set records which pale in comparison with those of Goran, Roddick and the rest, let alone Fed and of course Pete.
I understand your point about per match statistics being distorted by the length of a given match. Obviously, the best data would be percentage of service points that resulted in an ace or unreturnable serve. We don't have that data, so per match data is among the best we can go by. When the per match statistics are close, you can reason the difference away and make a case for the player with worse per match stats. The difference in per match statistics between Sampras and Karlovic is simply enormous though. Karlovic served close to double the number of aces/match as Sampras over the course of their careers. The various contexts we are talking about might make at most a 5% or 10% difference in those per match stats, which doesn't come close to accounting for the huge gulf. My conclusion is that Karlovic's serve is far superior to Sampras'. That's no knock on Sampras though, he has one of the greatest of serve of all time as well.
I've already addressed these points, but I understand not everyone has the time to pore over my dissertations so let me try one more time.
Before I start, though, there's something you and everyone else here should know. You may recall me saying that the ATP's '90s stats can't be trusted, and here I wasn't just talking about 1st- and 2nd-serve points won. In fact you can practically throw every '90s stat except the %s of service/return games won (though even these stats aren't without problems) from the ATP database out the window, for several reasons.
One, the ATP site doesn't have any pre-1991 match stats. Two, also missing from the database are stats for the following events:
- Grand Slam Cup
- Davis Cup (run by the ITF, so stats from today's DC ties still don't show up on the site)
- Olympics (ditto)
- World Team Cup before 1994
So while the ATP does have the (mostly) correct total number of matches for Pete or other '90s players their ace totals and whatnot don't include any input from these matches. And then we've got particular GS matches whose stats are entirely missing, like Pete's '96 Wimby and '97 AO 3rd-rounders or Chang's '97 FO 4th-round match, or even entire rounds like the 1st and 3rd of the '91 FO. slice serve ace has calculated that there are 176 of these missing matches for Pete, which means he actually served 8858 aces in 785 (961 per the ATP less 176) matches or 11.3 per match, well over the incorrect 9.2 average you see on the ATP site. (To make things even more complicated it seems that no match stats beyond 6-all in the 5th set seem to be included in the ATP database, which also includes incorrect info on the total number of breaks for some matches, but the effects of these inaccuracies on per-match stats should be negligible.)
That said, it's clear that Ivo still boasts significantly more aces per match than Pete, and as I've already acknowledged ace frequency correlates quite well with the rate of unreturned serves, which really is a better barometer of serving prowess. Like I said unreturned-serve stats are hard to come by, but I still have a sizable collection (thanks to slice serve ace, krosero, Moose and other contributors) and it shows all the usual suspects like Ivo, Goran, Raonic and Krajicek duking it out for the top spot.
There are some unexpected names, however, and two of them, again, are Sampras and Roddick. But before I continue here's a short primer on unreturned serves (slice serve ace has posted this before but I've modified it slightly). Obviously there are exceptions but this is what usually happens when a player has the following % of his serves unreturned:
<20% - You sure you didn't forget to clock in at a WTA event? Horrendous showing by the server.
20-29% - Still bad. Real bad.
30-34% - Now you're making some impact.
35% - Call this the middle ground.
36-40% - Getting warmer. You're starting to do some damage.
41-45% - Your opponent is now having fits, though there are openings here and there for a break.
46-50% - Almost in cruise control. Opportunities for the returner are few and far between.
50+% - Whoa, Nelly! Talk about total domination! Breaks highly unlikely.
Now it's true that we don't have a large enough sample size for most of these players, but I do have dozens of these stats for Sampras and I can tell you that he almost always had over 40% of his serves unreturned except on clay (and I suspect even on it quite often), often 50%, occasionally even 60%. And though my collection for Roddick is much less extensive what I do have shows quite a few of his %s in the 40s and 50s (topping out at 62.7% against Johansson in their '04 USO QF, though he eventually lost the 5-setter). Remember, anything over 55-60% is pretty rare even for the most dangerous ace machines, so I rather doubt that even Ivo and Goran had much higher rates of these freebies on average. (A sampling of my Karlovic collection shows, in order, 39.5%, 45%, 45.3%, 60.6% and 66.7+% of unreturned serves.)
There are other stats that reinforce this impression. You might have seen my stats regarding Pete's and Fed's victory runs at Wimbledon, where they respectively won 95.5% and 94.1% of their service games throughout the tournaments but 97.0% and 90.4% in the finals. Their overall %s or service games won may be surprisingly close, but they just show what we already know, that Fed was more consistent day in and day out, even on grass and even at Wimbledon. But the huge gap in their finals % also shows that Pete's serve is simply a more potent weapon than Fed's when they're truly tested by top opponents. In fact Pete's 59.2% of unreturned serves in his '97 Wimby final is a whopping 10% higher than the highest rate I've seen from Fed so far (again 49.2% from none other than his lone match against Pete, though he might have come fairly close during his recent serving streak), this against a pretty darn good returner in Pioline whose 26% of return games won in '97 would put him close to or within the top 10 in some other years.
As for Roddick, it may be hard to remember now but as you may know there was a time when he was quite the aggressor as opposed to his more conservative self in his final years. During the '04 Wimby final you could hear JMac marveling at Roddick's power and how he'd never seen anyone serve harder, and for once he wasn't exaggerating much:
http://web.archive.org/web/20040707025239/http://www.wimbledon.org/en_GB/bios/cmatch/ms/atpr485.html
As you can see Roddick's fastest serve in each round was in the 143-145 mph range, nearly 10 mph higher than Karlovic's at this year's Wimbledon, and if we assume that his mph would go up further still today due to superior radar and/or racquet technology (probably not by much in this case, but let's say about 2-3 mph) it's possible that this young Andy would be serving faster than Karlovic this year not only in top-end speeds but even on the average.
So in a way it's not really Karlovic but Sampras or Roddick who's an outlier, because Ivo's % of unreturned serves is what you expect from a guy of his size while Pete's or Andy's is well over the average success rate of their peers either in height or ace frequency. It's hard to say exactly why but again my guess is that Pete's unusually high topspin component made his serve that much harder to return, and though Yandell's article starts by comparing Pete's serve (favorably) to Roddick's I suspect Andy's topspin rate isn't too far behind. And I just talked about Roddick's sheer power in his youthful years. No doubt all that extra topspin and pace helped them hone their their 2nd serve into an all-time-great shot, which along with the spin probably made up for the height disadvantages their lesser counterparts can't overcome.
All that said, again I do think Karlovic's serve is better than Roddick's and even Pete's, but I don't say that just because of Ivo's superior numbers (though I suspect his average rates of unreturned serves are indeed higher than Pete's) but because my eyes and experience tell me so. Ivo and also Goran, Krajicek and their ilk often had these spells during which their serve alone would make them literally unplayable. Of course Pete (and Roddick) could and did put on such serving exhibitions as well, but they were relatively rare for him and I don't think even his 2nd serve makes up for this edge in Goran and Ivo's case. My intention here was to show that the gap between these two and Pete (or any other great server) isn't this unfathomable chasm that people think it is, and if they still think that after digesting all this info they need to think harder.