The British No 1, 32 a week ago, is enjoying one of his best periods in a professional career that stretches back to 1982. He won his first title earlier this year in Seoul, and at Queen's three weeks ago beat Boris Becker. But for tension and drama, few moments could match this one as Bates overcame the formidable challenge of the 6ft 5in German, Markus Zoecke, 6-4 6-4
3-6 6-3 in two hours 35 minutes.
In the last 16 of 1992 - the only other time he has got this far at Wimbledon in 13 appearances - Bates met Guy Forget of France and had a match point before losing in five sets. By a quirk of the draw it is the same man he will playing tomorrow, Forget having beaten Jakob Hlasek in straight sets. It will not be easy - Forget beat Bates decisively in the Beckenham final earlier this month - but Bates has every reason to feel full of confidence.
It was a memorable afternoon, virtually amounting to a celebration of British sport as Tom Finney, among other athletic alumni, gazed down from the Royal Box. Tennis does not usually figure when the nation gets self-congratulatory, but that is starting to change. With Andrew Foster in 1993, there has now been a British man in the last 16 of Wimbledon for three years running.
Wimbledon has seen some awesome serving down the years, but rarely anything to match the bludgeoning power of Zoecke, who had knocked out Petr Korda in the previous round. He produced 22 aces and equalled the record for the fastest serve ever recorded at Wimbledon when he sent the ball towards Bates at 134mph.
But Bates took it all in his stride. 'It was important to go on and start the match with this frame of mind, that I was just going to have to accept all the aces and unreturnables and not let it get frustrating,' he said.
Luckily for Bates, Zoecke's game did not extend much beyond his serve. When it came to the tennis proper, there was only one man in it, apart from a spell in the third set when Bates got into his only difficulties.
But as he has pointed out recently, the difference between the mature Bates and the one who used to tantalise us but little more is that now he is much less hard on himself in times of trouble than he used to be.
Not that he was in any trouble for a long time yesterday. On the day that Wimbledon keeps back 2,000 Centre Court tickets for the so-called real fans, and jazz bands set up in the car park, Bates's noticeably relaxed approach was entirely appropriate.
Bates took the first set in 33 minutes, breaking Zoecke in the fifth game. Although reconciled to losing a lot of points on Zoecke's serve, Bates made the most of those serves he did manage to reach, thanks to some inspired guesswork and the natural timing that has always been his gift. The break came when Bates sent a dipping return of serve to the feet of Zoecke, whose giant frame was not designed for such situations. He duly netted.
Bates's own serve - top speed a mere 102mph - needed to be accurate, and it was. He conceded only five points on it in the first set, moving swiftly to the net and hitting his volleys with precision and purpose. Zoecke looked primitive by comparison.
Bates made an even better start to the second set, breaking Zoecke in the opening game. But then came his first big test. At 40-30 in the next game Bates allowed his impeccable standards to slip and he volleyed carelessly into the net. There followed seven deuces and four break-points to Zoecke, which Bates eventually survived to come through with his equanimity apparently intact.
It was a clear sign that Bates could cope with a certain amount of pressure. But how much? We were to find out in the third set when Bates, having broken Zoecke again in the opening game and looking poised for victory serving at 2-1, suddenly disappeared into a dark hole and lost four games on the trot. Now the ungainly Zoecke was beginning to find his range with his groundstrokes, and it looked as if Bates might struggle.
He never lost his poise, though, and the fourth set went virtually all Bates's way until he stood ready to serve at 5-3, 'and the noise was just incredible . . . I thought the whole place was going to fall down'.
Bates survived a break point at 30-40, getting to match point when a second serve landed on the line and Zoecke returned long. Bates took his time, went to toss the ball up . . . and broke off. The ball had stuck in his hand. Bates, recalling that exactly the same thing had happened on match point against Forget two years ago, then relieved the tension with a histrionic tremble worthy of Andre Agassi.
You wondered whether this uncharacteristic piece of showmanship was altogether wise, the more so when Zoecke hit a winner with his backhand return. But again Bates proved us wrong, surviving another break point, getting himself back to match point and winning it with an assured volley. A first week full of incident had saved its best - domestically speaking - until last.
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