After countless years of play, the game of draughts was finally perfected in 2007. Jonathan Schaeffer, a professor of computing science at the University of Alberta, was the man who did it. He wrote a program named Chinook, which worked out that given perfect play by both sides, draughts always ends in a draw, regardless of the opening moves. The ancient Greeks played draughts or, at least, something rather like it. So did the Romans. It took Schaeffer a little under 20 years of work to bring the game to a terminal point. What he has done can't be improved upon by man, machine, or a combination of the two.

In sport we tend to expect relentless improvement. Faster, higher, stronger. So the running records fall and the jumping records stretch as techniques are enhanced, training is intensified and superior science is applied. But Glenn Fleisig, the research director at the American Sports Medicine Institute, has said this week that baseball pitchers are now operating at their absolute physical limit and that no one should expect to far outstrip what is currently the quickest pitch, the 105.1mph fastball thrown by the Cincinnati Reds reliever Aroldis Chapman in 2010.

The same is true, Fleisig says, in cricket. The likelihood is that the fastest ball that will ever be bowled has already been delivered. Which will please Shoaib Akhtar, listed as the quickest by the Guinness Book of Records, if not the Wisden Almanack, which refuses to record such vulgar things. Shoaib's famous delivery was bowled to Nick Knight in a group match during the 2003 World Cup. Knight nudged it around the corner for a simple single. "What did it feel like to face?" he was asked afterwards. "About 78mph."

Some think the gun that clocked it may have been cooked. There was a lot of hype about the race between Shoaib and Brett Lee to become the first man to bowl at 100mph, and the hoopla helped sell the tournament. The trouble is the technology used to clock bowling speeds is infamously imprecise, subject to wild inconsistencies and the whims of TV companies. Hawk-Eye once had Morne Morkel bowling at 108mph in the IPL. They had to issue a retraction after the match.

It's true too that the speed gun only registers the time it takes the ball to get from one end of the wicket to the other. It doesn't take into account how far it travels in between. Which is why taller bowlers – who release the ball from a much higher point and then make it bounce more steeply – are invariably timed as being slower than shorter, skiddier, bowlers. The ball travels further on the vertical plane before it reaches the batsman. It's still a better method than the one once used in baseball, where fastball pitcher Bob Feller was made to throw the ball as he was overtaken by a speeding Harley-Davidson. The ball beat the bike to the finish by three feet.

All of which means speed is not only something you measure on a gun, but see in the reactions of the batsmen. And that it is impossible to say precisely how fast the speed limit is. Something, it seems, up around 100mph or just under, a mark that has been reached by Shoaib, Lee and Shaun Tait. And, long before them, Jeff Thomson too, whose speed was measured frame-by-frame on recorded film and worked out at 99.6mph, a little more than Andy Roberts managed in the same test. The top speed, then, has barely changed in the course of three decades. And the odds are that Frank Tyson, perhaps even Harold Larwood when he bent his back, would have achieved similar figures in the high 90s had they been tested when they were bowling. Which seems curious, out of kilter with the kind of progression you may expect in other sports.

Fleisig says it is because of physiology and the constraints put on bowlers by frail tendons and ligaments. Bowlers may be fitter now than they ever were, certainly many are stronger. But Fleisig says that while muscles can be grown, the connecting tissue can only be marginally strengthened. "As muscles get stronger and technique gets better, then humans will go faster, but at some point ligaments and tendons will say 'that's all I can do'. Every sport has its physical limit."

In fact, if anything, bowling speeds seem to be regressing. Mike Brearley wrote a piece in the Times this summer about the homogenisation of speed, pointing out that in the Ashes "eight or nine fast bowlers played" and all averaged in the mid-80s. "Against most of them, for almost all the time, you wouldn't fear injury," Brearley wrote. "Where are the 90mph-plus men?" There were two right there in front of him, in Stuart Broad and Ryan Harris, but each tended to stick in a lower gear, only slipping into the red of the speedometer when the situation demanded it or their adrenaline commanded it, as on the final day of the fourth Test at Chester-le-Street.

Speed alone has never been enough, but now it seems to be almost actively discouraged. Steven Finn, England's quickest, has taken his wickets at a better strike rate than any of his regular team-mates since he made his Test debut (one every 48 balls, as opposed to one every 56 for Broad and Jimmy Anderson, and one every 64 for Tim Bresnan). But he's a lush, too expensive, and England like to bowl dry. Even Finn isn't in the very top rank of quicks. Thomson, for one, would scoff if you said he was anything like as fast as he once was. He may allow you Lee, Shoaib, Tait and perhaps Lasith Malinga, all four of whom ended up quitting Test cricket to concentrate on playing the one-day and T20 game.

There's the rub. As Fleisig says, bowling fast puts such a strain on the body that very few players are capable of sustaining high speeds over the course of successive five-day matches. Quicks increasingly prefer to play limited-overs games, where they can perform in short, discrete spells. Even those who do persist with Test cricket, such as Mitchell Johnson and Fidel Edwards, find themselves in and out of their sides, hamstrung by injury or a lack of control. Dale Steyn is the only exception and, like Broad and Harris, he increasingly tends to bowl well within himself.

That mindset has been passed down by coaches, who see the perfect action as being the one that bears the most repetition while minimising the risk of injury and maximising the degree of control. As Brearley says, Test cricket is poorer for it, stripped as it is of the physical threat to the batsman and robbed of one its most exciting elements. But bowlers have longer careers as a consequence. Fans and players love to argue about who was the fastest. That's a debate that can't be settled. But it is clear that you won't find many contenders in this day and age. We are in a time of tortoises, not hares. The perfectly fast action, like the perfect game of draughts, is a thing of the past, a target players have long since stopped pursuing.

• This is an extract taken from the Spin, the Guardian's weekly take on the world of cricket. Sign up for your free copy here.