Fatigue Limit: Explaining Why NBA Players Break Down

Introduction

Explaining longevity in the NBA is fraught with difficulties. Size helps because if you lose your athleticism as you age being seven feet tall still has its advantages, but how did Stockton play well every year until he was 40? Shooting helps, but the list of accurate long-range guards who fell off a cliff in their early 30's in long. Another common explanation is that the players with long careers worked incredibly hard to stay in shape, but why is Andre Miller having another great year when he's a point guard who can't shoot and admits he works himself into shape during the season because he doesn't work out much off-season?

There have to be other factors at play. I'll look into a field ignored for the most part by basketball to find an explanation. With the high school studs like Bryant and Garnett getting old after playing huge minutes since they were teenagers and the marvels of modern health care and training, it's difficult to assess who can play well at age 40 and who can't make it past 35. It's also very important to find a way determine who's susceptible, as the Dallas Mavericks figured Nash wouldn't last much longer but he improved and won MVPs, and a career-ending injury to a star player can derail a franchise for years.

When most people think of sports injuries, they think of freak plays where a guy's knee bends the wrong way or he tears a muscle attempting to exert enormous force through his legs, and we equate that to what ends a career. Among high-performing athletes, the truth is that age takes a heavy toll on a player's body, but no one's surprised by that. However, bodies also wear down due to an accumulation of stresses over the years, and coupled with how a person's ability to heal deteriorates with age you get Chris Webber on the 76ers or Tim Hardaway shooting 37% from the field. The end can be sudden, and no matter how dedicated you are one day the rim will seem higher, the players faster, the court bigger.

Basic Material Science

First a little background into materials engineering. You don't need a science degree to understand the basic principles. People are aware of how things break and we generally derive a bit of pleasure from watching it happen -- from a lumber board snapping in half to a building imploding to car crashes. In engineering, we need to know exactly why it occurs and how we can quantify it. Think of a table trying to hold progressively heavier weights. The average person will equate more weight to failure, but in actuality it's stress, which is the weight (or force) per unit area. If the table legs are twice as thick, then all other things being equal it should hold twice as much weight. The stress at which failure occurs is known as the ultimate stress limit, and it's typically subdivided into compression and tensile limits (squishing versus stretching.) There's also the yield limit, where the material reaches a point where its deformation is permanent like a bent metal pole versus a rubber band returning to its original shape, and fracture, where the material breaks apart.

How the table leg fails happens at the molecular level. When something is put under a force or stress, it responds by deforming either compressing or going into tension (stretching.) Bending is a combination of the two. Under lower stresses, the material, depending on its elasticity, can return to its original shape. Even if the material can reform there still are real effects as microcracks appear, tiny damage unseen from naked eye. Above a certain point, the yield limit, permanent deformation occurs and a significant number of microcracks begin to appear. You also what's called atomic slip, where atoms are not yet broken away from each other but begin to slide along fault planes. What people typically see as failure is when all those microscopic changes roar into effect with fracture at the object's weakest point. If the table leg was narrow in the middle and bulged above and below, it would most likely break in the middle. If it didn't, however, it would be because due to imperfections in the wood the weakest point was in another location. In the human body, innate imperfections in body tissue and cartilage limit what some players can handle, as it is in the material science world.

Bridges don't always fail because of a huge earthquake or bombing run from enemy forces. There are other modes of failure. One is known as fatigue, where repeated stress loadings cause structural failure below the ultimate stress limit. The microcracks mentioned above can reach a critical size and cause failure even below the yield limit. This is important because it highlights a method of failure that's subtle. While most research is done on fatigue is about metal, it's also true of other materials.  However, there is a point below which any number of loadings even into the millions cannot cause failure by themselves. This is known as the fatigue or endurance limit, and I think you can see how it can be applied to NBA veterans.

The Endurance Limit

The figure on the left shows where failure occurs for repeated loadings. The bottom part has number of cycles, or loadings, on a logarithmic scale where 10^6 means a 1 with 6 zeros -- 1,000,000. If you're not familiar with the measurement kPA, don't worry as it's only recording how big the load is. Different materials have different tendencies with the endurance limit. It's also found in other types of material like concrete and wood and can be applied to most materials.

Recent research, however, has found that the endurance limit does not exist with new equipment capable of 10^6 to 10^10 cycles (or loadings), but clearly if you reduce your stress enough you can avoid that failure provided your number of cycles is low enough. By "low enough" this is on the order of magnitude of millions to billions to trillions, and even in the thousands you can significantly reduce the limit.

No one can put an athlete through a series of engineering tests in a lab environment due to the Geneva convention, but estimates can be made from minutes played. Let's say a hypothetical player named Kobe Duncan has played exactly 40,000 minutes in NBA regular season games. Every minute that he's played an event happens where the stress on the knee (right or left: it's arbitrary for the example) is at least X amount. This is not saying every minute he's on the floor in a game this event happens because it's an approximation that includes playoffs, practice, exhibition games, and everything else; it's saying that for every minute played in a regular season game the event with that specific stress has occurred in some place.

At 40,000 minutes, this is 4*10^4 total cycles estimated. It's not quite halfway between 10^4 and 10^5, but because most charts are in log form (non-linear) it's roughly sixty percent of the distance from 10^4 to 10^5. The chart on the right shows the percentage decrease in the stress limit (where failure occurs) for various materials. The percentage decrease varies greatly on what the material is. It's hard to say what material bone behaves like since I couldn't find the research, but let's use the average of around 50% for failure at 4*10^4 cycles for our purposes.

Note this is a highly simplified version of reality because the body, even your bones, heal and that healing rate is slowed by age and genetics. Your knees as well as other body parts are complex with various parts and materials. Players' knees also don't have the same amount of stress exerted each time a play happens and some are much greater than others; the loading is variable. Now the problem is a complicated calculus equation. The exact fatigue limit is hard to pin down, but it's reasonable to assume it exists.

After 40,000 minutes, Kobe Duncan has reached a point where one of his knees should soon fail and his career is in peril. The next game Kobe Duncan falls in pain and the results aren't good. It's not a major injury akin to one suffered by a player in his early 20's when his body could heal faster; it's an injury from the cumulative stresses over the course of his career. If he does recover, it's likely another body part, muscle, or tendon will soon fail, and he will be further debilitated. He was only 36, and even though Kobe Duncan had few major injuries prior in his career, kept himself in maniacally good shape, and was a genetic paragon of the human body, the ravages of time and the 40,000 career minutes have ended his body to the NBA graveyard where previous athletic superhumans like Wilt Chamberlain, Michael Jordan, and Karl Malone now lay.

What could Kobe Duncan have done to avoid his fate? He could have played less minutes, but he was in the NBA when he was very young and went deep into the playoffs many seasons. His playing style was a problem -- he was a big forward who regularly jumped high for the rebound or blocked shot, and even when he aged he preferred to drive rather than shoot from outside. To get up for his signature dunk, since he's six-seven, he needs to jump higher than his center, and even if he hangs on the rim and gently lets go he's falling 16 inches and for a 240 lbs body that is still a lot of energy.

Ageless NBA Ironmen

Perhaps one can look to the career minutes leaderboard for guidance on what playing styles are best. Looking at a list of who's played the most minutes in the regular season plus the playoffs, it's mostly a mix of centers and point guards, but you also have every other position represented. In fact, there really isn't much of a pattern based on size or position because the two most common ones, PG and C, are the most dissimilar.

Rank	Player	Regular season minutes	Playoff minutes	Total minutes	Position
1	Kareem Abdul-Jabbar	57,446	8851	66,297	C
2	Karl Malone	54,852	7907	62,759	PF
3	Wilt Chamberlain	47,859	7559	55,418	C
4	John Stockton	47,764	6398	54,162	PG
5	Elvin Hayes	50,000	4160	54,160	PF/C
6	John Havlicek	46,471	6860	53,331	SG/SF
7	Reggie Miller	47,619	5308	52,927	SG/SF
8	Jason Kidd	47,148	5697	52,845	PG
9	Gary Payton	47,117	5482	52,599	PG
10	Robert Parish	45,704	6177	51,881	C
11	Shaquille O'Neal	41,918	8099	50,017	C

Another way to find these age-defying players is seeing who has performed well at, say, 38 years and older. I searched for players who played the most minutes in a season above the aforementioned age and provided their other basic statistics. I used minutes played as the filter because if you're playing well you'll get minutes and it would also eliminate guys who kept getting injured in their twilight years. The results below are interesting, and besides the guys in the previous table you have Ewing, Michael Jordan, Kevin Willis, Cliff Robinson, Johnny Green, and Grant Hill. You can quickly see the three ageless freaks are Malone, Stockton, and Abdul-Jabbar. Together they have most of the best seasons at 38 years and above.

Player	Age	Games	Points	Rebs.	Assists	PER	Minutes	Position
Karl Malone	38	80	22.4	8.6	4.3	21.1	3040	PF
Michael Jordan	39	82	20	6.1	3.8	19.3	3031	SG
Karl Malone	39	81	20.6	7.8	4.7	21.7	2936	PF
Kareem Abdul-Jabbar	38	79	23.4	6.1	3.5	22.7	2629	C
John Stockton	39	82	13.4	3.2	8.2	21.9	2566	PG
Kareem Abdul-Jabbar	39	78	17.5	6.7	2.6	17.9	2441	C
Grant Hill	38	80	13.2	4.2	2.5	14.7	2409	SF
John Stockton	38	82	11.5	2.8	8.7	22.3	2397	PG
Kareem Abdul-Jabbar	40	80	14.6	6	1.7	15.8	2308	C
Robert Parish	38	79	14.1	8.9	0.9	18.9	2285	C
John Stockton	40	82	10.8	2.5	7.7	21	2275	PG
Reggie Miller	38	80	10	2.4	3.1	16.1	2254	SG/SF
Robert Parish	39	79	12.6	9.4	0.8	19.2	2146	C
Patrick Ewing	38	79	9.6	7.4	1.2	12.9	2107	C
Reggie Miller	39	66	14.8	2.4	2.2	16.6	2105	SG/SF
Michael Jordan	38	60	22.9	5.7	5.2	20.8	2092	SG
Robert Parish	40	74	11.7	7.3	1.1	16.1	1987	C
Johnny Green	38	82	9.8	6.8	1.5	15.6	1914	PF/C
Clifford Robinson	39	80	6.9	3.3	1.1	9.6	1863	PF/C
Kevin Willis	38	78	9.3	6.8	0.6	14.6	1830	C

What do these players have in common then? Of course since this article has been about the endurance limit it stands to reason that's my hypothesis -- these guys increased their respective careers by minimizing events that cause a high amount of stress in the their bodies and the number of such events. Namely, they avoid large physical exertions and hard landings on most of their plays.

Running through the above two tables again, you can see a pattern. What the big men and skilled guards have in common is a playing style that doesn't rely on jumping very high Stockton was never one to dunk, and guys like Kareem were so tall they barely needed much of a vertical to dunk anyway; those two also weren't known for his explosive speed and quickness. Karl Malone is actually a prototypical built to play forever guy -- he could never really jump (reportedly his vertical was 28 inches); he was always in great shape; he had a nice jump shot; and his post game didn't need the explosiveness that would have destroyed his knees. 

Centers are definitely the most common position to join the above tables for good reason. Shaq was always injured, but he would always be 7' 1" with great strength and a nice touch inside. His 330-360 lb weight was countered by how short of distance he needed to clear to dunk, and being out of shape meant he could barely get over the rim on some nights later in his career. Robert Parish and Willis don't have the MVPs of Kareem or Shaq, but they were big bodies who could retain their value even without jumping high.

Steve Nash's current season would just miss the cut-off point because he turned 38 days after February 1st, which is when basketball-reference.com (the site I used to gather the stats) determines age for the season. However, he'll probably have a great season next year, and looks poised to join Stockton as the best of their kind. Stockton is particularly amazing in that his stats per minute were virtually the same at age 40 compared to nearly any other point in his career. What they have in common is great skill that doesn't decline with age (shooting and passing) and a game tied to the floor, not above the rim. Other point guards may go high even for a layup, but Nash uses deception and a nice touch to get by any rim protectors. Jason Kidd likewise stays close to the ground and Payton stuck around for a while because of his defense and playmaking. 

Players at other positions also base their games below the rim. Reggie Miller rode his three point shot into impressive seasons for a wing his age; Grant Hill has low career minutes because of the time he missed earlier in his career and now he uses his length, skill, and intelligence to full force; Havlicek was relentless but played below the rim and was known for his conditioning, and stayed away from things like cigarettes and alcohol unlike others of his day; and Michael Jordan, a freak exception to any list, rested his knees through two different retirements and transformed his game to feature post-up's and a midrange jumper. 

Future members of the 50,000 total minutes club include a wing, Kobe Bryant, who emulated Jordan by focusing on his midrange game and currently sits at 49,223 minutes. He was, however, a high-flyer in his earlier days, and he's been largely grounded the past few seasons along with lots of nagging injuries. What he's done is remarkable this season, but he had to adapt to deal with the reduced athletic ability from the cumulative stresses on his legs, and his high points per game average is explained by his historically high shots per game with career low shooting efficiency. It'll be interesting to see how long he plays.Another wing, Ray Allen, is in the Reggie Miller mold as a great shooter with top of his field conditioning and dedication.With 45,753 minutes and 2659 three pointers, he shows no signs of slowing down as he's shooting 56.6% from the outside distance currently. His teammate Paul Pierce also has a shot, though he's only at 40,742 minutes, because he has a typical old man midrange game.

Kevin Garnett will likely join Kobe as he has 48,669 total minutes. After a season with 39 minutes a game and a 22 points and 13 rebounds average, Garnett lost the explosiveness that had defined his career. Given how hard he played and how high he would jump, it's not surprising he lost so much of his athleticism. He's so tall (measured at 6' 11.5" in barefeet, a height at which most players would fudge to say they're 7' or 7' 1") and so skilled that he's been able to play at a high level below the rim. Tim Duncan lags behind at 45,340 minutes because his coach rests his players obsessively -- a good strategy since it allows his players to heal and repair from the small stresses from games -- but if he wants to he could keep playing for a long time. If you adjust for Popovich's minutes reduction and look at his stats on a per minute basis, he hasn't slipped very much and still remains quite effective. Nowitzki is another player to watch since he's a seven-foot jump shooter who combines the size of centers who have played into their late 30's and the shooting touch of guards who have also done so.

Conclusion

How do you ward off Father Time? Play as though you can't jump, and you'll be jumping longer than anyone else. Andre Miller now makes sense. His only missed game since the 2002-03 season was a suspension because of this play, he's a key member of the surprising Denver Nuggets, and at 35 even his advanced statistics agree he's playing as well as he ever has. He has, as NBA commentators like to say, an old man's game, and is more described by crafty than athletic. His post game is underrated, he's an amazing passer, he can't shoot from outside but he has a good midrange jumper, and he knows the game intuitively as well as anyone.

The anti-Andre Miller is Dwyane Wade, who's usually in superb shape but his playing style is hard on his body as he still dunks the ball high above the rim and plays with reckless abandon. At 6' 4", he has to rise higher than other dunkers and as such he usually lands with more force. He's already missed large stretches of seasons because of injuries, and the older he gets the harder it will be to come back. He also lacks the shooting touch of players like Kobe and Jordan who were able to forestall the steep decline. Already 30, Wade's battle against the endurance limit is a difficult but ultimately impossible task. Blake Griffin should take note.

The fatigue (or endurance) limit is mostly used in the material sciences, but the same principles apply to the human bodies. Our legs are the first to go -- the knees, the ankles, the feet, and all the muscles and tendons connecting. A jump of over 30 inches won't destroy your knees, but do it enough over the course of your career and your body will break down. Unlike steel, our bones and tissues heal, but there's a finite repair rate and as we get older our ability to heal lessens. If you build your game on a low impact style, you have a chance to keep playing  as your athletic peers falter and crumble from their years of high impact landings. The high-flying dunk is electric, but the price you pay will find you later; Father Time is patient and he understands materials science.