There's a reason your insurance goes up if you get into a car accident. There is no such statistical theory. This is like saying if you flip a coin 10 times and you keep getting heads, then the probability of flipping tails goes up. Preposterous.
The insurance goes up because the insurance company perceives you to be reckless/more risky. There's no scientific proof saying that you are more likely to have a second accident than somebody who has not had one.
LOL ... buddy, but your analogy and theory are flawed, with all due respect. A more appropriate way of saying is if a dude had a car accident last year, the chances of him having another auto accident this year are likely to increase if he drives the same car and the car wasn't fixed properly. On your other point, even if he switched to a new car, when you eliminate the human factor and treat the case study as if it were a random and independent event, the likelihood of the same dude having another accident is just about the same as anybody else.
T-mac is underrated so it seems, if his back doesn't screw up anymore and since most players primes are when they're 28-30, isn't that this year he's turning 28?
you are making an erroneous assumption that the car wasn't fixed properly. You are introducing fiction (not a fact) into the analysis of this statistical hypothesis
Well, while my assumption could be wrong (which I hope that's the case), your assertion that TMac is completely cured with his back injury is just about as reliable as your auto-mechanic told you your wrecked car is now fixed and problem-free.
No, he's introducing a possible scenario. There are many such scenarios which would make a person more accident-prone (they're simply not a very good driver being the most obvious one). I would expect there is proof for it. If you're seriously suggesting that past injuries do not positively correlate to future injuries, then you're simply wrong. Use common sense, man. I mean, to say that a player who's been healthy has a greater chance of getting injured indicates a severe misunderstanding of basic probability.
I am not wrong. If you have empirical evidence to the contrary, I'll drop the subject. Jordan missed his rookie year, then he never missed any substantial time.
macfan, maybe you haven't ever had back problems. The reason Tracy is more likely to get injured than most players is back injuries tend to get progressively worse. Even JVG, or someone else in the Rockets organization, said the main injury concern the team had was Tracy's back. Back problems never go away. At best you can minimize the pain and how it affects your life. This can involve diet (for overweight people) or just exercises and stretching. Hopefully Tracy doesn't come down wrong and hurt himself again. Using auto repairs as an analogy of back problems is ridiculous. Human bodies don't have parts that can be switched out with brand new ones. You are stuck with the same hardware from birth to death for the most part. Definitely in the case of our backs.
Actually I do have a chronic back problem and it can be a biatch sometimes. His problem is not structural. My back gets much worse when I am stressed out. That was the case with Tracy last year. The spinal cord is the center of all nervous impulses. If you are emotionally unstable, it exacerbates back pain. His back issues are totally manageable with today's medical remedies. He doesn't have a bulging disk or anything like that As far as JVG goes, he even worries about Yao's shoes and about a flea on the parquet floor
I'm not going to dig up empirical evidence for something that's common sense. The tendency to get injured is more for players with a history of getting injured than for players with a history of being healthy. That's so obvious, it's basically a truism. You want "evidence" for that? Actually, the very nature of empirical evidence is based on the fact that we can forecast future events based on past events. What you're suggesting, future events will tend to oppose past events, invalidates all empirical evidence.
Tracy doesn't have a history of injuries. He has injured his back twice during his 10 year career. No other major injuries. Shaq, Kobe, Carter, Duncan have all been injured more times
The recent past should be weighed more heavily, though, than the distant past. McGrady's coming off a year in which he missed nearly half the season due to back problems. And he himself has said that the back issue is "chronic" and it's something he's going to have to deal with for the rest of his career. Shaq arguably has a higher risk of injury than McGrady. If I was betting money, I'd expect Kobe, Carter, and Duncan to play more games though. Question: Who would you say is likely to play more regular season games this year: McGrady or Paul Pierce? Pierce hasn't missed more than 3 regular season games in the past 6 years. Does that make him "due" for an injury-riddled year? Does McGrady's troubles last season mean he's "due" for a healthy year this time around?
I didn't say that future events will oppose past events. Let's say that Tmac and Kobe will have a 15 year career and they have an equal chance of getting injured. So they both are likely to get injured say 4 times during their career. If Kobe has already had 3 injuries and they are not due to a persisting or chronic problem, his chances of having another injury are lower than KG's who let's say has never stepped on somebody's foot and rolled his ankle.
Ok. At the beginning of their careers (without knowing anything other than they will have a 15 year career), they are likely to get injured 4 times. But what happens during that career can change the expected number of total injuries within that 15 year window. For example, if Kobe happens to get injured 4 times in his first year, does he have a 0% chance of getting injured the rest of the way? Of course not. He'll probably get injured 3 or 4 more times, based on the initial estimates of how injury prone they are, which means we can revise our initial projection from 4 injuries in his career to 7 or 8 injuries in his career. No. Even assuming that all injuries are compeltely independent of eachother, that doesn't follow. For instance, what if Kobe sustained those 3 injures all in his first year (by chance). Are you saying that he'll likely only get injured one more time in the next 14 years, because the original expectation was 4 injuries in 15 years? If that's what you're saying, your logic is screwed up. No. Sorry, that's not true. I'll ask this again. Say you flip a perfectly unbiased coin 10 times and each time you flip heads. Since, in the long run, we expect only 50% of the flips to be heads, would you say that the next flip will most likely be tails? If that's what you're saying, it's not true. Trust me. Each flip has an equal probability of turning heads, regardless of past flips. Similarly, if we're saying that two players have the exact same injury risk and each injury is completely independent of each other, then we can expect them to suffer the same number of injuries between now and some future date regardless of their past injuries.
The price on insurance policy goes up after accident because people's perceive you to be more reckless than originally thought. The accident may or may not have been caused by your lack of skill or impetuity, as life is essential random and bizzare things occur which are beyond your control. But the matter of fact is the probability of having an accidents do go up with reckless driving or ineptitude, and moreover, there is no way to distinguish the events generated by chance from genuinely human driven cases. So naturally insurance companies "update" their belief with more information coming in. This is a simple application of Beyes' probability theory and almost universally regarded to be the rational way of updating beliefs. How does this apply to McGrady's case? Well, as you have mentioned McGrady's back problem is something that is real. McGrady either have it or he does not, since it is condition determined by the physical state with real existence (Unless you are Deckardian Sceptic). And Tracy knows the state of his back a lot more than Kelly ever will. Furthermore, his backproblem isn't going to get a lot better or worse because people speculate that to be the case. The problem is that we do not have anyway to infer the condition of Tracy's back, and thus naturally you have to assume that he is more risk averse than you once thought because from what we do know is that people with certain past injury records are more likely to suffer from future injuries. So to sum the matter up: If Tracy suffers from freak thumb injury rather than back problem then would people label him as "injury prone". And what would be reaction of people if McGrady do stay injury free this year (Hopefully)?
