I mentioned in another thread that "Yao-haters" and "Yao-worshippers" have a problem in common that they don't realize and that is they both have unrealistic expectations regarding his development and where he should be today. I thought I would put a little science to work to start setting some realistic expectations on Yao's development. 1st - In 1936 T.H. Wright demonstrated that for aircraft production that costs dropped the same % everytime cumulative production doubled. The idea is that people got better at building airplanes at a fixed % everytime they reached producing double the amount of planes previously. This concept has been well recognized and has been proven that it can actually be generalized for a variety of disciplines and therefore applied in many different fields since then today. 2nd- another concept regarding learning curves is that a person's development in skills is NOT LINEAR but in the shape of a s-curve. The implication is that novices learn slowly with each trial. However as experience builds, they fairly quickly acquire enough experience so that the proficiency they gain from each successive trial increases, and then remains constant over a broad range of experience. Eventually experience builds up to the point that there is little room for improvement due to physical or mental limitations and performance gain from additional trials declines. A stair-stepped learning curve can be imagined for iterative learning. For instance morse code operators were seen to have these successive peaks and plateau's has they increased their capability in the letters/min in encoding & decoding messages. What does this have to do with Yao Ming's development? Let's just apply the 1st concept and see where in offensive production Yao should be in season #3. Known stats --- Season --- # c*m. games --- avg FGA/gm --- avg pts/gm 1 -- 82 games -- 9.8 FGA -- 13.5 pts 2 -- 164 games -- 12.5 FGA -- 17.5 pts So now let's apply the production learning curve theory and see what we get. Using a 20% increase in production in FGA's & pts/gm for every cumulative doubling of # of games played (20% being a well known factor typically used) we get the following stats. Season --- # c*m. games --- avg FGA/gm --- avg pts/gm 3 -- 246 games -- 13 FGA -- 18.1 pts 4 -- 328 games -- 14.1 FGA -- 19.7 pts 5 -- 410 games -- 15.2 FGA -- 21.2 pts 6 -- 492 games -- 16.3 FGA -- 22.8 pts 7 -- 574 games -- 17.4 FGA -- 24.3 pts 8 -- 656 games -- 18.5 FGA -- 25.9 pts Now the interesting thing is that from 82-164 games (double the games) Yao's increase was better than 20% in FGA's & pts/game (27% & 29% respectively). If we use the 27% & 29% we would get the following: Season --- # c*m. games --- avg FGA/gm --- avg pts/gm 3 -- 246 games -- 13.5 FGA -- 19.1 pts 4 -- 328 games -- 14.9 FGA -- 21.2 pts 5 -- 410 games -- 16.4 FGA -- 23.4 pts 6 -- 492 games -- 17.8 FGA -- 25.5 pts 7 -- 574 games -- 19.2 FGA -- 27.6 pts 8 -- 656 games -- 20.6 FGA -- 29.8 pts The reality is that the performance curve is not smooth but spikey. 2ndly there are factors that are other variables that put a limit on the number FGA's & points per game. However the point here is this - what did you expect Yao to be offensively THIS YEAR? If you thought it would be better than 19 points per game then you weren't being realistic. Time to wake up and smell the coffee and have a realistic expectation on Yao's development as a player.
Nice work with the stats. For me, the problem isn't that he's scoring 18 ppg. The problem is that he's not scoring 18 pts. every game. In the last 13 games, he's scored 14 points or less 8 times. That is... unsettling.
Tango, nice analysis. Although personally I don't think stat tells the whole story, but a good analysis almost always on the money.
I have no problem with Yao not getting enough points lately. People tend to forget points scored is not the only way to measure Yao's contribution. If we lose those games, then there's some reasons to whine about it. This team just has enough good scorers they don't really need Yao in those games to score that much. I think Yao somehow would worry about his teammates not trusting him anymore because the guys are just keep passing up chance to feed him the ball in the post and decided to score themselves. Once Yao consistently getting good positions downlow and the guys are starting feeds him in the post more, his points will go up to >20 range. He's the kind of baller that needs consistent support from teammate to put up good numbers.
I want Yao Ming to succeed as much as the next guy, but this kind of statistical analysis is meaningless. It conveniently assumes that Yao's entrance into the NBA coincides with the beginning of his learning curve. Yao has been playing basketball his whole life. He's nearly 25 years old. It would make much more sense to assume that Yao is actually in the middle of his learning curve. It would be more worthwhile to analyse NBA players and their statistical development in the NBA over the years. For example, you could look at centers in the NBA and see how their stats progressed over the years. From this, you might be able to develop a decent model that could predict Yao's future success. Even this would be pretty meaningless, but according to your present model, every player in the NBA who averaged 13 points in their rookie year would eventually end up averaging 30 points.
So I have to wait until 2020 for Yao to average 50pts a game, I can't wait. Most original analysis I have seen on this BBS, I wish NBA players made widgets.
Winwook: The learning curve assumes no "entrance", no "middle", no "end". The curve is a continuous power function. 2ndly what do expect him to be today? The point here is that any improvement "better" than the power function is bordering on fantasy. 3rdly NBA basketball is vastly different than any basketball that Yao has played. I by no means say this is perfect but the learning curve concept is time tested in a variety of fields. When I get a chance to do some analysis of other players of fame I'll do it and post the results.
Is it funny how when Yao is attacked, their defenders say HEY, HE'S AVERAGING 18 POINTS AND 8 REBS...but when you start looking at the stats they all are saying YOU CAN'T JUST LOOK AT STATS. Well, enough is enough...just watch him play and tell me he looks inspired in his play.
that was a very good post. I'm not going to comment on it since I'm Yaod out right now. Give me a few days, maybe I can muster up the will to do it.
My thought exactly. Statistical analysists are much more uncertain when applied to an individual rather than a group.
Well, it is a joke to think Yao will ever average more than 25 points a game with his stamina. I think the only realistic number I saw up there is the 21+ average in points. I think Yao eventually will get there. As for rebounding? Yao won't ever average more than the 8-10 rbs range.
People are not comparing Yao to "learning curve", they will compare him to other players. If you compare him to Amare, you may be disappointed. If you compare him to K.Brown, you love his development.
Tango, an interesting post. But have you back tested it. It seems to me that the really great players came in and make an immediate impact. They do improve, but again, they do start out dominating almost immediaetly. I agree with you that we are likely to see improvement in Yao Mings game, but I no longer think he will be one of the truly greats.
I spent a little time doing some estimating against a variety of NBA players past and present using the method I did above with Yao - that is using for the most part the 82-164 game point to calculate a players fixed % performance increase. For Kobe & Kevin Garnett I had to use the 164-328 game interval since the 82-164 game interval were more like anomalies. Notes to come later on this. Here's output from that analysis: Est PPG is the "learning curve" prediction. Graphs provided as well. My comments to follow in a subsequent post.
Nice post Tango...you have got to be an engineer... People feel that they have to compare Yao to "somebody" to some how position him in their own mind which is unfaire to Yao and truly not a fair comparison as most other NBA centers that he is compared to had the luxury of not playing in an era where they allowed the zone defense. If you compare Yao to Amare you will find that he is eight inches taller and sixty five pounds heavier and oh by the way doesn't have Steve Nash as his point guard...
ahh...no! It has nothing to do with Nash, Amare has simply made a huge leap in his development, and Yao is simply not as good as Amare is offensively, but he is more of a complete player (i.e. defensively) than Amare is. However, if you look at the numbers those other great Centers have put up, they were ALL (almost without exception) putting up dominant stats right off the bat. Hakeem did it, the Admiral did it, Duncan did it, Shaq certainly did it, Ewing did it, etc. I think that is why it is just unrealistic to say Yao will be a "great" player comparable to those names I mentioned above. Yao will be a very good, solid Center that will cause opponents many problems. But he won't be no Shaq or Dream or even Ewing. But I am more than willing to live with that, and have adjusted my expectations accordingly. I usually like to compare Yao to the traditional Centers of our era, so I won't compare him to smaller, more mobile Power Forwards like Amare, Garnett, Nowitzki, or others. I think those guys have a different game. So I like to compare Yao to the standard idea we have of the traditional Center, that would probably be a more accurate standard to use.
Alright some notes & repsonses: I didn't make up the concept of the production learning curve. It's widely applied to a lot of different fields besides just making widgets. Before you poopoo the statistics you might want to do a little reading on it. It's widespread applicalibility speaks for itself. This is just a reasonable attempt at bringing an objective view on the controversial topic of Yao Ming's development as a player. I never said the method was fullproof . However after doing some back analysis represented above I'm somewhat surprised at the findings. As I mentioned earlier there are a lot of variables not taken into account - one of the main ones is that the production learning assumes no degradation in life-cycle. An NBA player's body wears down overtime. I think we can see that in the graphs above. That being said I'm actually somewhat surprised at how close the learning curve method tracks for what appears to be the period of performance increase for an NBA player in the 164-800 game range. Shaq was the the player that didnt' track at all with the curve. That was an interesting one to note. He came in and by his 2nd year was making the same impact offensively as he has since then. You can draw several different conclusions from this. For Kobe & KG - I had to use a different portion of the interval because their performance improvements from the 82-164 game improvement bordered on the phenomenal. Alright Rocket Fans, I have more thoughts but alas I need to head off to bed for work in the AM. Look forward to your posts!
tigermission - there is a different conclusion you can make... Shaq, Duncan, Hakeem, & Robinson all had the benefit of playing US collegeball. Yao didn't. That said however note that the learning curve isn't that far off with Duncan, Hakeem, & Robinson. If that's true then it may not be far off for Yao either. Yao's learning curve is more akin to the likes of Kobe & KG coming in straight from high school vs. the Dream, the Admiral, and Shaq. OK off to bed!
