How consistent are our stars: a statistical analysis

exactly right. all of this seems to be coming back to shooting percentage. i think we should all expect a guy who is 7'6" and playing close to the basket to have a higher shooting percentage than a guy who plays the perimeter. that's blatantly obvious to me.

but this is not what is meant if your'e trying to counter the notion that Yao is inconsistent. i don't think that's what his critics mean at all.

 

MFW...

Can you tell me the ppg averages month-by-month for both Yao AND T-Mac, up to the month of March?

The reason is that the ppg averages for both players have evolved since the beginning of the season, so I am not sure if that affects the "above average/below average" performances analysis, because these averages have changed and evolved as the season has evolved.

I don't know if that would affect your analysis or not.

 

Then after learning that Yao was injured in Suns game (March 11),
according to Houston Chronic, how do you think about all the critics we heard in Clutch BBS?

 

LOL!

Yah, that is the excitement part of the watching NBA basketball, if Yao or T-Mac were dead-on to their averages every game, it would be deathly boring to watch the games.

so in that sense, HAIL INCONSISTENCY!

 

That's why we go/watch games, after all. We expect UNEXPECTED!

However those lousy losses make fans depressed everywhere. So ... calm down, look forward, and expect UNEXPECTED.

 

whaaaat?

 

ok so both are inconsistent,. but TMac's inconsistency ranges from 25 points to 45 points, while Yao ranges from 5 to 25, and lets not even talk about his rebounding

 

I would bet good money that the last time Yao and T-mac played together barring injury or ejections and scored less then 13 points was NEVER.

How's that for debunking your results?

T-Mac is far more consistant. No his jump shot may not fall with all that much consistancy, but his overall play is.

 

The only thing that this debunks is your understanding of statistics .

The 95% confidence interval means there's only a 2.5% chance that T-MAC & Yao combine for 13 pts or less in a game. That's some pretty good odds meaning that we should be pretty confident that they will never combine for 13 pts or less.

 

Ah, too slow in my response. MFW - remember it's 2.5% above and 2.5% below = 5% total on the outside of your ranges.

 

Actually it's much less, as your statistical analysis is quite naive and full of false assumptions.

First of all, you're assuming that T-macs play and Yao's play are mutually exclusive - which clearly it's not.

Second of all, both players would have the have their worst night ON THE SAME NIGHT - a very low probability.

You're analysis states this would occur 1 in every 20 games. Take a look at the data - it's never happened this season.

In fact, you could do the same analysis with any two teammates and find out that their two worst nights occur far less then 1 in 20. You can't just add the lower bounds and assume it's still a 95% confidence interval.

It's not as simplistic as you're making it out to be. Just because you have some numbers and it seems like you're doing something logical doesn't necessarily mean that...the world is full of people with B.S. stat knowledge who try to force a mathematical intrepretation on something they don't fully understand.

 

You're correct the variables not being mutually exclusive. However MFW's premise of the comparative statistical variation between T-MAC and Yao is correct. If you're saying his statistical premise is incorrect then perhaps you should try to disprove with some deductive reasoning which you haven't done yet.

 

Let's assume that T-Mac and Yao's play are mutually exclusive.

Then, what was it, Yao's lower bound was 5 points and T-macs 7 points? And since it's a normal distribution two-tailed, then there's a 2.5% chance that in any given night they will score below their lower bounds.

Since 2.5% = 1 in 40...


The chance that both will both score below their lower bounds (less then 12 pts or whatever) is...

1/40 * 1/40 = 1/1600 or 0.06%

They would have to play an average of 1,600 games before it happens once.

Therefore, I'm 99.94% sure that they won't score less then 12pts in a game combined....a lot higher then the 97.5% you're claiming.

 

Actually 2.5% is still not correct.

The probabablity for Yao and Tmac combined to get less
than 13 can be obtained by enumeration.

P(Yao = 0, Tmac = 12 and vice versa)
+
P(Yao = 1, Tmac = 11 and vice versa)
+
...
+
P(Yao = 6, Tmac = 6)



P(Yao < 4.2, Tmac < 8.4) is only part of the story, and that
probability is way lower than 2.5%.

Assuming their scores are mutually independent
The joint probability
P(Yao < 4.4, Tmac < 8.2) = P (Yao < 4.2) x P(Tmac < 8.4)
= 2.5% x 2.5% = 0.0625%

Sorry to make it too academic