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How consistent are our stars: a statistical analysis

Discussion in 'Houston Rockets: Game Action & Roster Moves' started by MFW2310, Apr 2, 2005.

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  1. snowmt01

    snowmt01 Member

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    That's why the coefficient of variation is a better criteria.

    Think about it. The range of speed of an aircraft is definitely
    much bigger that of a car. Now adjust them by

    coefficient of variation = standard deviation / average speed

    e.g. average aircraft speed = 500, standard deviation = 80.
    average car speed = 70, standard deviation = 20.

    coeff of var for aircraft is 80/500 = 0.16
    for car it is 20/70 = 0.28

    so car speed is more variable than that of the aircraft.
     
    #41 snowmt01, Apr 2, 2005
    Last edited: Apr 2, 2005
  2. fa7999

    fa7999 Member

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    I did not have time to go over all the posters, but your analysis is flawed. You need to look at cv (coefficient of variance).

    cv=stand error/mean x 100%
     
    #42 fa7999, Apr 2, 2005
  3. michellexiao

    michellexiao Member

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    anyone here got quantative study book for free download?

     
    #43 michellexiao, Apr 2, 2005
  4. MFW2310

    MFW2310 Member

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    Incorrect. The stats by Yao and TMac shows what they get TOGETHER. Hence, that means their stats are not independent. The only time you can assume independence is if you have Yao play with the Rockets without TMac and TMac play with the Rockets without Yao against the same teams on the same dates, under the same circumstances, etc. Since that is impossible without another dimension, any such speculation is just that, speculation. As I've said already, if there is anything intangible (call it the X-Factor), it is likely already included in the stats. If it's not then there is no reason to assume that their stats are not mutually exclusive (although I wouldn't use that word).
     
    #44 MFW2310, Apr 2, 2005
  5. MFW2310

    MFW2310 Member

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    1. As I've mentioned already, there is no reason to believe that any "synergy" between the two players isn't already reflected by the stats. Because if those stats of them playing together doesn't already include that, then what are we arguing about? Such synergy would likely have no effect on the PPG aspect any ways if it's not already included by the existing stats.

    2. You are getting hung up on semantics. The 95% CI was never meant to tell you exactly what the probability is. As I've stated, the 2.5% is just the worst case scenario.

    3. The rule is, the SD of the two events is the sum of the SD of the two events independently. While I'd like to assume that the two are mutually independent (because it makes for much easier calculations), that's not likely to be the case. Thus, I've made no attempts to speculate either way.

    4. I think the message is getting lost here. The intention of this post isn't exactly how "inconsistent" are our stars. It was is IF they are inconsistent and if so, approximately how inconsistent they are. At the beginning I suspected that they are inconsistent but that may be just an opinion. Now we know they are inconsistent, if the definition of inconsistency is varying significantly from the mean.

    All in all though, I can see where you are coming from, although that requires me making too many assumptions that at this point I am unwilling to make.
     
    #45 MFW2310, Apr 2, 2005
    Last edited: Apr 2, 2005
  6. NewYorker

    NewYorker Ghost of Clutch Fans

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    I think you are spewing a lot of garbage now - no offense....but you're not saying anything anymore.

     
    #46 NewYorker, Apr 2, 2005
  7. snowmt01

    snowmt01 Member

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    Unfortunately the worst case scenario is > 2.5%.

    If Yao < 4.4 implies Tmac < 8.2, then
    P(Yao < 4.4, Tmac < 8.2) = P(Yao < 4.4) = 2.5%.

    But Yao + Tmac < 13 is a much larger set than "Yao < 4.4, Tmac < 8.2".
    If Yao scores 0, then even Tmac scores 9~12 they will still
    score < 13 jointly. So
    P(Yao + Tmac < 13) >= P((Yao < 4.4, Tmac < 8.2).
    This formula is true regardless of assumptions.

    By the way,
    when you constructed the confidence interval, you were
    assuming the data are normally distributed, which may not be true.
     
    #47 snowmt01, Apr 2, 2005
  8. fa7999

    fa7999 Member

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    Nope. You can construct a confident interval for both parametric and nonparametric test. The only major difference is that nonparametric test usually gives your a wider confidence interval (about 5% difference) assuming the sample size is large enough.
     
    #48 fa7999, Apr 2, 2005
  9. fa7999

    fa7999 Member

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    BTW, nonparametric test is used when the underlying distribution is unknown.
     
    #49 fa7999, Apr 2, 2005
  10. snowmt01

    snowmt01 Member

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    His C.I. was based on normal assumption.
     
    #50 snowmt01, Apr 2, 2005
  11. MFW2310

    MFW2310 Member

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    No I understand what you are saying. But here is why I chose to simplify the issue:

    We know that P(A and B) = P(A) x P(B) assuming independence or P(A and B) = P(A) x P(B) - P(A|B) assuming no independence (in terms of the performance of our stars, this is most likely to be the case). P(A) being Yao scoring x points and P(B) being TMax scoring y points. And then you take the sigma of all the x and y combinations.

    But how would we know P(A) and P(B)? We have 4 games in which we were without TMac and 2 games without Yao, hardly a large enough sample size. I would argue that what we do have is P(A|B) and P(B|A), meaning what Yao scores with TMac present and vice versa. So out of the above equation, we have one of the factors out of the three.

    Now, if we do have P(A) and P(B), we could find out the probability in the way you described above. But since we don't, I simplified the issue. We know that P(4.4 and 8.2) is something lower than 2.5%. Then I looked at the SD and said, well, the chances of TMac scoring 13 is pretty probable but the chances of Yao scoring 0 is pretty much a statistical 0... same with TMac scoring 0. So even if you assume P(4.4 and 8.2) is exactly 2.5%, I would argue P(13) is not signficantly more than that.

    All in all, I was being lazy (the other part being not having enough information) and you caught me. But I'm glad you did.

    You are also right that I assumed it was normally distributed. I mean, it is plausible that, say... Yao's curve, is beta distributed with more data points closer to 0. However, a vast number of performance curves are normally distributed; and plotting Yao's and TMac's curves, that also appears to be the case. Nevertheless, this would be one of the potential fallacies.
     
    #51 MFW2310, Apr 3, 2005
    Last edited: Apr 3, 2005
  12. MFW2310

    MFW2310 Member

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    And I think you just don't know anything about stats.
     
    #52 MFW2310, Apr 3, 2005
  13. NewYorker

    NewYorker Ghost of Clutch Fans

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    I clearly knew enough to know you were full of it.

     
    #53 NewYorker, Apr 3, 2005
  14. MFW2310

    MFW2310 Member

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    Look in the mirror lately?
     
    #54 MFW2310, Apr 3, 2005
  15. NewYorker

    NewYorker Ghost of Clutch Fans

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    Everyday my man, gotta shave and comb my hair.

     
    #55 NewYorker, Apr 3, 2005
  16. Himalayas

    Himalayas Member

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    Basically, I love the way you lit the stats up. I agree that the further you jump from rim, the more inconsistent.

    Some thing I have to remind of is that the data sets are asymmetric, so when comes to p-value, it's hard to see it's under 2.5% LHS tail.
     
    #56 Himalayas, Apr 3, 2005
  17. fungyee77

    fungyee77 Member

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    MFW, thanks for making the analysis. However, the above assumption seemed fishy to me for the reasons already discussed by other posters. I have massaged your data a little and eliminated all games which either one of the two players have recorded a DNP. The results are as follows:

    Ypts Yrbs Yast Tpts Trbs Tast Pts Rbs Ast
    Det - Loss 7 10 0 18 2 1 25 12 1
    Tor - Loss 17 9 2 21 4 5 38 13 7
    Mem - Win 8 4 0 30 4 9 38 8 9
    Sac - Win 33 12 3 23 13 5 56 25 8
    Mem - Win 14 11 1 12 6 7 26 17 8
    NJ - Win 6 2 1 14 1 4 20 3 5
    Atl - Loss 27 11 3 21 4 2 48 15 5
    NY - Loss 23 11 4 24 6 8 47 17 12
    LAC - Win 10 8 0 32 7 5 42 15 5
    Por - Win 19 6 0 16 4 11 35 10 11
    Sac - Loss 29 9 0 25 8 6 54 17 6
    Utah - Loss 9 4 1 17 2 1 26 6 2
    Den - Loss 8 6 0 14 5 7 22 11 7
    Det - Loss 19 7 2 16 6 5 35 13 7
    Dal - Loss 13 14 0 48 9 9 61 23 9
    Phi - Win 20 13 2 17 8 7 37 21 9
    NO - Win 21 9 1 18 5 4 39 14 5
    SAS - Win 27 10 1 33 8 2 60 18 3
    Dal - Loss 13 6 0 15 2 3 28 8 3
    Atl - Win 23 8 0 25 6 4 48 14 4
    GSW - Win 15 17 1 27 9 4 42 26 5
    Cha - Loss 16 9 0 29 7 9 45 16 9
    Tor - Win 40 10 1 34 12 7 74 22 8
    Cha - Loss 20 14 0 25 9 6 45 23 6
    LAC - Win 20 11 2 21 7 9 41 18 11
    Mil - Loss 10 3 0 20 3 5 30 6 5
    Cle - Win 20 7 0 34 7 5 54 14 5
    Utah - Win 15 4 0 25 5 6 40 9 6
    Pho - Loss 14 10 0 24 9 5 38 19 5
    LAL - Loss 25 5 0 26 4 8 51 9 8
    Den - Win 21 7 1 45 12 5 66 19 6
    Dal - Win 20 6 1 30 5 11 50 11 12
    NJ - Win 6 9 0 18 5 7 24 14 7
    SAS - Win 13 8 1 28 5 4 41 13 5
    Mem - Loss 8 5 0 28 5 5 36 10 5
    Ind - Loss 21 9 0 28 6 4 49 15 4
    Orl - Win 20 6 0 27 6 4 47 12 4
    NY - Win 22 12 0 35 6 5 57 18 5
    NO - Win 12 13 1 33 8 5 45 21 6
    Sac - Loss 13 9 0 30 7 12 43 16 12
    Mia - Loss 22 9 2 28 9 4 50 18 6
    Bos - Win 23 8 0 16 5 4 39 13 4
    Phi - Win 12 5 2 34 4 9 46 9 11
    Min - Win 23 14 2 40 13 4 63 27 6
    LAL - Win 23 8 1 21 2 7 44 10 8
    Chi - Win 21 10 0 24 5 9 45 15 9
    Ind - Win 16 4 0 16 7 7 32 11 7
    Por - Win 23 8 0 18 4 9 41 12 9
    Was - Win 23 9 1 34 6 9 57 15 10
    Sea - Loss 30 9 2 17 5 9 47 14 11
    SAS - Loss 20 4 0 22 3 6 42 7 6
    Utah - Loss 12 4 2 23 5 3 35 9 5
    Chi - Win 14 3 0 32 3 7 46 6 7
    Was - Loss 11 7 0 26 9 7 37 16 7
    Dal - Win 14 11 1 32 10 5 46 21 6
    Sea - Win 22 4 2 35 8 5 57 12 7
    Pho - Win 27 22 1 38 9 6 65 31 7
    Sac - Win 17 6 1 22 5 7 39 11 8
    GSW - Win 14 15 0 20 7 4 34 22 4
    Por - Win 13 7 0 19 6 6 32 13 6
    Bos - Loss 18 6 2 22 5 5 40 11 7
    Min - Loss 21 5 1 15 7 4 36 12 5
    Mia - Win 12 9 1 26 4 2 38 13 3
    Cle - Win 13 8 2 31 4 5 44 12 7
    NO - Win 12 7 0 0 1 0 12 8 0
    SAS - Loss 18 6 0 26 7 4 44 13 4
    Utah - Win 15 4 0 44 6 4 59 10 4
    Por - Win 29 7 0 26 10 4 55 17 4

    Mean 17.86764706 8.279411765 0.764705882 25.19117647 6.117647059 5.676470588 43.05882353 14.39705882 6.441176471
    SD 6.79970239 3.615247925 0.948174162 8.457545166 2.685113254 2.458255518 11.7064625 5.499361444 2.588045727

    The last 3 columns are the combined numbers of TMas and Yao. It is clear that the SD of the two combined is much lower than the sum of the individual SDs, which is consistent with reason.
     
    #57 fungyee77, Apr 3, 2005
  18. fungyee77

    fungyee77 Member

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    Ypts Yrbs Yast Tpts Trbs Tast Pts Rbs Ast
    Mean 17.9 8.3 0.8 25.2 6.1 5.7 43.1 14.4 6.4
    SD 6.8 3.6 0.9 8.5 2.7 2.5 11.7 5.5 2.6

    There, that might make it easier to read.
     
    #58 fungyee77, Apr 3, 2005
  19. Tdogg

    Tdogg Member

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    I am sorry that my mind is in the gutter, not to take anything away from this topic, but when I read this line and couldn't stop laughing.
     
    #59 Tdogg, Apr 3, 2005
  20. Houkom

    Houkom Member

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    Thanks for the analysis,

    It is too bad I cannot show you the distribution of the point per player, because this would illustrate better why people perceive Yao as inconsistent compared to T-mac.

    T-mAc's distriubution is closer to a Normal distriubtion than Yao's is.

    Yao peaks twice at 15 and 25 points. T-macs only peaks at 25.

    Sometimes a picture (graph) is better than a ton of words.

    Really too bad I can't show you the graph, I have the image, but i have to figure out how to post a pic on this forum.

    But I'll give you the table instead:

    <table x:str border=1 cellpadding=0 cellspacing=0
    <tr >
    <td height=18 width=108 style='height:13.5pt;width:81pt'>Points</td>
    <td width=64 style='width:48pt'></td>
    <td width=64 style='width:48pt'></td>
    </tr>
    <tr >
    <td height=17 class=xl25 style='height:12.75pt'>Frequency</td>
    <td class=xl25>Yao</td>
    <td class=xl25>Tracy</td>
    </tr>
    <tr >
    <td height=17 class=xl26 style='height:12.75pt'>DNP</td>
    <td align=right x:num>1</td>
    <td align=right x:num>5</td>
    </tr>
    <tr >
    <td height=17 align=right style='height:12.75pt' x:num>5</td>
    <td align=right x:num>0</td>
    <td align=right x:num>0</td>
    </tr>
    <tr >
    <td height=17 align=right style='height:12.75pt' x:num>10</td>
    <td align=right x:num>9</td>
    <td align=right x:num>0</td>
    </tr>
    <tr >
    <td height=17 align=right style='height:12.75pt' x:num>15</td>
    <td align=right x:num>20</td>
    <td align=right x:num>5</td>
    </tr>
    <tr >
    <td height=17 align=right style='height:12.75pt' x:num>20</td>
    <td align=right x:num>15</td>
    <td align=right x:num>14</td>
    </tr>
    <tr >
    <td >25</td>
    <td align=right x:num>18</td>
    <td align=right x:num>17</td>
    </tr>
    <tr >
    <td height=17 align=right style='height:12.75pt' x:num>30</td>
    <td align=right x:num>6</td>
    <td align=right x:num>15</td>
    </tr>
    <tr >
    <td height=17 align=right style='height:12.75pt' x:num>35</td>
    <td align=right x:num>2</td>
    <td align=right x:num>12</td>
    </tr>
    <tr >
    <td height=17 align=right style='height:12.75pt' x:num>40</td>
    <td align=right x:num>1</td>
    <td align=right x:num>2</td>
    </tr>
    <tr >
    <td height=17 align=right style='height:12.75pt' x:num>45</td>
    <td align=right x:num>0</td>
    <td align=right x:num>3</td>
    </tr>
    <tr >
    <td height=17 align=right style='height:12.75pt' x:num>50</td>
    <td align=right x:num>0</td>
    <td align=right x:num>1</td>
    </tr>
     
    #60 Houkom, Apr 4, 2005
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