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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. MFW2310

    MFW2310 Contributing Member

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    Following tonight's lousy shooting by TMac, I've decided to analyse just how consistent we are. I've based this analysis based on this season's numbers. I may decide to do a running total in the future to see if we are improving, consistency wise. But before the results...

    Disclaimer: I make no attempt to explain any results, you draw your own conclusions. For example, if you think that the numbers don't tell the whole story, you are right, but that is subjective and goes too far beyond the scope of this analysis. Also, stats DON'T lie. People with ulterior motives lie with stats and people who don't understand them gets fooled by them. So once again, to remain neutral, I draw no conclusions. I may later in the thread (maybe after more studies), but not in the initial post.

    I used PTS, boards and assists as the basis for this study. PTS and boards are fairly obvious. I also included dimes because TMac gets a significant portion of that on this team. I didn't include blocks because I'm too lazy and that number is unlikely to fluctuate too far from 3 (Yao's portion + TMac's portion).

    For the SD, I used the STDEV function in Excel. The numbers look somewhat odd so I may have used the wrong function. Somebody double check that.

    If the formating here really messes up the results, email me and I'll email somebody a copy of the spreadsheet so somebody can upload it somewhere.

    Any ways, here are the results:
    Yao TMac
    PTS Boards Assists PTS Boards Assists
    Det - Loss 7 10 0 18 2 1
    Tor - Loss 17 9 2 21 4 5
    Mem - Win 8 4 0 30 4 9
    Sac - Win 33 12 3 23 13 5
    Mem - Win 14 11 1 12 6 7
    Min - Loss 25 5 0 DNP
    LAL - Loss 32 7 1 DNP
    NJ - Win 6 2 1 14 1 4
    Atl - Loss 27 11 3 21 4 2
    NY - Loss 23 11 4 24 6 8
    LAC - Win 10 8 0 32 7 5
    Por - Win 19 6 0 16 4 11
    Sac - Loss 29 9 0 25 8 6
    Utah - Loss 9 4 1 17 2 1
    Den - Loss 8 6 0 14 5 7
    Det - Loss 19 7 2 16 6 5
    Dal - Loss 13 14 0 48 9 9
    Phi - Win 20 13 2 17 8 7
    NO - Win 21 9 1 18 5 4
    SAS - Win 27 10 1 33 8 2
    Dal - Loss 13 6 0 15 2 3
    Atl - Win 23 8 0 25 6 4
    GSW - Win 15 17 1 27 9 4
    Cha - Loss 16 9 0 29 7 9
    Tor - Win 40 10 1 34 12 7
    Cha - Loss 20 14 0 25 9 6
    LAC - Win 20 11 2 21 7 9
    Mil - Loss 10 3 0 20 3 5
    Cle - Win 20 7 0 34 7 5
    Mil - Win DNP 42 10 5
    Utah - Win 15 4 0 25 5 6
    Pho - Loss 14 10 0 24 9 5
    LAL - Loss 25 5 0 26 4 8
    Den - Win 21 7 1 45 12 5
    Dal - Win 20 6 1 30 5 11
    NJ - Win 6 9 0 18 5 7
    SAS - Win 13 8 1 28 5 4
    Mem - Loss 8 5 0 28 5 5
    Ind - Loss 21 9 0 28 6 4
    Orl - Win 20 6 0 27 6 4
    NY - Win 22 12 0 35 6 5
    Orl - Win 22 10 1 DNP
    NO - Win 12 13 1 33 8 5
    Sac - Loss 13 9 0 30 7 12
    Mia - Loss 22 9 2 28 9 4
    Bos - Win 23 8 0 16 5 4
    Phi - Win 12 5 2 34 4 9
    Min - Win 23 14 2 40 13 4
    LAL - Win 23 8 1 21 2 7
    Chi - Win 21 10 0 24 5 9
    Ind - Win 16 4 0 16 7 7
    Por - Win 23 8 0 18 4 9
    Was - Win 23 9 1 34 6 9
    Sea - Loss 30 9 2 17 5 9
    SAS - Loss 20 4 0 22 3 6
    Utah - Loss 12 4 2 23 5 3
    Chi - Win 14 3 0 32 3 7
    Was - Loss 11 7 0 26 9 7
    Dal - Win 14 11 1 32 10 5
    Sea - Win 22 4 2 35 8 5
    Pho - Win 27 22 1 38 9 6
    Sac - Win 17 6 1 22 5 7
    GSW - Win 14 15 0 20 7 4
    Por - Win 13 7 0 19 6 6
    Bos - Loss 18 6 2 22 5 5
    Min - Loss 21 5 1 15 7 4
    Mia - Win 12 9 1 26 4 2
    Cle - Win 13 8 2 31 4 5
    NO - Win 12 7 0 0 1 0 Injured
    SAS - Loss 18 6 0 26 7 4
    Utah - Win 15 4 0 44 6 4
    Por - Win 29 7 0 26 10 4
    NO - Loss DNP 21 3 3

    Mean 18.22535211 8.23943662 0.76056338 25.37142857 6.128571429 5.628571429
    SD 6.924484887 3.567571358 0.93296438 8.589125968 2.712939625 2.444582467
    95% CI 4.376382339 1.104293904 -1.105365381 8.193176636 0.702692179 0.739406495
    32.07432189 15.37457934 2.626492141 42.54968051 11.55445068 10.51773636

    Contribution
    Low 12.56955898 1.806986083 0.739406495
    High 74.62400239 26.92903001 13.1442285


    Looking at this, Yao averages (arithmetic mean) 18.22/8.23/0.76 per game with SD of about 6.92, 3.57 and 0.93 respectively. This means that his 95% confidence intervals are:

    4.38 - 32.07 PPG
    1.10 - 15.37 RPG
    0 (since you can't get -ve assists) - 2.63 APG

    TMac averages 25.37/6.13/5.63 per game with SD of 8.59, 2.71 and 2.44 respectively. That means that his 95% confidence intervals are:

    8.19 - 42.55 PPG
    0.70 - 11.55 RPG
    0.74 - 10.52 APG

    This brings up an interesting point. Everybody here think that Yao is the more inconsistent one. Now that I think of it, I don't know what the term "consistent" means in this case. What do we intend to measure when we say consistent? But I'm sure as hell it doesn't mean putting numbers close to the average, because TMac has the larger SD and therefore fluctuates more from his average.

    So if you were to ask me "hey MFW, what numbers do you expect Yao and TMac to put up on any given night," I'd give you the range of:

    12.57 - 74.62 PPG
    1.81 - 26.93 RPG
    0.74 - 13.14 APG

    That's the 95% Confidence Interval for the two of them together, meaning I'm sure that > 95% of the the time, they'll put up numbers between this range. But after hearing that you might not be too confident at all.

    Btw, Rockets are 1 - 1 without Yao and 2 - 2 without TMac.
     
    #1 MFW2310, Apr 2, 2005
  2. wakkoman

    wakkoman Contributing Member

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    wow
     
    #2 wakkoman, Apr 2, 2005
  3. vunny1408

    vunny1408 Contributing Member

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    WTF!? :confused:
     
    #3 vunny1408, Apr 2, 2005
  4. Zboy

    Zboy Contributing Member

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    Interesting analysis.


    The confidence interval in your analysis is too large to really draw any sort of meaningful conclusion. It's like saying 99.99% of the time Tracy Mcgrady will score between 0 to 89 points.

    Choosing a lower interval will perhaps reveal a little more. There are lots of factors though that are still unacounted for. Its a very simple approach to a somewhat complex statistical analysis problem. I say complex because of several unaccountable variables.
     
    #4 Zboy, Apr 2, 2005
  5. pirc1

    pirc1 Contributing Member

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    A 75% cofidence interval is more accurate, but tmac would still have a larger range.
     
    #5 pirc1, Apr 2, 2005
  6. Tango

    Tango Contributing Member

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    MFW2310:

    Nice analysis :). If you have the time, try plotting a histogram for each of the variables you looked at. It's another nice graphical way of displaying the information and probably give you a little more insight as well since it's harder to "see" the spread and amplitude of the normal curve by just quoting the mean and standard deviation. Use the excel "data analysis add-in" for the histogram function.

    I started a similar little study looking at some shooting pct's as well but never finished it because it was taking too long to pull the data to crunch for the team. I was more interested in the perimeter shooting vs. inside shooting. If I ever finish that I'll post it.

    Nice work!
     
    #6 Tango, Apr 2, 2005
  7. snowmt01

    snowmt01 Contributing Member

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    the coefficient of variation might be useful. It's the ratio of
    the standard deviation and the mean. Tmac scores more, so
    he should have a larger range.

    Another analysis is to obtain the empirical confidence interval.
    Order those scores first and then keep xx% values in the
    middle, whose range will be the empirical confidence interval.
    This is more robust because it doesn't depend on distribution
    assumption.

    [EDIT] I agree. Graph is the best way to represent data.
    Magic numbers are only good for scientists.
     
    #7 snowmt01, Apr 2, 2005
    Last edited: Apr 2, 2005
  8. Kenrui

    Kenrui Contributing Member

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    when you consider 'consistency' of a player's performance, you wouldn't say he has an inconsistent game if he outscored his own's average. So I think you should remove the best-performance games when you calculate variance (or standard deviation).
     
    #8 Kenrui, Apr 2, 2005
  9. tigermission1

    tigermission1 Contributing Member

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    You are forgetting a very, very important and crucial point to your analysis/conclusion: T-Mac is more "inconsistent" in your statistical analysis because he deviates from his average a LOT more than Yao does.

    For example: how many 40+ pts performances has T-Mac had this season? How many 30+ pts has he had (I reckon he has nearly 20 games this season above 30 points)?

    However, let's take Yao. Yao is much more "consistent" stats wise because he usually falls in the range of 13-19 points on any given game, and rarely does he score, say, above 23-25 points in single games.

    So basically, while T-Mac can explode in you on any given night, and thus is much less predictable that way (this applies to many other top guards in the league like Lebron, Kobe, etc.). Yao, on the other hand, is a lot more predictable in the numbers he will put up on any given night.

    So this skews your analysis, IMO.

    When people talk about Yao being more "inconsistent", I very much doubt that they are talking about it in a statistical sense: instead, they are talking about his overall demeanor/aggressiveness etc. It is not something stats can capture in this case. On the other hand, whether his shot is going or not, T-Mac is much more consistent (with few exceptions) when it comes to offensive aggressiveness, that is, he keeps attacking and attacking the opponents' defense whether he is shooting well or not.

    So I think the consistency talk is more about the intangibles that each player brings, not their statistical performances.
     
    #9 tigermission1, Apr 2, 2005
  10. MadMax

    MadMax Contributing Member

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    i think tigermission just hit it dead on.

    you could have just posted both guy's averages and said, "see...they're consistent...there's what they average." no one can deny that they average what they average.

    but that's not what's meant by inconsitency. and if being inconsistent means you explode for 45 points occasionally, i'm fine with inconsistency!
     
    #10 MadMax, Apr 2, 2005
  11. choujie

    choujie Member

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    While Tmac has a lot more 30+,40+games, he has a lot more 5-20,6-22 nights too. That's inconsistency.
     
    #11 choujie, Apr 2, 2005
  12. MFW2310

    MFW2310 Contributing Member

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    Unfortunately I did not choose the 95% CI. That is a staple of statistical that says at least 95% of all data points would fall within 2 SD of the mean. So, if I were to venture with the hypothesis that "the definition of consistency is how actual performance varies from the mean," then I'd say that both of our stars are wildly inconsistent (you could have known that from SD alone), with TMac being more inconsistent. However, as I said, I'm not willing to draw that conclusion right now without further studies.

    Just for comparison's sake though, the rule also says that at least 67% of points (66.xx actually) falls with in 1 SD. For this season, the 1SD (67% interval if you will) are as follows:

    Yao
    11.30 - 25.15 PPG
    4.67 - 11.81 RPG
    0 - 1.69 APG

    TMac
    16.78 - 33.96 PPG
    3.42 - 8.84 RPG
    3.18 - 8.07 APG

    Together, on any given night, TMac and Yao will bring:
    28.08 - 59.11 PPG
    8.09 - 20.65 RPG
    3.01 - 9.77 APG

    Now one thing I think that may have caused the huge fluctuation in the 95% CI is just that the sample size is too damn small (as I used this season only), which is why at this point that I wouldn't say that our stars are wildly inconsistent with TMac being more inconsistent, not until I added more stats from say, last year (if they are still available on nba.com). But like I said, you draw your own conclusions.
     
    #12 MFW2310, Apr 2, 2005
  13. MFW2310

    MFW2310 Contributing Member

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    Thanks for the tip Tango. Let me add some more data points before I do that.
     
    #13 MFW2310, Apr 2, 2005
  14. bfunw

    bfunw Contributing Member

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    That would be very nice. Can't wait...(Thanks for your time!)
     
    #14 bfunw, Apr 2, 2005
  15. tigermission1

    tigermission1 Contributing Member

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    A "lot more" 25-30% shooting games? I think you are exaggerating a bit. I know he had some, but not a "lot more".

    Overall, his 42-43% shooting usually holds true most games. The bad shooting games he has had, he has balanced them out with above-average shooting games.

    So that's the whole point of averages, because it tells you what a player is "expected" to shoot and how he is expected to perform.
     
    #15 tigermission1, Apr 2, 2005
  16. MFW2310

    MFW2310 Contributing Member

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    It doesn't skew anything at all. Out of the 71 games Yao played this season, he scored:

    Above Average: 35 games (with 2 18 PT games)
    Below Average: 36 games (with 2 19 PT games)

    Now, I understand that picking 18 PT versus 19 PT is completely arbitrary, but you have to draw the line somewhere.

    Out of the 69 games TMac played (I did not include the 3 min injury game against NO), he scored:

    Above Average: 35 games (with 4 25 PT games)
    Below Average: 34 games (with 5 26 PT games)

    When TMac gets going, he performs signficantly above average more often and when he has a stinker, he performs signficantly below average more often than Yao, who generally will score in the 21 - 24 PT range when he has a good game and 14 - 18 range when he stinks it up. This explains why TMac has the higher SD.
     
    #16 MFW2310, Apr 2, 2005
  17. MFW2310

    MFW2310 Contributing Member

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    That's a fundamentally flawed argument. If he is inconsistent only when he performs below 18.22 PPG for Yao, he would have a higher PPG.
     
    #17 MFW2310, Apr 2, 2005
  18. tigermission1

    tigermission1 Contributing Member

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    I think it is pretty much an accepted reality that big men (alas Shaq, Yao, etc.) tend to probably be more consistent than guards: that is their performances flactuate a bit less than, say, a Kobe or a T-Mac or an AI, etc.

    On most nights, try to observe, say, Shaq's statistics (usually he is very consistent with his 21-25 points performances, and rarely does he go out of that range).

    On the other hand, observe Kobe's performances, and watch how much fluctuation there is, almost to the point of being unpredictable.

    I think that is the nature of the guard game v. the big man game today. I am sure the same was true of the Hakeems, Ewings, and Robinson's of the league.

    Now, the "new age" big men in today's league (KG, Nowitzki, etc.) might prove this a less dependable standard, since while they are (size-wise) big men, they DON'T play a traditonal big man's game, like Yao and Shaq do.

    So call me bias, but I don't consider those "fake" big men, well, "real" big men; that is when you shoot threes and shoot 45% as a big man, which KG does (Karl Malone/Charles Barkley are rolling over in their graves! ;) )

    So in that sense, it is rather an obvious observation to say that Yao's game is "statistically" more consistent than T-Mac's game. It is the other intangibles, I believe, that people tend to argue.
     
    #18 tigermission1, Apr 2, 2005
    Last edited: Apr 2, 2005
  19. MadMax

    MadMax Contributing Member

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    exactly. where am i??? if he has a "lot" of lesser games in shooting percentage...then he must be having a helluva lot of "greater" games in shooting percentage to average what he's averaging.

    again...it's an average.
     
    #19 MadMax, Apr 2, 2005
  20. bfunw

    bfunw Contributing Member

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    But he/this thred is talking about "tangibles." He let people define their own consistency or inconsistency. You can use the word "inconsistency" either way, positive or negative.

    I do agree with you that T-Mac can explode in you on any given night, and that's why I expected him to do so last night, but he didn't. That's why he "thus is much less predictable." Of course this "inconsistency" could be very exciting. Like the Utah game TMac made 44 pts and "360' spin dunk," and the Blazer game Yao made 29 pts and that "dribble behind back and dunk."
     
    #20 bfunw, Apr 2, 2005
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