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Measuring Lin's scoring consistency (as well as that of other Rockets)

Discussion in 'Houston Rockets: Game Action & Roster Moves' started by hollywoodMarine, Feb 3, 2014.

  1. hollywoodMarine

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    Hey guys. Been lurking on CF for awhile now, and read a lot of posts complaining about Jeremy Lin's inconsistency. It got me thinking, and wondering... namely, how does one actually measure consistency? How inconsistent is Lin really? How inconsistent is he compared to his teammates? Has he improved in this area? This post will be an attempt to provide some possible insights into these questions and issues. Specifically, the area that this post will focus on is scoring.

    Before I start, I want to be candid about myself so I will lay my cards on the table and say that I am a huge Lin fan, and I am “one of those guys” that only began watching basketball because of Linsanity. So I may have some bias (though I do try my best to be objective about these things) and I'm most likely not as knowledgeable about basketball as most of you. I do, however, have some bit of knowledge of statistics, and I figured this would be a great opportunity to practice using SPSS (and good practice for my class :) ) while at the same time gain more knowledge about the exciting world of basketball by, hopefully, engaging in some enlightening discussions here.

    Aim of this Post

    So for those of you who have not already put me in on your ignore list, thanks for sticking around! This post will be mainly focused on Lin, but it will also provide descriptive statistics on other Rockets (specifically, Harden, Howard, Parsons, Beverley, Jones, Casspi, Brooks, and Motiejunas) in case you are curious about their consistency. This post will also, as mentioned earlier, focus on scoring (so if you see some data that suggest Beverley is inconsistent, for example, this is NOT me saying that he is as a whole an inconsistent player, since we all know he provides many other things consistently, like steals, rebounds, defensive presence, and other intangibles). The reason I want to focus on scoring is because I feel Jeremy Lin's role, as the sixth man, is mainly to provide a scoring punch off the bench, so that is the most important thing to examine here. Of course, if there happens to be demand for investigation of consistency values for other things on the box score, like assists etc., I can try and provide insight on those variables as well when I have time.

    As I've mentioned before, my basketball knowledge is not that great, so please forgive me if I make some basketball inference or something in this post that is just blatantly wrong. I'll also probably make mistakes in my statistical analysis or maybe explain some statistical concept incorrectly as well, so if you are an expert in this field (looking at you Torocan), feel free to correct me. Better I make them here than on my future exams!

    “Shake” as a Measure of Consistency

    So the first question is, how do we measure consistency? For those who didn't know, in statistics, the standard deviation (SD) of a group of a scores represents variation or dispersion from the average of those scores. A group of scores with a lot of “spread out values” (e.g., 1,10,25) will have higher SD than a group of scores with values closely clustered together (e.g., 9,10,11). For basketball players, the SD for points per game is a good way of looking at how consistent they are. But it does not provide a complete picture. If player A scores 0,10,20 points in 3 games, he would have the same SD as player B, who scores 40,50,60 points, or lets say in an extreme case, player C, who scores 90,100,110 points in 3 games. But player A is clearly more inconsistent than the other two. A better measure of consistency would be to divide the SD by the average of those scores (and the lower the value of this, the more consistent the player). This way, for players who normally average 25 points, having a range of scores that typically spread out by +/- 5 (i.e., their SD is 5) does not make them appear as inconsistent as players who average 5 points, but who also have the same amount of dispersion. Instead, the former would have a consistency value of 5/25=0.2 (which is quite consistent), while the latter would have a consistency value of 5/5= 1 (extremely inconsistent).

    This is the same formula of consistency that is used in this cbssports article (although the author used the wrong term.. it should be standard deviation, not variance). The article termed this consistency value of SD/PPG, as “Shake,” which is how I'll be referring to the consistency value as well.

    Data Screening

    In order to find the “Shake” values for each Rocket, I used SPSS to examine the scoring numbers and find the standard deviation. Before doing so, however, I screened the data for cases where a player did not play enough minutes for his scores to accurately reflect a good or bad game (or really reflect anything at all). So all cases where the minutes played was under 5 minutes were removed. Additionally, cases where minutes played was under 9 but where the field goal attempts (FGA) was under 3 were removed as well. I know this is arbitrary, but this is to make things fair for bench players like D-Mo, who sometimes would play 6 or 7 minutes and make only one field goal attempt or less (which is NOT an accurate representation of his skills), and at other times would play the same amount of minutes and make 4 or 5 field goal attempts. Over 9 minutes, cases where FGA is under 3 were NOT removed because there are some games where a player would play 13 minutes and make one field goal attempt... I felt that once a player has been playing that amount of minutes, not making more than 2 FGA would be a reasonable reflection of a poor shooting game. Once again, I know it's all very arbitrary, but if you feel you have a better criteria for how to screen the data, I'm all ears!

    PPG, SD, and “Shake”

    So how do Lin and his fellow Rockets look in terms of scoring consistency?

    [​IMG]

    [​IMG]

    Average points per game: Lin (13.79), Beverley (9.31), Harden (23.8), Parsons (17.11), Howard (18.29), Jones (12.66), Casspi (8.56), Brooks (8.79), Motiejunas (6.1)

    Scoring SD: Lin (6.59), Beverley (4.75), Harden (8.53), Parsons (6.14), Howard (7.33), Jones (7.07), Casspi (4.85), Brooks (6.24), Motiejunas (3.89)

    “Shake” (SD/PPG): Lin (.48), Beverley (.51), Harden (.36), Parsons (.36), Howard (.40), Jones (.56), Casspi (.57), Brooks (.71), Motiejunas (.64)

    The first chart plots the Rockets' PPG vs Scoring consistency. The x axis represents PPG, the y axis represents scoring consistency, or “shake.” The lower you are on the chart, the more consistent you are in scoring. The further to the right you are, the more points you score on average. So the best place a player could be on this chart, would be in the lower right hand corner (that would mean you score a lot AND you are consistent). The worst place would be the top left vicinity (that would mean you score little AND you are inconsistent), although if a player has an extremely low PPG, having high shake value may not always be a bad thing (more on this later).

    In this chart, you can see why Harden is our best player in terms of scoring, as he is tied with Parsons for the highest level of consistency on this team while also contributing more buckets on average than everyone else. Harden, Howard, and Parsons as a group appear to have the highest level of consistency and scoring for the whole team which may be why some people consider them the big three. Lin has a higher level of inconsistency than those three, and scores less on average. Beverley is more inconsistent and scores less, but scoring is not really his role, while Jones's high shake value was a bit surprising to me (Keep in mind the 4 games at the beginning of this season where he played 7 minutes or less were all removed from this analysis).

    Lastly, while D-Mo, Brooks, and Casspi are all at the top left area of this chart, it is understandable for them to be inconsistent given that they are bench players and have inconsistent minutes.

    The boxplot chart reinforces the shake chart. The line in the box represents the median (50th percentile), the box top and bottom edges represent the 75th and 25th percentile respectively, and the whiskers represent the 1st and 99th percentile. Any small dots/circles above or below the whiskers represent outliers (e.g., case "9" for Lin is his 34 point game in Philly). The smaller the length from the top whisker to bottom whisker, and the smaller the box, the more consistent the player. We can see in this chart that Parsons's box and overall length from top whisker to bottom whisker is relatively small compared to other high scoring players. This is consistent with his low SD values. And while Harden's box and overall length from whisker to whisker is larger, he also has a much higher PPG, which gives him a lot more leeway in terms of scores dispersion (and is the reason why he is still tied with Parsons for lowest shake value of all the Rockets players).

    Just for those of you who are curious: How to interpret SD value and why inconsistency with very low PPG may be a good thing

    Think of SD as a way of determining what a “good” game or a “bad” game for a player would look like. For Lin, a typical game is one where he scores his average, which is around 14 (remember, his 4 minute game in Atlanta was not included in this analysis, so it is slightly higher than his official stats). On a bad day, around 16% of the time, he would score less than or equal to one SD below his average (so 7 points or less), and on a good day, also around 16% of the time, he would score more than or equal to one SD above his average (so around 20 points or more). On a rare exceptional occasion (less than 3% of the time), he would score 2 SD above the mean (around 27 points or more) or 2 SD below the mean (also less than 3% of the time), which is almost zero. We've seen both of these types of games from him before.

    What about for players with high SD values whose average is very low? Brooks, for example, averages 8.79 PPG, but has similar SD value to Lin (hence why he has a much higher shake value). When he has an excellent game where he scores two SD above the mean (so 12 points above 8.79), he scores in the 20's. And indeed we have seen this on several occasions. On a rare terrible day, however, it's actually impossible for him to score two SD (around 12 points) below his mean, because that would put him in the negative! The lowest he can score is zero. The reason we have such SD values is because the scoring samples are positively skewed, but don't worry about that... the point is that in his case, being very inconsistent is actually a good thing. To a lesser extent, the same can be said of D-Mo as well. It is better to be inconsistent with a very low PPG (because you'll still have a chance of scoring big every once in awhile), than to be very consistent with a very low PPG.

    “Per36 Shake”

    The original concept of SD/PPG as a measure of consistency is a good one, but it has some disadvantages, especially when measuring the consistency of players who are given inconsistent minutes. Jeremy Lin is one of those players. Because this post is already getting really long, I will not post the boxplot or table for minutes per game (MPG) and MPG SD, but the data suggest that Lin is probably being given some of the most inconsistent minutes in relation to his teammates- his MPG has the highest SD of out of all Rockets (If anyone wants the data, I'll post it up).

    How many of Lin's games are low scoring due to poor shooting and how many are due to him simply not being given many minutes (for example, the game where he played against the Grizzlies on January 24th when he had a good shooting night going 4/6, but only scored 9 points)? Conversely, how many of Lin's high scoring games are more due to his being given MORE minutes than normal, and how many are due to him simply being very productive?

    In order to remove the effect of inconsistency in minutes played on scoring consistency, I've decided to make a modified shake value, of the standard deviation of per 36 points divided by the mean per36 points. Basically a player has an individual per 36 points for every game (points for that game divided by minutes and then multiplied by 36). The collection of these per 36 scores are used to determine the per 36 points SD, which would be divided by the average per 36 points per game. Note: This average per 36 PPG is slightly different from the official per 36 stat (which I believe -correct me if I'm wrong- plugs in the total points, divides it by total minutes, and multiples by 36). For this case, the formula is applied separately for each game. The average Per 36 PPG is simply the average of all the individual game calculations.

    So how do Lin and other Rockets look in terms of Per 36 scoring consistency?

    [​IMG]

    [​IMG]

    Average Per 36 PPG: Lin (15.07), Beverley (11.10), Harden (21.97), Parsons (16.24), Howard (19.08), Jones (14.74), Casspi (14.73), Brooks (14.67), Motiejunas (13.75)

    Per 36 Pts SD: Lin (4.90), Beverley (6.28), Harden (7.02), Parsons (5.42), Howard (6.56), Jones (6.86), Casspi (6.83), Brooks (8.18), Motiejunas (8.13)

    “Per36 Shake” (Per 36 Pts SD/Average Per 36 PPG): Lin (.33), Beverley (.57), Harden (.32), Parsons (.33), Howard (.34), Jones (.47), Casspi (.46), Brooks (.56), Motiejunas (.60)

    As you can see in the top chart, Lin's Per 36 shake value is actually on the same level as Harden, Parsons, and Howard. In the box plot, you can also see how much smaller Lin's box and whisker lengths are. So what does this suggest with regards to Lin's scoring consistency? One can interpret these charts in two different ways. The optimistic interpretation (and as a Lin fan, this is how I would like to interpret it :cool: ) is that on a per minute basis, Lin's scoring production may actually be just as consistent as Parsons, Howard, and Harden! Note, this is not the same as saying Lin is just as consistently productive as Parsons, Howard, or Harden. Rather, he is as consistent producing at a rate of 15.07 points per 36 each game as Harden is at producing 21.97 points per 36 each game (remember that his SD value is lower than that of Harden's to compensate for his lower productivity). Still, 15.07 is not bad, and keep in mind his official per 36 scoring numbers is actually higher at 15.6 which I believe is around the league average for starting point guards. Most importantly, these results suggest that perhaps Lin's issues with inconsistency, the primary gripe that people have with his play, may not really be all that bad. A sizable portion of Lin's inconsistency in scoring that we have seen in the first “shake” chart may thus be a consequence of him being given inconsistent minutes.

    Skeptics may instead offer an alternate explanation which is that because McHale is quick to bench Lin when he appears to be playing a bad game, we rarely get to see instances where Lin plays and shoots poorly for 35+ minutes. Consequently, by this interpretation, McHale may actually be doing him a favor as this indirectly improves his Per 36 numbers.

    Both interpretations are valid, but keep in mind that there has been quite a few occasions where Lin bounced back very well in the 4th quarter after a miserable first few. For example, as I recall he was 1 for 5 for the first half of the Raptors game where he ultimately scored 31 at the end. So in any given game where Lin sees his minutes cut short, while there is a chance that McHale benching him may have saved him from another quarter of awful shooting, there is also some likelihood that he may have prevented the appearance of “Mr. 4th quarter” as well.

    “True Shooting Percentage Shake”

    Lastly, the Per 36 Shake is not perfect either. If some player consistently scores 15 points per 36 minute every game, but does so with very inconsistent FG% from game to game, then you can't really call that player consistent. This may be more what people are referring to when they talk about Lin's inconsistency. For example, there may be two games where he plays the same amount of minutes, produces the same amount in terms of points, but one game may be 4 for 12 (like the January Lakers game), and another may be 5 for 10 (like the Spurs game on Christmas day).

    True Shooting Percentage (TS%) Shake would thus be a good measure of consistency in terms of shooting performance. As with the Per 36 Shake, in this case, the TS% is calculated for each game. The collection of TS% scores are then used to find the SD value, and average TS% score (this will also be different from the official TS stat, as that one plugs in the total points, total FGA, and total FTA all into one formula). TS% shake will be calculated by dividing the TS% SD over mean TS%.

    [​IMG]

    [​IMG]

    Average TS%: Lin (.57), Beverley (.50), Harden (.59), Parsons (.60), Howard (.58), Jones (.55), Casspi (.54), Brooks (.50), Motiejunas (.47)

    TS% SD: Lin (.15), Beverley (.21), Harden (.13), Parsons (.20), Howard (.15), Jones (.18), Casspi (.21), Brooks (.23), Motiejunas (.23)

    TS% Shake (TS% SD/Average TS%): Lin (.26), Beverley (.42), Harden (.22), Parsons (.33), Howard (.26), Jones (.33), Casspi (.39), Brooks (.46), Motiejunas (.49)

    Once again, the shake value for Lin is actually quite decent when compared to his teammates. Lin's TS% consistency is higher than that of Parsons, and is right around Howard's (Harden, of course, blows everyone out of the water, although his average TS% is not as high as that of Parsons). I do believe that Howard's TS% shake should be significantly lower if not for the fact that he is inconsistent with his free throws. The box plot paints a similar picture (for any of you wondering by the way, the outlier in Parsons's boxplot that says case “66” is that game against Brooklyn when he went 7 for 7, 6 of those being 3 pointers).

    Comparing Lin's Consistency for the 2013-2014 Season vs 2012-2013 Season

    So the results suggest the possibility that Lin is actually more consistent than we think (or that his inconsistency stems more from him playing inconsistent minutes than inconsistent shooting performances). What about Lin's consistency this year compared to last year?

    When we look at PPG, PPG SD, and (regular) shake, we see only a slight improvement:

    2012-2013 PPG: 13.35, SD: 6.65, Shake (SD/PPG): .50
    2013-2014 PPG: 13.79, SD: 6.59, Shake (SD/PPG): .48

    Once again, this does not take into account the fact that Lin had much more consistent minutes last season (Mean: 32.21 minutes, SD: 5.84) compared this season (Mean: 31.68, SD: 7.53)

    So what do the following Per36 Shake, and TS shake suggest?

    2012-2013 Average Per36 PPG: 14.75, Per36 Pts SD: 6.43,
    Per36 Shake (Per36 Pts SD/Mean Per36 PPG): .44
    2013-2014 Average Per36 PPG: 15.07, Per36 Pts SD: 4.9,
    Per36 Shake (Per36 Pts SD/Mean Per36 PPG): .33

    2012-2013 Average TS%: .53, TS% SD: .16, Shake (TS% SD/Mean TS%): .30
    2013-2014 Average TS%: .57, TS% SD: .15, Shake (TS% SD/Mean TS%): .26

    Both in terms of production per minute, and true shooting percentage, Lin's Shake values have gone down, meaning he has gotten more consistent compared to last year, even if his overall PPG consistency level has improved only slightly.

    Conclusion and Other Thoughts

    These descriptive statistics suggest that in terms of scoring, Lin's issues with inconsistency may not be as bad as we think. In fact, looking at Per 36 numbers and TS%, Lin's consistency values are comparable to that of our two super stars (Harden, Howard) and emerging star (Parsons). A quick reminder (because I often forget too), having the same consistency value for Lin is different from having that same consistency value for Harden, or any of the other big three. Because Lin has a lower TS% and Per 36 PPG than the other three, it is necessary for him to have a lower SD value (lower spread and dispersion of scores) than them to maintain the same shake value.

    There are some limitations of this analysis. If you notice, I've tried to be very careful saying things like “this may suggest” or “the evidence suggest the possibility” etc... The reason is that I cannot find a really good test of significance to provide support that the difference in consistency values between player A and player B, or between player A last season and player A this season, is a significant difference. The only test on SPSS that does this is the Levene's test of homogeneity of variance, but it has a very high criteria for determining if the difference between the SD of two samples is significant (and I am not sure how to incorporate the concept of “Shake” into that). If anyone has any idea on how to test significance in this case, please do tell!

    Also, the SD values are very sensitive to outliers (extreme values). Such values, especially extreme positive outliers, can sometimes affect SD, and subsequently shake values, in ways that would be counter-intuitive. For example, take Lin's current PPG (13.79), SD (6.59), and Shake (.48) values. If this Wednesday, he were to somehow, some way, score 50 points, his SD would increase significantly to (8.71). And even though, his average PPG would jump to 14.72, it would not increase nearly enough for balance out the sudden rise in SD. As a result, his shake would rise to be nearly .60, which on the surface, if you didn't know that he just dropped a 50 point game, you would think is a really bad thing. An extremely good game can affect this inconsistency value just as much as a really bad game, but when we talk about inconsistency, we usually talk about the bad kind (shake values do not differentiate!). For Parsons, Jones, and Lin, who all had a couple of these exceptional outlier games, their shake values may actually make them look slightly worse than they really are.

    There are a couple other limitations and weaknesses of this analysis, particularly when it comes to the TS% and Per 36 Shake, but I can't remember what they are (I'll edit this post when I do!)

    Finally, I'm sure some people are wondering how consistent our players are compared to the League average. Unfortunately, no such statistic exists (when I have time, I can maybe write a script to find the average Shake values). If you want to get a picture of where our Rockets players stand compared to arguably the most consistent superstar in the League (Kevin Durant), know that KD's shake value is .27, Per 36 shake is .22, and TS% shake is .173!

    Wow, this post ended up being much longer than I thought. For those of you who actually read through it, thanks for your patience! I am sure I probably made some mistakes in some of these calculations, or maybe copy and pasted the wrong values somewhere, so if you see anything that may not look right (e.g., a Rocket's TS% just seems higher or lower than your gut feeling tells you it should), or may look like a typo (e.g., you see a value like PPG SD for one player that is identical somehow to another completely unrelated value like Per 36 Shake of another player, that means I probably copy pasted the wrong values), let me know! I'll re-check the values for mistakes.
     
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  2. jbasket

    jbasket Member

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    Please provide a tl;dr section; will be helpful for many people.

    Edit: reading through later, well done. Excellent first thread.
     
    #2 jbasket, Feb 3, 2014
    Last edited: Feb 3, 2014
  3. Bo6

    Bo6 Member

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    yeah it's called conclusion and other thoughts.....
     
  4. AvgJoe

    AvgJoe Contributing Member

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    welcome to CF. Good analysis, but you only evaluated points and TS. There are a lot of other factors contribute to being inconsistent, for example: TOs, Defense, Assists.

    I think his scoring was never that much an issue to people. His TOs, defense and ability to attack and create for teammates can be quite inconsistent.

    And his 3 % has dropped from beginning of this season. Would have been great if he could keep it up, but too bad it is averaging back to norm.
     
  5. FTW Rockets FTW

    FTW Rockets FTW Contributing Member

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    Then we need a TL;DR section for the conclusion and other thoughts as that is long in itself ;)
     
  6. rlivz

    rlivz Contributing Member

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    To add on to this, the biggest complaint most have with Lin in regards to consistency is his mindset and body language between individual games. It's pretty night and day, ie. Lin vs. Cleveland compared to Lin 2 weeks ago.
     
  7. jbasket

    jbasket Member

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    Behind pages of evidence and walls of text, and is still quite long for people rushed on time.
     
  8. quatin

    quatin Member

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    I did this about a month ago and I arrived at the conclusion that our starters have roughly the same consistency (Lin included). I used the GameScore rating per 36 from bball reference, which is some forumla that takes into account all the counted stats. I plotted it on a scatter plot with all our starting guys per game. The results were pretty much the same. Parsons was the most consistent producer, but Harden produced at a higher level. Lin and Howard were pretty much the same, with a lower GS average and a higher variance.

    I didn't post the data, because injuries caused inconsistent minutes for our starters. This made the "consistentcy plot" inconsistent, but at a first glance, there wasn't much of a difference. I think Lin's inconsistency is blown out of proportions, because he's under a microscope every game. The trolls are quick to post their hate every time Lin has a bad game, so we all see the topic brought up constantly.
     
  9. hollywoodMarine

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    Thanks. You are right, here is a TL;DR in bullet points (if anyone can tell me how I can edit my original post to add it in there that'd be great :grin: )

    Statistics suggest that scoring wise:
    - In terms of PPG, Lin may be more inconsistent than Harden, Howard, and Parsons

    - In terms production per minute, Lin may be just as consistent as the Harden, Howard, and Parsons

    - In terms of TS%, Lin may be more consistent than Parsons, just as consistent as Howard, and more inconsistent than Harden.

    - In terms of all the above 3 variables, Lin may have improved in consistency from last year (but less so in PPG)

    - Lin's greater inconsistency in PPG may be due to being given inconsistent minutes
     
  10. Panda23

    Panda23 Member

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    god forbid people must read on a basketball forum LOL
     
  11. hollywoodMarine

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    Really? I had thought his role was no longer to be a playmaker (to limit TOs), and that scoring had become his main role off the bench. I can look at assist consistency after midterms are over this week.

    In terms of defense consistency, Lin is actually quite consistent... he's just consistently not very good. However, that same article also suggested that Beverley was pretty much on par with Lin (only Bev is more inconsistent). So I don't really know what to make of it. This goes to show also that it is difficult to examine an individual player's defensive impact or consistency.
     
  12. steady

    steady Member

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    nice work on the tl;dr ... my mind appreciates it


    I wonder if the shake factor on the consistency of Lin's minutes will change post trip dub. ;)

    QUOTE: "the data suggest that Lin is probably being given some of the most inconsistent minutes in relation to his teammates -- his MPG has the highest SD out of all Rockets"
     
  13. qiantom1999

    qiantom1999 Rookie

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    Great analysis. My point would be simply that consistency is not something you demand from the #4 player of the team. You demand consistency from your stars. There are not enough touches, shots or plays run for the #4, 5 players on the team for them to be consistent.
     
  14. dwanga

    dwanga Member

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    Well done! It'll be even better if you could do consistency analysis on PER, usage and/or even defensive efficiency and opponent %. In fact, throw in a couple comparable players from other teams, ie: Parker, Conley, Vasquez, Thompson, Wade, Lowry, Hibbert...
     
  15. conquistador#11

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    more shot attempts = an increase in ppg.
    lets say dragic was a rocket, no way does he average 20 points, shooting 10 times, unless he magically found a way for his european baskets to be converted to american baskets at current inflation rate, 1fg= 4 points.

    However he would average .8 less of a turnover and around 5.8 assists since no one can hit a three. And the guy that can, brooks, is sitting on the bench. If only brooks played the SF position. one can dream

    In all,
    shoot less threes and keep taking it to the hole. good things happen.
     
  16. Easy

    Easy Boban Only Fan
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    I agree with AvgJoe. Lin's inconsistency is not really his scoring but his play making, defense, TO, and shooting percentage (especially his 3pt shooting).

    Beverley is clearly more inconsistent than Lin in terms of scoring. But his value is not in scoring or on offense in general. So nobody complains about his inconsistency. Lin is given higher expectations on offensive production. So PPG is only a small part.

    That said. You did a great job on scoring. If only you could provide similar analyses for other areas of the game.
     
  17. WaitForIt

    WaitForIt Member

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    ^ does not add on to the post.
     
  18. gene18

    gene18 Rookie

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    It is my understanding that arithmetic operations cannot be performed on percenteges. (TS%) A percent is a rank order. Thus, A mean and SD or any other value using arithmetic operations comprising percentages has no meaning. Look it up. It will help you in your stat class.
     
  19. gene18

    gene18 Rookie

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    Addition: You use of PPG and other ratio data is very acceptable and your analysis is quite good. Just remenber nominal, ordinal,interval, and ratio and the permissable operations on each type of data.
     
  20. jocar

    jocar Member

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    His inconsistency is in his attitude and confidence. Some days he's on top of the world, the rest of the time he looks like he's depressed out there. Fix that, and his stats will follow.
     

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