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

Smaller sample size => more SD

 

??? Standard deviation of a variable has nothing to do with how many samples you draw from that variable. You might be confusing the variance of an estimate with the standard deviation of a variable.

For example, think of the number if people posting on GARM everyday. It's standard deviation does not depend on how frequently we check that number. On the other hand, if you want to estimate the average number of people visiting the site, then the SD of your estimate gets smaller as you accumulators more days in your data.

 

Fixed.

 

Definition of TS: http://en.m.wikipedia.org/wiki/True_shooting_percentage

I should not have brought up order statistics. The OP was not looking at that.

 

Say you had a couple of real outliers, but were generally pretty consistent. Wouldn't a larger sample size (100 games, vs. 10 games, for example) smooth out the result, so that you had a smaller SD?

Hence "Smaller sample size => more SD", as Stats said.

 

So the conclusion....

is Lin inconsistent or not?

 

For the late comers ...

 

Lin: good thing or a bad thing?

 

consistent if he played 36+minutes.

 

Linconsistency

I didn't want to impose on the OP of the other inconsistency thread with a tangent topic since there's alot of discussion over there using a different method, but I wouldn't mind if this post gets merged onto it.

I made an attempt to check our player consistency a month ago, but there were too many injuries on our team to have meaningful data. I figured with the new "inconsistency" thread, I might as well publish my findings with more games in. So here's what I did. I got the Game Score data from bball reference and normalized it to 36 minutes. GameScore incorporates all the recorded stats in a game, much like PER. I did this for our top 4 offensive players only.



The GS average data confirms my eye test. We have two star players in Harden and Howard. Then we have two role players in Lin and Parsons.
The standard deviation shows that there isn't much of a consistency difference from each player to another, in fact having Lin being the most consistent player of the 4. This didn't meet my eye test, so I made up another metric to measure consistency. I took the suggestion that a Game Score of 10 is an average performance. (from the bball reference glossary) I then found the % of games from each player with a score below 10, indicating a poor game. Now the data seems to meet the eye test. Lin and Parsons have the same % of poor games. Harden and Howard have much less poor performing games.

If you just look at the box score, you would think Parsons is more consistent, but in reality he just gets a lot more minutes. You would also think Lin is less consistent, but I think it's a combination of scattered minutes, plus all the trolls flooding the board every time Lin has a bad game, so we see it brought up all the time. Despite that, playing well 65% of the time isn't bad at all, especially for two rookies.

 

Lin's GS avg is about 11, and Parsons' is 13, and below 10 is called a bad game?

While Harden and Howard start out at around 16. Your results just showed that Harden and Howard are better players in terms of GS, that has nothing to do with consistency.

The std dev of GS may suggest some consistency issues, but not "below avg" of GS 10. "below avg" should be done for the GS avg for the individual players, not an absolute value of 10.

And yeah, put this in the other Lin consistency thread.

 

I did the "below average" based off the average GS, but guess what happens when you look for % of numbers below an average of numbers? They all show up around 50%. Their standard deviations are pretty close already, so this method gives you the same results as the Std Dev method, so I didn't include it.

I thought about using a different standard for Harden and Howard, because their GS averages were so high and you would expect a higher performance from "super stars". However, in reality everyone has a different guage to what they think is a good or bad game. 10 is the league average so I figured it would be a good starting point.

 

How about just a histogram of individual players' GS, since you only look at 4 players anyway.

 

Yea, technically the "below avg" should be done in terms of the GS avg for the individual players (thus below avg for them). So that part of the OP's analysis is off, at least regarding consistency in a technical sense.

But wouldn't we all agree that for each of these 4 players, if they scored below 10 on a game, we would think that's a "bad game" (at least from scoring perspective) for them. And isn't that often what we care about when we think about player contribution, at least for the 3 and 4 options -- not: how much is a game off their individual average? but did they manage to get us at least some minimum number of points that we'd like a 3 or 4 option to get us in a game.

From that contribution perspective, I found the numbers interesting. I did not expect the number of Parsons' below 10 point games (when averaged out per 36), to be so close to Lin's.

 

That is true, considering Parsons has on avg almost 2 points more than Lin's GS.

 

I did that, but everyone's averages are so close and the difference of their std dev was so small you couldn't actually tell anything by overlaying their GS plot in a chart. I felt the table showed the difference more clearly than the histogram plot, so I left it out. Unless you're looking for something specific that I left out?

Game Score includes assits, turn overs, rebounds and etc. The actual formula can be found from bball reference.

 

Below are two references. Percentages measure more or less. Thus, they are rank order data. Arithmetic operations are not permissible when using percentiles. TS% is a rank order stat. It indicates if one player is shooting better than another. Thus you cannot add, multiply, subtract or divide percentages. If you did this in your analysis it is incorrect, (I cant'look back at your data at this time,sorry,but i recall that you computed the SD of the true shooting percentage of each player. This would be incorrect. Percentiles do not specify the size of the interval . Many people are confused about this. That's why I mentioned it.
A Summary of Measurement Scales, Their Characteristics, and Their Statistical Implications

Nominal
A scale in which the numbers serve as labels rather than have numeric value (i.e., 1=male; 2=female).

Ordinal Scale
A scale which "measures" in terms of such values as "more" or "less," "larger" or "smaller," but without specifying the size of the intervals (i.e., 78 %iles). Can be used for determining the mode, percentage, chi square, median, percentile rank, or rank correlation.

Interval Scale
A scale which measures in terms of equal intervals or degrees of difference, but whose zero point, or point of beginning is arbitrarily established (i.e., 32 degree Fahrenheit). Can be used for determining the mode, the mean, the standard deviation, the t-test, the F test, and the product moment correlation.

Ratio Scale
A scale which measures in terms of equal intervals and an absolute zero point of origin (72 inches tall). Can be used for determining the geometric mean, the harmonic mean, the percent variation and all other statistical determinations.


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Statistics and Probability Dictionary

Percentile
Assume that the elements in a data set are rank ordered from the smallest to the largest. The values that divide a rank-ordered set of elements into 100 equal parts are called percentiles

An element having a percentile rank of Pi would have a greater value than i percent of all the elements in the set. Thus, the observation at the 50th percentile would be denoted P50, and it would be greater than 50 percent of the observations in the set. An observation at the 50th percentile would correspond to the median value in the set.

See also: AP Statistics Tutorial: Measures of Position

Browse

 

You should probably normalize the std deviation by dividing by the mean. I.e. how big is the deviation w.r.t. the average

In that case, Harden will be the most consistent, followed by Howard. Lin and Parsons are essentially the same. In any case, the variation between all these players is small.