Shake Charts: Measuring and Visualizing (In)Consistency

It's amazing (kinda creepy sometimes) how Dave and I approach the same topic at the same time without even mentioning it to each other. This morning, Dave took up the topic of roster management and concluded at the end of his piece that a key problem as currently constructed is the inconsistency of the role players. Dave wrote...

Having Jerryd Bayless dominate a couple games, Rudy Fernandez set a rookie record for threes, Martell Webster churn out awe-inspiring quarters, and Travis Outlaw hit buzzer-beaters certainly makes the team more exciting.  In the long run having it all happen on the same team, a team which lacks consistent performances from any of said players, probably doesn't make the team better.  Eventually we need fewer guys to get excited about (that kind of excited, anyway) and more guys to depend on.  Clockwork predictable .700 ball beats randomly exciting .550 ball every time.

That elusive "clockwork predictable" basketball is valued here in Portland as much as it is anywhere else in the league.  With a slow-down, ball-control, super-efficient offense led by two uber-reliable players in Brandon Roy and LaMarcus Aldridge, consistency is perhaps the number one attribute the coaching staff and management is looking for from the rest of the roster.  

"Consistent" (or "Inconsistent") is one of the most used adjectives to describe Blazers players.  I'm too embarrassed to go back through my media row reports to see how often I use it.  If almost any player at any time follows up a 20 point game with an o-fer the first word that comes out will be "inconsistent."  Often, other contributions such as defense and rebounding will find themselves washed away in the inconsistency talk as well.  That's one reason Nate McMillan will regularly go out of his way to praise those efforts from players that perhaps weren't hitting from the field.  

While labeling a player "inconsistent" can be a crutch, there is no doubt that some players bring it every night, some simply don't and everyone else falls on a continuum in between.  My goal in this post is to explore scoring (in)consistency for the Trail Blazers by quantifying it and then visualizing it.  From there, we'll take a brief look at the relationship between scoring consistency and playing time consistency.   

If you're bored already, stay with me.  I'm about to put some pretty charts on your face.  And take a look at the Camby trade from a different perspective.  And rank the Blazers in terms of scoring consistency this year (and last year).  And show you the correlation between consistency of minutes and consistency of scoring for the Blazers over the last two years.  And and and and just click through the jump and read this please.

-- Ben Golliver | benjamin.golliver@gmail.com | Twitter

What Is "Shake?"

"Shake" is a term I made up to refer to a player's scoring (in)consistency.  It is essentially a measure of a player's variance in scoring.  For those interested, here's how I calculate it.

1. Calculate the absolute value of the difference between a player's one game point total and his season average.  If a player averages 10 points per game and he scores either 8 or 12 points, the number is 2.
2. Do this for every game of a season or, in this case, through the 2009-2010 All Star break.  Add them all up to get "Total Shake."  Brandon Roy is the Blazers' most consistent scorer. His total shake through the All Star break was 254 points.
3. Divide the "Total Shake" by the number of games played.   For Roy, this would be 254/40 or 6.35.  This becomes Roy's "Average Shake Per Game."
4. Take the player's average shake per game and divide it by his average points per game.  In Roy's case, that's 6.35 / 23.1.  This step yields a percentage.  In Roy's case: 27.49%.  This is what I call his "Shake."

Shake therefore represents the relationship between a player's scoring variance and his scoring average.  If a player scored 10 points (or 20 points, or 30 points) every single game his Shake would be 0%, perfectly consistent.  If he alternated scoring 0 points 41 times and 20 points 41 times over the course of a season, his shake would be 100%, perfectly inconsistent.  

What's a Good Shake?

Generally speaking, if you're an NBA coach you want a relatively low "Shake" from your players.  Nate McMillan probably has dreams during which guys like Rudy Fernandez, Martell Webster and Jerryd Bayless turn into robots that produce exactly the same amount of points every single night.

As you might expect, a Shake of 27.49% for Brandon Roy is very good (although not as good as his Shake last year).  Here's a little table to give you some perspective.

Some notes on this:

• Kevin Durant is currently going through an historically consistent stretch of scoring.  He's basically an outlier in and of himself.  
• From the numbers I've run so far, a shake between 20% and 30% for a go-to scorer is a pretty good sweet spot. It's enough room to account for the occasional blast-off game but also includes a baseline of stability that reflects an inability to avoid too many debacles.  

Shake and This Year's Blazers

Now that we've defined Shake and seen how some of the league's best scorers stack up, let's take a look at this year's Blazers.  Here are the Shake ratings for the top 8 Blazers in terms of minutes played.

Some notes on this: 

• If you like to praise Roy's steady play, it's difficult to dog LaMarcus Aldridge for being inconsistent.  The two players are surprisingly close when it comes to Shake and Aldridge is right in that sweet spot zone that I mentioned earlier.  For a guy that's had to change positions, adapt to new roles and play heavy minutes, it's downright remarkable.  If I had to grade Aldridge's season to date I would give him no lower than an A.
• Andre Miller has been called inconsistent by me a number of times and his Shake supports that but only to a degree.  Amazingly, he's a clear cut #3 on this team in terms of consistency.  I wasn't necessarily expecting that going into this exercise.
• Finally, you can see the bane of Nate McMillan's existence this year.  5 of his top 8 players are all over the map when it comes to consistency of points production.  You might be thinking: Well, he should stop yanking their minutes around!!!!  We'll look at the relationship between playing time and scoring later.  But for now the takeaway is that McMillan has been dealing with a lot of scoring shakiness this season.

Numerically we can see the impact of all the injuries this season.  Look how many games guys played last year and look how they responded.  Five Blazers scored more consistently last year than Andre Miller (3rd this year) is scoring this year.  The top 7 last year were more consistent than Blake, who was 4th this year. Even Brandon Roy and LaMarcus Aldridge have been slightly less consistent this year than last year.

A note: as the number of games increases, it's reasonable to expect Shake to decrease to some degree. As the last third of the season plays out, we'll see whether some of these guys find an equilibrium and increase their consistency. 

Shake and Outlaw and Blake 

I found it extremely interesting that Travis Outlaw and Steve Blake were last year's 3rd and 4th most consistent scorers respectively and that both were traded this week.  

Obviously, Outlaw was lost for most of the season this year due to injury.  After looking at his consistency of production last year and the team's vacuum of consistency this year, I believe he would have lasted the full season here in Portland had he not been injured and performed close to the standard he set last year.  He would have likely been no worse than the 4th most consistent scoring option and he would have had plenty of minutes to shine.  Keeping this in mind while watching his Clippers press conference is even more painful.  This, more than anything, helps put into perspective how cruel the "Breaks of the Game" can be. 

As for Blake, "Steady Steve" simply was no more.  While he was the Blazers' fourth most consistent option last year and remained so this year, his shake increased from 39.55% to 55.92%, a drop of more than 16%.  That's pretty big, especially when you consider his points per game average dropped from 11 to 7.6 as well.  

On Tuesday night, I asked Kevin Pritchard for his explanation of Blake's drop in production this year. "I think it is a change of roles," Pritchard told me. "We felt like he played well for us and I give a lot of credit to him. He's a terrific human being first and he's a great basketball player. We're going to miss him. There's going to be times where we're going to miss him. He's been everything we've asked of a player in this rebuilding process. He's been in the core of it. He'll be missed."

With all due respect to both Pritchard and Blake, the Blazers already missed the 2008-2009 version of Blake. Will they miss this year's Blake too?  Yes, but not nearly as much.  I believe had Blake performed with the same consistency and volume as last year, he would still be a Blazer today.

Shake Charts: Eye Candy

OK, enough number crunching, let's get to the fun stuff. I've designed what I call Shake Charts.  The idea of the Shake Chart is to visualize a player's scoring (in)consistency. This is a shake chart.

Not only is that a Shake Cart but it's Brandon Roy's Shake Chart for this season through the All Star break.  

How to Read Shake Charts

I've set up the Shake Charts like seismographs.  The X axis represents a player's point production in a game.  The y axis represents the games played during the season: the top is opening night and you work down through the course of the season.

The blue line connects the player's scoring as it goes through the season.  It's the main graphical element to focus on.  As I mentioned earlier, Roy has been the most consistent scorer for the Blazers this year.  As a result, the blue line doesn't vacillate all that much on his chart.  Especially when compared to someone like Jerryd Bayless.

The more blue, the more Shake.  It's that easy. 

The red line running up the middle of the each Shake Chart represents a player's scoring average.  It's included as a visual baseline.  The green and purple lines represent one degree of "Average Shake" from the player's per-game average.  This is included to mimic standard deviation but isn't really standard deviation.   Roy (6.35) and Bayless (5.50) actually have similar average shakes even though Roy averages more than twice as many points as Bayless. 

It's fun to note as you look at these charts how often players score within their average shake range (between the green and purple lines) compared to how often they don't.  Just compare Roy and Bayless's charts again.  Roy mostly rolls in that comfort zone down the middle while Bayless is much more often outside the lines.

A final, important note on the charts themselves: for maximum visual impact, the X axis on each chart is individually calibrated based on each player's minimum and maximum point totals.  Using the same X scale for each player made it difficult to see the scoring inconsistencies of the role players who haven't produced the same high-end individual game scoring totals. So be sure to take note of the X axis domain when you look at each chart. 

With that said, here are some more Blazers Shake Charts.  First, here's Aldridge.  A great visualization of his overall consistency, his slow start and then the increased production as of late.

Here's Andre Miller.  The 52 point game never looked so hilarious.

Martell Webster remains all over the freaking map despite some blast-off nights in 2010.

Rudy Fernandez hasn't played a ton this season due to injury and has struggled to find consistency when he has played.

I think Juwan Howard just broke the seismograph.

Earlier I mentioned Steve Blake's increased shake from last year.  Here are two charts for Blake: first last year's and then this year's.  I think they do a nice job of illustrating the increased inconsistency point and also his downward shift in scoring.

Do you want to see shake charts for Kevin Durant, LeBron James, Dwyane Wade and Kobe Bryant?  Click here.

Shake and Minutes

Again, comparing the numbers from this year to last year, you can see the turmoil caused by all the injuries. You can also be reminded that only 4 of the Blazers top 8 minutes played guys from last year are in the top 8 again this year (Roy, Aldridge, Fernandez and Blake, who just got traded).  That's a ton of turnover.  In turn, Nate McMillan deserves a ton of credit for managing this.  

Now that we know the players' minutes Shake and their scoring Shakes, let's compare them on a graph.  

Click on the image below to enlarge it or click here.

On the X axis you have the players' Minutes Shake.  On the Y axis, their scoring Shake.  So as you move left to right you find players whose minutes are more prone to go up and down.  As you move up the chart you have players who are less consistent in their scoring.  No surprise: Brandon Roy and LaMarcus Aldridge lead the pack by quite a distance.  

What's most striking about these charts is how nearly linear the relationship between (in)consistency of minutes and (in)consistency of scoring is for the Blazers, regardless of personnel.  This makes sense. If someone is scoring off the charts well, their minutes will increase.  If they go cold and stay cold, their minutes decrease.  

But man the two are tied together tightly. The correlation between playing time consistency and scoring consistency for the Blazers' top 8 players last year was .6671.  This year it's .6482.  Nearly identical. Given everything that's happened, the development of some players and the loss of others, that's pretty incredible.  It makes total logical sense but it's still interesting to quantify and visualize.

As to my original question: is there anyone who should be playing a lot less or a lot more minutes based on their scoring consistency?  Not really.  The biggest discrepancy is Rudy Fernandez, whose scoring Shake rates him 7th on the Blazers while he plays the 5th most consistent amount of minutes.  The trade of Blake and Outlaw should further increase his consistency of minutes; hopefully his scoring output follows suit.  Otherwise, McMillan is pretty much on point.

Conclusions

• LaMarcus Aldridge deserves much more credit than he has received for his consistency in scoring this season.
• If Outlaw hadn't been injured and Blake had played to his standard from last year, I think both would still be Blazers.
• The Blazers just traded away last year's 3rd and 4th most consistent scoring options and their #1 scoring option both this year and last year is injured.  Their role players have been all over the map.  That's a major issue (if not the single biggest issue) to keep in mind down the stretch.
• The relationship between playing time and point production over the last two years for the Blazers is incredibly similar despite all the changes in personnel and injuries.
• Seismographs don't get enough love, generally speaking.

-- Ben Golliver | benjamin.golliver@gmail.com | Twitter

(Note: The first table was updated on 2/23 to fix a previous typographical error that overstated Kobe Bryant's inconsistency.  His shake chart was formatted properly.)