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An analysis: Who should shoot more for the Jayhawks?

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Many times, Kansas coach Bill Self has talked about Sherron Collins or Cole Aldrich needing to get more shots.

And I've always wondered if that was true or not.

Sure, it's easy to look on the court and see that Collins and Aldrich are two of KU's most talented players.

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But does it actually help KU's offense when those guys are increasing their shot totals? And what about the other major players on the team? Would KU be benefited by having any of them shoot more (or less)?

It's a question I set out to answer using the best method I could think of: statistics.

The following blog will show the correlation between individual KU players' shot percentage and the team's points per possession. I'll try to go one step at a time to explain what I did in simple terms.

First off, if you're not familiar, shot percentage is an advanced statistic that measures the percentage of a team's shots a player takes during the possessions he is on the court. This statistic tells us more than field goals attempted, as it takes into account how many possessions are in a game and also whether an individual played much or not. For example, if Sherron Collins puts up 20 shots in a 70-possession game while playing 40 minutes, that's quite a bit different from putting up 20 shots in a 50-possession game while only playing 25 minutes.

In the examples above, Collins' field goals taken would be the same, but his shot percentage would be much higher in the second case.

As you probably have figured out, points per possession simply is a team's points divided by the number of possessions. It's more useful than the final score, as a team scoring 80 points in 60 possessions actually played better offense than a team that scored 85 points in 85 possessions*.

* — All advanced statistics in this blog come from StatSheet.com.

My goal was to find out if the two numbers were correlated. For example, if Collins' shot percentage was high in a certain game, were KU's points per possession as a team more likely to be higher or lower?

To help illustrate the game-by-game statistics of each player, I plotted each player's points on a scatter plot. An example of this is below.

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As you can see, Marcus Morris' shot percentage is shown on the horizontal axis, while KU's points per possession is shown on the vertical axis. The line on the graph is the best-fit line, which helps us to determine the best approximation for the set of data we have.

If you look at the graph, the best-fit line is just barely going up. This would be a positive correlation, meaning, on average, the higher Marcus' shot percentage is, the more points per possession KU scores.

But the line doesn't go up very steep at all. Isn't there a chance that this data could just be a fluke?

For this reason, I consulted webprince from the KUsports.com message boards (You can read his interesting KU basketball-based statistical analysis on his blog, Sports and Numbers) for help to figure out which data was relevant.

I won't bore you with all the details, but in short, we needed to do confidence testing on all the graphs. For each graph, I ran some numbers (with webprince's much-needed help) to determine a confidence level. This confidence level simply states that how confident we are that there actually is a correlation between one player's shot percentage and the team's points per possession.

In many studies, a 95-percent confidence level is needed to prove the data is correlated, but for basketball, webprince told me he prefers an 80-percent confidence level, mostly because a basketball study is a bit different than a medical study.

So in this study, for me to consider making a conclusion, I would need at least an 80-percent confidence level.

Let's examine the three most interesting findings below: The graphs of Tyshawn Taylor, Aldrich and Collins.

Tyshawn Taylor

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Confidence level: 95.47 percent

Most fans have been extremely pleased with Taylor over the last few games. He has played unselfishly for the team, posting 25 assists to go with just five turnovers in the last five games while only shooting an average of five times per game.

So this graph might be contrary to popular opinion, but here goes: The stats say KU is better offensively when Taylor shoots a higher percentage of shots.

Look at the five games when Taylor fired up the highest percentage of shots. In four of those games, KU had its best offensive outings of the entire season.

Interestingly, this trend was the same last year as well.

http://worldonline.media.clients.ellingtoncms.com/img/blogs/entry_img/2010/Jan/06/Picture_5_.png

Confidence level: 87.29 percent

Though Taylor's unselfish actions have been admirable this season, the graphs and confidence levels tell us that KU's offense might be even better if he decides to be a bit more aggressive.

Let's now look at Cole Aldrich. I want to start by looking at his 2008-09 graph.

Cole Aldrich

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Confidence level: 94.3 percent.

Remember all those times last season when Self said that Aldrich needed more touches and shots? The stats tell us that the coach was right on with his analysis. It seems fairly safe to say that the more Aldrich shot, the more efficient KU's offense was.

Now, let's fast-forward to this season.

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Confidence level: 58.86 percent

As you can see from the extremely low confidence level, Aldrich shooting more shots this season, at first glance, doesn't seem to be correlating to KU scoring more points per possession.

But take a closer look. See that dot to the far right? That's KU's game against Memphis this season.

In that game, Aldrich had his highest percentage of shots taken (31 percent), but KU had its worst offensive game of the year (0.86 points per possession).

After going back to the box score, KU's low point-per-possession total doesn't appear to be Aldrich's fault. The big man was efficient, hitting seven of his 10 field-goal attempts to finish with a team-high 18 points. Many of KU's struggles offensively appeared to be because of a season-high 21 turnovers, not because Aldrich jacked up too many shots.

So, I wondered, what would the graph look like if we took out the Memphis game, which appears to be an outlier? Let's take a look.

http://worldonline.media.clients.ellingtoncms.com/img/blogs/entry_img/2010/Jan/06/Picture_10__.png

Confidence level: 99 percent

Without the Memphis outlier, the confidence level soars. I think it's still safe to say that one of the easiest ways KU can improve its offensive efficiency this season is to continue to feed the ball to Aldrich to get him more shot attempts.

Let's get to Collins. Once again, we'll start with last year's graph.

Sherron Collins

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Confidence level: 82.07 percent

You'll notice something different right away from Collins' graph. Instead of trending upward like Taylor's and Aldrich's, Collins' best-fit line is trending downward.

Because of our confidence level of 82.07 percent (which isn't as high as the others), we could tentatively say that the higher Collins' shot percentage was, the fewer points per possession KU scored a year ago.

There are exceptions, of course. The far right dot, which was KU's game against North Dakota, Collins shot 42.7 percent of possessions, and KU posted an impressive 1.24 points per possession.

For the most part, though, the Jayhawks had better point-per-game showings when Collins shot the ball less.

Let's take a look at this year.

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Confidence level: 79.21 percent

It's important to note that this graph did not meet our confidence level requirement, so we cannot assume that there is a correlation between Collins' shot percentage this season and KU's points per game. But it's really, really close.

From the graph, we can say this: KU's four best offensive performances have been in the five games when Collins shot the least. That could be due to chance or other factors, but I think it's interesting nonetheless.

Below, I will put the other graphs I compiled in case you want to view them. None of the graphs below had a confidence level of 80 percent or above, meaning there is not enough evidence to suggest that that particular player's shot percentage has a correlation to KU's points per possession.

Xavier Henry

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Confidence level: 66.4 percent

Marcus Morris 2009-10

http://worldonline.media.clients.ellingtoncms.com/img/blogs/entry_img/2010/Jan/06/Picture_1___.png

Confidence level: 52.2 percent

Marcus Morris 2008-09

http://worldonline.media.clients.ellingtoncms.com/img/blogs/entry_img/2010/Jan/06/Picture_13_.png

Confidence level: 62.1 percent

Markieff Morris 2009-10

http://worldonline.media.clients.ellingtoncms.com/img/blogs/entry_img/2010/Jan/06/Picture_15.png

Confidence level: 66.99 percent

Comments

hirschtodd 12 years ago

Jimmy Chitwood....oh wait...you probably won't get that reference Jessie...

Christopher Johnson 12 years ago

Wow, I know Collins stats weren't found significant enough this season to show that he should shoot less, but it's interesting that it pans out for last year. I definitely thought he should have shot less last year. Remember all those shots he felt like he had to force to keep us in the game? This year I feel that he's playing his best basketball of his career. He's not scoring 30 points per game, but thats ok. He's also not making stupid mistakes this year. Collins' fantastic play probably has to do with the ball being in his hands less . . . but no knock on Collins. If the ball is in Collins hands less, that means the ball is being shared more (assuming its not in another players possession too long). This team is so amazing because the way it spreads the ball around. Less shots from many players means a more balanced team. A more balanced team without any one individual taking a large majority of the shots probably means better shots and a better shot percentage. I would agree that maybe Cole should shoot more. It probably has less to do with shots. He just needs more touches. Tyshawn definitely plays it conservatively with how much he shoots. He's talented enough to shoot more, but it doesn't seem to hurt us much if he doesn't. All in all, I definitely think KU is better with Cole touching the ball more and Sherron shooting a tad bit less (than last year - not this year). Cole isn't playing the best ball of his career and Collins is defintely playing the smartest ball of his career. Even though statistics don't show cause and aren't perfect, I'm glad these statistics at least hint at those conclusions. KU looks good. Rock Chalk!

KU 12 years ago

Great stuff, Jess. So Cole and Tyshawn and (to a less degree, Marcus) need to shoot more and Sherron and X need to shoot less.

And Sherron and X also need to tighten up their defense. I don't have any stats to prove it, but I can see it with my eye. Tyshawn is starting to play better D. Cole is great and Marcus has come a long way in a year on the defensive end.

Ben Kane 12 years ago

great work jesse, can tell you put forth the effort on this one.

would like to point out one thing though and I will use TT as the example. While the line suggests he shoot more, I contend that it depends on what kind of shot it is. I don't want him hefting more 3's but if he's dipsy doing down the lane for some sort of bank/layup, well I'm fine with that.

Ben Kane 12 years ago

Jesse,

go see hoosiers already!

Jesse Newell 12 years ago

chuck — Good point on Tyshawn. It's worth pointing out also that correlation doesn't necessarily mean causation. So just because Tyshawn shooting more has coincided with KU's higher efficiency doesn't necessarily mean it was caused by Tyshawn shooting more. It just means that the two sets of numbers show a correlation.

KU — I wouldn't jump to any conclusions about the correlations of Marcus, Sherron or X this season because they didn't hit our confidence level of 80 percent.

sphase 12 years ago

If you want to break it down further, when tyshawn shoots a lot it is normally going to the basket and also likely that it is off a turnover on a break. Assuming those two things you are basically saying what HCBS says all the time: the team clicks when they are playing defense and causing easy offense and going to rim. Since tyshawn is our best on the ball hawk and one of our top ball handlers he plays significant roles in how much we do both of those two keys.

I would assume X's trend would reverse if he would take it to the buck, because it would mean more foul shots and stops in play increasing available time for more possessions and hence points.

Jonathan Allison 12 years ago

My hypothesis: Tyshawn Taylor shoots more in games when KU is winning big and our offensive efficiency is already high. Collins shoots more in games when nothing is going right and no one else on the team can buy a bucket. That explains the trends. KU doesn't score more per possession because Taylor is taking more shots and doesn't score less per possession because Collins is taking more shots. I don't however deny that KU scores more points per possession when Cole is taking more shots. I buy into that one and only that one.

easyfive 12 years ago

I think Sherron should do what ever he thinks is needed to get the W.
It's Sherron's team and it is not for us to say either way. X should get more touches too.

JonSimon 12 years ago

I don't really care to include games like alcorn state in these. I think we'd really like to know how the team scores in games where the guys break a sweat. Jesse, could you break these down later in the season by competitive teams and non-competitive games? Or maybe by first and second half since we've had a lot of throwaway second halves?

keithpreston 12 years ago

Jesse, as someone with a math degree, I love the statistical analysis, but this statistical correlation is horrible. There are so many other factors in points per possession rather then shot percentage of a certain player. There are probably much better statistics to compare to points per possession.

As an example, I bet that points per possession is highly correlated with the quality of the opponent we play. I would also say though our shot percentage per play correlates fairly highly with the quality of opponent we play. This would explain why when Sherron's shot percentage goes higher (more likely against good opponents), points per possession for the team go down(also more likely against good opponents). The same is probably true for Cole Aldrich, and probably the opposite for Tyshawn Taylor.

So a better measure would be to either adjust this based on the opponent's defensive quality (points per possession average for season). Or you can change shot percentage to a hybrid shot percentage/efficenciy (eFG%). I bet the graphs would make a lot more sense as to who should really shoot more for the Jayhawks

Jesse Newell 12 years ago

keithpreston — Thanks for the feedback. Webprince and I are looking at some ways to try to clean some things up that go well beyond my math skills.

hawkward1 12 years ago

Hope the team and coach see this and then hire Jesse to run deep stats on a number of schemes and players.

John Myers 12 years ago

I'm going to agree with keithpreston on this one.. I think the correlation is pretty bad..

The first thing that comes to mind for me is that it's more of a chicken and the egg deal.. I would contend not that we do worse as a team when Sherron shoots more, but rather that Sherron shoots more when we're playing worse as a team..

As keithpreston said, there are just WAY too many factors that come into play with this to pull anything meaningful from this particular study..

KGphoto 12 years ago

Bit of a statistical overkill, eh?

Create better shots. More will go in. For anybody. -finis

Ben Kane 12 years ago

austin & keith, probably true but that doesn't mean it isn't fun to do.

certainly this kind of analysis lends itself way better to baseball then it ever will to basketball.

NH_JHawk 12 years ago

Keith Preston/Jesse -

Disclaimer: I'm not a math major or claim to be very good at math, period.

If I'm understanding this correctly, part of the reason the confidence interval was lowered from 95% to 80% is to take into account that other factors (such as the quality of opponent, quality of a shot, etc.) may indeed be part of the reason that points per possession could go either up or down rather than just due to a player's shot % alone.

Confidence intervals are really nothing more than saying a data set is correlated (beyond a reasonable doubt) to a specific cause rather than by a random chance. So the lower you go with the confidence interval, the odds become greater and greater that the event happened by something other than a specific cause.

So my question is, using your hybrid statistic of eFG%, would you boost the confidence interval back up to 95% to prove beyond a reasonable doubt that a player's shot % is the cause of a better/worse points per possesssion?

didjabuti 12 years ago

I have to agree with austin5string and plasticJHawk. When the team is not hitting shots and/or struggling, Sherron takes over. Especially last year. The only game I was able to watch in person last year was at Nebraska while I was home on leave. Nothing was going right and I believe KU was down the entire first half. Sherron willed that team to the win and there is no way they would have if he didn't increase his shots. That was not the only time it happened either, it was just much more evident in person.

Christopher Johnson 12 years ago

For Sherron last year it was less about how many shots he took or his shot percentage. It was about decisions. The more Sherron felt he had to do the worse decisions he made. That makes sense for anybody. Anybody shouldering a lot of pressure has a higher chance of making bad decisions. For Sherron that definitely showed last year. He's matured a lot this year. He doesn't take as many bad shots, he doesn't try to force possessions, and he looks for teammates more. He's got that luxury this year. I agree that it was Sherron's team last year and it still is this year, but I think Sherron definitely benefits from HAVING to touch the ball less. That doesn't mean he SHOULD touch the ball less . . . he maybe could use more possessions, but he isn't FORCED to handle the ball as much this year and he's playing smarter because of it. His skill was never questioned in the past, just his decision making. Sherron is a better floor general than a standout stand alone guy like he had to be last year. This year he can be the general with all the talent in the world around him. He's playing his game. He's being himself and he's thriving. He has a couple less points and less shots, but he's definitely playing and leading better.

keithpreston 12 years ago

Correlation (even with confidence) will never imply causation. If we are searching for who should shoot more, all I am saying is that this correlation has little meaning with respect to causation and that possibly my recommendations would have more meaning.

melrank 12 years ago

This is fun stuff that bares out the simple facts of the last two years.

Last year, we had to have Sherron do everything and if no one would help, he had to shoot more. If we could get Cole involved, it helped.

This year, we are more balanced. IF Sherron has to shoot alot it's bad. If Cole gets to shoot alot, it's good. The analysis on X is inconclusive just like his play is relative to our overall results. (What I mean by this, if X doesn't play so well, we can still win).

I'm not a math major, but . . .

I did stay at a Holiday Inn last night.

Jesse - thanks for feeding us more Jayhawk info.

Dustin Gudde 12 years ago

Good study. I'm empressed with how much time you put into this article. Side note, although there were correlations in this evidence doesn't mean that they are causations. On games when Sherron is taking more shots, it's because the rest of the team is laboring offensively and he is taking much more contested shots and forcing a little be more. When the offense if flowing, Sherron doesn't need to take more shot. But, it is up to him being the leader to take on on that responsibility. So a gain correlation doesn't mean causation. Good research none the less.

Jesse Newell 12 years ago

keith, dusty — Thanks for pointing out that correlations aren't causations. I said the same thing in the sixth comment above, but it's worth repeating.

A couple of add-ons to the end. For one, keith pointed out correctly that the numbers above don't account for the opposition KU played. webprince provided me with adjusted offensive efficiencies for each game from KenPom, which factors in how tough a defense is when KU faces it.

After re-running the significance tests, Aldrich still was at 99 percent without the Memphis outlier, Taylor fell from 95.47 percent to about 82 percent and Sherron fell from 79 percent to about 74 percent. So the same two we had above (Taylor and Aldrich without the outlier) would have passed our 80-percent significance test, while Sherron would have still fallen below it. Even after taking opposing defenses into consideration, there are still going to be other factors that affect the numbers. There's simply no way around that.

You guys are right. It is only a correlation and not a causation. There are many factors involved. To get any more definitive answers, we'd have to address many more variables that we haven't above.

I, for one, was surprised with the way the graphs turned out when I took the time to plot them. If nothing else, I hope it was at least an interesting topic that gives fans something else to think about when watching KU.

KGphoto 12 years ago

Still, all I can think about while watching the hawks is shot quality. That just doesn't show up in a stat column. If the shot quality is high, the hawks look good, and the stats reflect it. If the quality is bad... well you get the idea.

Christopher Johnson 12 years ago

wow, this is one of those games where Sherron HAS to take a bunch of shots . . . he looks as impressive as ever. I wish the team around him did tonight as well.

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