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.

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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.

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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

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Confidence level: 52.2 percent

Marcus Morris 2008-09

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Confidence level: 62.1 percent

Markieff Morris 2009-10

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Confidence level: 66.99 percent