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Looking forward by looking back

Now that Late Night with Roy is over, and practice in full swing, it is time to begin looking forward to what is expected to be a bounce-back year for the North Carolina basketball program. Heading into the season, much of the focus has been, and will continue to be, on the talented trio of incoming freshmen. This has not been unexpected, nor is it entirely unwarranted, as Marshall and Bullock are top talents who directly address a weakness of last year’s roster and Harrison Barnes is the type of elite recruit that makes it legitimate to wonder if he will be the last player to ever wear the #40 as a Tar Heel. However, as good as there freshman appear to be, and as much fun as it will be to talk about in November and December, when push comes to shove in March, it is usually the returning players on a teams roster the determine a team’s ultimate level of success. Evidence of this is the simple fact that only 4 of the USBWA National Freshman of the Year winners have made it to the Final Four during their rookie campaigns (Chris Webber, Carmelo Anthony, Luol Deng, and Marvin Williams).

So what exactly is Carolina returning for the 2010-2011 season? More importantly, can we compare what is coming back to the Heels this year, to what Roy Williams’ previous teams have returned, and develop a statistical model to try and predict the most likely outcome for the upcoming season?

For anyone who has paid even a little bit of attention to the program since Roy has returned to Chapel Hill, no deep analysis is needed to tell you that this year's “return” is unique.  Over the past six seasons, Tar Heel teams have started their seasons with almost all, or almost none, of the previous season’s production.  The 2011 team, on the other hand, will return between 36% and 66% of its previous year’s production in each of the six “major” statistical categories (points, rebound, assists, turnovers, steals, and blocks), which makes any comparisons between this team and Roy’s past six teams relatively moot.

Table 1. Percentage of last season's production returning for 2010-11.

[table id=39 /]

In order to get a better idea of what is a reasonable expectation for a Roy Williams-coached team that returns this level of production, I wanted to see if a “reliable” model could be generated through an analysis of Roy’s entire (head) coaching tenure.  Thanks to the availability of the online databases at StatSheet and Rock Chalk Zone, I was able to go back and calculate the productivity return (PR) for each of the aforementioned statistical categories, in each of Roy’s returning teams.  (To avoid the introduction of an uncontrolled variable, i.e. players learning a new system, Williams’ first seasons at KU and UNC were excluded.)  The regular-season winning percentages of Williams’ previous teams were then plotted as a function of the level of production that team returned in each of the statistical categories so as to determine the level of correlation between the return of past production and future winning.

Table 2. Production Returns (PR) and results for past Roy Williams teams.

[table id=40 /]

After all of the data were plotted, a quick glance at each of the six graphs revealed two things.  First, there does appear to be a noticeable linear relationship between PR and winning percentage.  Second, while none of the data fit the linear model extremely well, certain data do appear to be a more reliable predictor than others.  In this case, the PR for points and steals clearly fit the model the “best,” while the PR for blocks is clearly the worst predictor.  This result is not altogether surprising when one considers that Roy’s system puts little emphasis on the blocked shot, while placing a huge emphasis on forcing steals and transition opportunities, all in the name of scoring as many points as possible.

So what do the models tell us?  Despite the variability observed in the fit of each data set to the model, the results they produce when the 2011 PR are plugged in are remarkably consistent:

Table 3. 2010-2011 predictions based on PR-models.

[table id=43 /]

The average of all the predicted winning percentages is 0.791, which actually makes a fair bit of sense considering that Roy Williams has a career winning of just under 80% and the team is returning a median percentage of production.  Should this prediction hold, the 0.791 winning percentage would equate to approximately a 23-7 record (Exact record: 23.7 - 6.3, based on UNC's 30-game schedule) heading into the ACC Tournament.  The two individual models in which the data fit the best, Points PR (Exact: 23.0 wins) and Steals PR (Exact: 23.6 wins), also point towards a 23-7 regular season, adding further support to this prediction.

But what about a comparison of what this team is returning to teams from Roy’s past?  If we focus on the two statistical categories that seem to have the highest correlation to a teams performance (points and steals), then two teams stand out:  Roy’s 1999 team, which returned 42% of its points, and his 1995 team, which returned 47% of its steals.

Table 4. Previous seasons with similar PR to the 2011 team.

[table id=42 /]

The 1995 and 1999 teams each missed their projected regular-season win totals by about 2 games, with the 1995 team winning 2 more than would have been expected, and the 1999 team winning 2 less than would have been predicted.  For the most part, this two-win spread represents the maximum deviation from the model.  (The obvious exception are the 2006 and 2010 teams, each of which had so little production returning it would have been difficult to make an accurate prediction.)  Numbers aside, there is not much to the comparison of this 2011 UNC team to the 1999 Kansas team, as that team was dealing with the loss of two great players (LaFrentz and Paul Pierce) and it's top incoming freshman was Jeff Boschee, who only warranted a ranking of 40 by the RSCI.  On the other hand, a comparison with the 1995 team is particularly interesting in that it featured a group of highly regarded sophomores who took a step up in performance (Vaughn, Pollard, Hasse) and one of the most highly regarded freshmen in the country (LaFrentz).  As was previously mentioned, the 1995 team outperformed the model by a little more than 2 wins.  If this year's class of freshmen is "as advertised," and the returnees have grown, and continue to grow, into their potential, then a similar performance by this year’s team is probably the highest “reasonable” expectation.  Such a performance  would result in a 25-5 or 26-4 record going into the ACC Tournament, could have them in contention for a #1-seed, and would make last season seem like a long, long time ago.