After spending a significant portion of the summer writing Smart Texas Basketball 2016 (available from Amazon and iTunes) I have kind of been all over the place in terms of my predictions and expectations for the coming season. There are just so many unknowns with this team, as last season’s upperclassmen-heavy team will be replaced by a group that contains many newcomers. Predictions are always difficult, but faced with all of the changes on Shaka Smart’s team this season they seem particularly hard.

To try to focus my thinking about how to make a guess as to how this season will play out for Texas, I spent a bit of time thinking through just how I might make simple predictions for a basketball team in general. This, not surprisingly given my odd way of grappling with reality, involves some mathematics. But not too much. First comes the math and then the predictions follow.

The Part That Contains Math

Math time. Look away if you find it unsettling.

Behold.

This equation is something I have used many times. It allows us to accurately calculate the number of points per possession scored by either an offense or a defense given the following inputs:

Turnover percentage (TO%), which is the percentage of a team's possessions that end with a turnover.

Effective field goal percentage (eFG%), which is like field goal percentage, but weighs three-point attempts more heavily, because they result in a greater number of points. eFG% can further be broken out into two-point field goal percentage (2FG%), three-point field goal percentage (3FG%), and the fraction of total shots taken from beyond the arc (3FGA/FGA).

Free-throw percentage (FT%), which is the percentage of free throws that a team makes, and you surely already know about.

Free-throw rate (FTR), which is just the ratio of free-throw attempts to field-goal attempts.

Field-goal percentage (FG%), which is the boring old field-goal percentage that everyone knows.

Offensive rebounding percentage (ORB%), which is the percentage of total possible rebounds grabbed by the offense.

You can read more about where this comes from here, and by following the links in that article to the derivation. The equation works pretty well.

Using this equation, by knowing just seven things (2FG%, 3FG%, 3FGA/FGA, TO%, ORB%, and FT%, and FTR) you can typically calculate a team's points per possession total for either offense or defense to within a few points per hundred possessions.

What We Learn From The Math

Starting from this framework, we can make a series of statements:

1. Team performance on a per possession basis is almost completely defined by 14 team statistics -- seven on offense and seven on defense. The support for this claim is that with these 14 measures it is possible to make highly accurate predictions for both offensive and defensive performance. This tells us that contemplating these 14 statistics should give us a rational basis for making projections about team performance.

2. Some statistical categories are more important than others, and achievable changes in these categories will have a much larger effect on offensive or defensive performance. One simple way to assess this is to look at the distributions of these across Division I basketball, and see how big of an impact a realistic change will have on offensive or defensive performance using the equation above. It is possible to define “realistic changes” in different ways, but a simple and obvious thing to try is to see what effect a change in going from the 25-percentile to the 75-percentile in a given category will have on offensive or defensive performance in order to get a feel for how much effect a move in each category will have on overall efficiency.

Following the logic outlined above, four statistical categories for offense and four for defense are disproportionately important. These categories, in approximate order of importance, are: 2FG%, TO%, ORB%, and 3FG%. While I have ordered these by importance using the analysis I describe above, the truth is that the differences aren't all that large, and perhaps we can view them of roughly equal importance. The best offenses and defenses nationally (as determined by Ken Pomeroy's ratings) tend to do very well in at least two or three of these categories.

If we can anticipate 2FG%, TO%, ORB%, and 3FG% at both ends of the floor, it gives us a decent shot at projecting overall team quality. Starting from a baseline of team performance in the prior season, we ought to be able to take a shot at predicting team quality in a new season by guessing at the changes in these categories. For a team to improve, an overall improvement in the balance of these categories is needed.

Now, predicting these numbers is hard. But what if we try something simpler? It may be very hard to predict the magnitude of a particular change, but making a reasonable guess as to the direction of the change seems comparatively easy. It may ultimately end up wrong -- this is the tricky thing about predictions -- but at least we stand a decent chance of making some progress with this approach. And even if we turn out to be wrong, we can hopefully be wrong in a manner that is useful; by framing the prediction problem in this way we get the chance to reason through the things that will need to happen during this coming season in order for a team to get better.

So let's start reasoning, first looking at the Texas offense before progressing to the defense.

Projecting The Texas Offense

When we look back on the Longhorn offense last season, Shaka Smart's squad excelled at avoiding turnovers, was about average shooting from inside the arc, ranged from average to below average on offensive rebounding (depending on if we are talking about before or after Cameron Ridley was injured), and was below average at shooting threes.

So what is likely to change this season? Texas' turnover rate is likely to go up, given the change from a bunch of upperclassmen handling the ball to a bunch of freshman and sophomores making most of the decisions in the Texas offense. On the other hand, three-point percentage is very likely to improve, as Shaka Smart now has a greater number of effective perimeter shooters on his team.

Meanwhile it is hard to figure out what will happen to two-point shooting percentage and the offensive rebounding rate. My best guess is that offensive rebounding rate will look more or less like what it did after Ridley's injury and that at best, a small improvement in two-point field goal percentage is possible. (More detailed reasoning for these statements shows up in the Offense chapter of Smart Texas Basketball 2016.)

So let's summarize for the Texas offense:

2FG%: same

TO%: worse

ORB%: same

3FG%: better

Based on this, I suspect that the offense is likely to be comparable to what we saw last season in terms of overall performance. How it is likely to get there will look very different. For Texas to be better on offense than it was a season ago, better shooting will have to offset a greater number of turnovers, or some unanticipated improvement on the glass or scoring near the basket will be needed.

This isn’t entirely good news for Longhorn supporters. The Texas offense experienced its share of struggles last season, particularly during Big 12 play. Taking just the results of the conference season, Smart’s team scored 1.04 points per possession, which ranked seventh out of ten teams in the Big 12.

Projecting The Texas Defense

We can run through a similar analysis for the Longhorn defense. Last season, a Texas D that was anchored by Big 12 Defensive Player of the Year Prince Ibeh did well holding down opponent two-point field goal percentage. Meanwhile, Texas was about average in terms of opponent three-point shooting and opponent turnover rate, while slightly below average on the defensive glass. Overall Smart’s defense was good, as as it typically is for teams that excel at one important thing (in this case rim protection) while being more or less average at everything else.

We can play the same guessing game as we did with the Texas offense. Moving from a front court that featured Cameron Ridley during the first portion of the season and Prince Ibeh during conference play to one that does not contain either one of these players leaves a big hole in the interior of the Texas defense. Additionally, the loss of Connor Lammert doesn’t help things. Freshman Jarrett Allen will do his best to cover the inside defensively, but it is asking a freshman to do the work of several seniors is asking quite a lot. My best guess is that Allen does well, but the Longhorns lose a little ground on two-point shooting defense.

On the positive side, I think the Longhorns make up ground by forcing more turnovers this season — or at least I hope that they will. Shaka Smart’s team probably needs to force more turnovers than it did a year ago, or a defensive slide will be a likely outcome. Because I don’t think significant gains will come on the defensive glass, and I subscribe to the theory that for most teams opponent three point shooting percentages is largely a random variable over the course of the season.

Given that Texas’ opponents shot nearly the D-I average on three point attempts last season, for forecasting purposes our best guess is to assume that it will be about the same. As for rebounding, I am somewhat optimistically going to state that Texas will hold the line on the defensive glass, but with a young front court there is some significant potential here to get worse.

Summarizing the defensive results:

2FG%: worse

TO%: better

ORB%: same, but could get worse

3FG%: same, but largely random

This leaves us in a situation fairly similar to what we had with the offense, anticipating an improvement in one category, a reduction in another, and the balance of categories staying about the same. If the Longhorns do manage to field a defense as successful as last season’s squad (which ranked fourth in the Big 12 during conference play) this won’t be a bad thing. Doing so will require strong work by Allen on defense and on the glass (containing losses in these two categories) while Shaka Smart’s roster shows more success in his preferred style of pressure defense.

Such an improvement is certainly possible, although it clearly fits on the more optimistic end of the range of potential outcomes for the season.

Wrapping Everything Up

Running through this analysis, I am coming into the season with the expectation that the 2016-2017 Texas Longhorns will be of comparable quality to last season’s team. This is somewhat more optimistic than I was prior to working through things in this way, where I was mostly focused on all of the minutes played last season by upperclassmen who are no longer with the team. This season’s team will clearly be different, but having a similar expectation for results (middle of the pack Big 12 finish followed by an NCAA tournament invite) seems reasonable.