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There's a lot of reasons to be optimistic about the South Carolina Offense in 2018. Dan Werner was hired as QB coach. The Gamecocks may actually commit to running a tempo-based system under Bryan McClendon. The O-line (especially the inside positions) should be beefier and more experienced, helping the run game. Oh, and some guy named Deebo Samuel is back. A preponderance of evidence suggests that indeed the Gamecocks will put more points on the scoreboard this coming season. But what does the recent history of college football have to say about the magnitude of that improvement? I took Points per Game (PPG) data for every FBS team for the past four season (2014 - 2017) and used that to look at year-over-year change for each team. This won't be very useful in making a prediction about the specific PPG totals we can expect from the Gamecocks in 2018, but it should be very informative for creating some boundaries around expectations.

FBS Points per Game

Let's start with taking a look at the raw data for the entire FBS in the table below. (Note: I removed UAB and Coastal Carolina from the main body of the data due to both of those teams entering FBS in 2017. The data for those two teams is displayed at the bottom, and included in the average values for 2017).

In 2017 South Carolina was 97th out of 130 teams with a PPG figure of 23.7. This putrid output was amazingly 4.9 PPG above the total for 2016, in which the Gamecocks finished 118th out of 128.
Overall average PPG numbers for FBS teams are very consistent year-over-year. The average PPG over the past four season is 28.2 PPG, so the Gamecocks have another 4.5 PPG improvement to go just to match the 4-year FBS average.
If a team wants to be in the Top 40 in PPG in a given year, it needs to score more than 31 PPG. In 2018 South Carolina probably needs to improve their total by at least 8 PPG to be Top 40 scoring team.
The average year-over-year change in PPG over the past three season is -0.1 PPG. This basically represents no change overall, as you would expect given the stability in average PPG over the past four seasons. Teams realized decreases in their PPG totals 195 times over the past three season, while increases were seen 189 times.

To better visualize the data, I've rounded each team's year-over-year change in PPG to the nearest integer, and plotted the frequency of occurrence in Figure 1 below.

Figure 1. Frequency of changes in PPG year-over-year for FBS teams from 2015 to 2017, with changes in PPG being rounded to the nearest integer.

As seen in Figure 1, the data forms a classic normal distribution curve around the mean average near zero. What's interesting, however, is the relatively few number of teams that realized little to no change in their PPG in a given year. Teams were much more likely to improve by 1 or 2 points or regress by 1-3 points than they were to have no change in PPG.
As seen at the bottom of the table above, the standard deviation of the entire 3-year range of PPG changes is 7.2. Combined with the mean, this means that in any given year, 68.27% of FBS teams will have PPG totals between -7.2 PPG below to 7.1 above their PPG totals from the previous year.
For the sake of example let's say I expect the Gamecocks to be in the Top 40 in PPG in 2018. We said earlier that to do this they would likely need to improve their PPG number by at least 8 PPG from the 23.7 PPG they achieved in 2017. Based on the past three years of yearly PPG change data in the FBS, we can expect only 13%, or about 17 out of 130 FBS teams, to be able increase their totals by this much. Impossible for the Gamecocks to pull off? Not at all, but as we can see from the probabilities, not very likely either.
Keep in mind that the Gamecocks have certainly been on the flip-side of this, however. In 2015 South Carolina scoring dropped a full 10 PPG from the 31.9 PPG achieved in 2014. Based on the distribution you'd only expect 8.3%, or 11 out of 130 teams, to decrease their scoring by 10 or more PPG in any given year. So the Gamecocks have certainly achieved unlikely feats related to scoring in the recent past.

Power Five Points per Game

For the sake of thoroughness I've decided to do the same analysis above, but for Power Five teams only. My assumption is that yearly performance by teams in Power Five conferences are generally more consistent overall given their ability to maintain quality depth better than smaller schools. This means I think it is more difficult to improve scoring when competing in a Power Five conference. You can see the raw data for just the Power Five teams in the table below.

South Carolina was 52nd out of 65 Power Five teams in scoring in 2017.
The mean Power Five PPG since 2014 is more than a point higher than that of the full FBS roster of teams at 29.3 PPG.
In terms of average year-over-year change in scoring, this figure was slightly more negative for Power Five teams, with an average of -0.3 PPG per year.

Figure 2. Frequency of changes in PPG year-over-year for Power Five teams from 2015 to 2017, with changes in PPG being rounded to the nearest integer.

With only around half the number of data points used for the analysis on the FBS, the normal distribution evident in Figure 2 is 'lumpier' and not as symmetrical as that seen in Figure 1, but the shape is unmistakable nonetheless.
No Power Five team has improved their scoring by more than 15.4 PPG since 2015 (Arizona 2017, Missouri 2016).
With a smaller standard deviation of 6.8 PPG, the overall magnitude of changes in scoring for Power Five teams can be expected to be lower.
Based on three years worth of Power Five data, only 11.2%, or about 7 out of 65 Power Five teams, can be expected to improve their scoring by 8 or more PPG in a given year. If you lower the bar to an increase of 7 PPG, 14.2%, or about 9 teams, can be expected to pull that off.
Statistical probability estimates that only 7.9% of teams would be expected to shrink their scoring by 10 or more PPG in a given year. Over a three year period, this works out to about 15.3 occurrences amongst the Power Five. As discussed above, South Carolina achieved this feat once over the past three years, and was one of exactly 15 teams to do so.

Conclusions

Here are some final thoughts on this:

I would expect close to 70% of college football teams to stay within one TD of their 2017 scoring average in 2018.
Only about 9 Power Five teams will be able to improve upon their 2017 scoring by 7 or more PPG. 7 teams will improve by 8 or more.
Given all the positives going for SC on Offense heading into 2018, will the Gamecocks make it to the Top 40 by adding at least 8 PPG to their average scoring? I think they've got a better chance than most of being one of the 7 teams to improve by the amount necessary.
- Deebo Samuel demonstrated in 2.5 games last year that he's probably worth at least one extra TD per game all by himself.
- Running more plays equals more points. It also means more possession for the opponent, so expect Defense to potentially take a step backwards.
- Factoring in the schedule, the Gamecocks theoretically have the ability to increase average scoring for the year by up to 2.7 PPG just by replacing NC State with Coastal Carolina to open the season (would need to hang 70 on the Chanticleers to do so).
- Marshall has a tough defense though, and the Gamecocks will have to replace three defensive scores last year against rotating SEC West opponent Arkansas in an away match-up with Ole Miss.
- My general opinion concerning the SEC East is that defenses overall will take a step back due to loss of talent. This is backed up by not much other than casual observation of other teams in the division.
All things considered, put me down for expecting the Gamecocks to be one of the rare teams to achieve more than a TD worth of improvement in PPG and barely eke out a Top 40 finish in Scoring Offense.