Last year, Doug Martin and Mike Evans were the leading rusher and receiver, respectively, for the first Tampa Bay Buccaneers team ever to gain more than 6,000 yards. Both players were encouraged by the success of the offense in its first year under the guidance of Dirk Koetter – though Evans was not quite as satisfied with his own season – but they also see plenty of room for improvement.

The primary issue is that the Bucs' record yardage total, which was good enough to rank fifth in the NFL overall, did not translate into enough points. Tampa Bay scored 342 points in 2015, good for 20th in the league. The Buccaneers peaked at 45 points in a blowout win in Philadelphia in Week 11 but followed that by scoring an average of 17.7 points per game over the final six weeks. That's one reason a 6-6 start that had Tampa Bay on the edge of playoff contention in December devolved into a 6-10 final record.

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Fortunately, those key figures in the Bucs' attack – two-thirds of what could be one of the league's most productive "triplets" if second-year quarterback Jameis Winston builds on his impressive rookie season – have a very clear idea of how the offense can be more productive in 2016.

"On third down – we were good on third down but we could have been better, with the drops, fumbles, things like that," said Evans. "Limit the turnovers and bigger plays down the field, and I think we can be one of the best offenses in the league."

As Evans notes, the Buccaneers were pretty respectable on third-down conversions, succeeding on 41.6% of their tries to rank 10th in the NFL. However, the team dropped to 16th in those same rankings when in the red zone. Even a modest improvement of a few percentage points would lead to more sustained drives – Tampa Bay was seventh in 2015 in number of 10-play drives mounted by the offense, but only 12th in points scored off those drives.

Turnovers were a more obvious problem; the Buccaneers committed 28 of them, tied for the eighth-most in the NFL. The desire for more big plays likely stems from the fact that the Bucs proved they could create those in Koetter's offense but felt they left some opportunities unanswered. The Bucs ranked fourth in the NFL in offensive plays of 20 or more yards, though that number was spiked by a league-leading 20 such gains on the ground. Evans wants more of them through the air. He has previously spoken of building better personal chemistry on the field with Winston, and there's a good bet that will happen as the Bucs start a second season under Koetter, who has moved up from offensive coordinator to head coach.

"We get to play fast, that's the main thing," said Evans. Last year we came into training camp not being able to play as fast as we wanted. Now we don't have to learn the offense, so that's great. We're familiar with it, we like this offense and we're ready to go."

Evans didn't include it specifically on his list, but flags were a major problem for the Buccaneers in 2015, when they tied for the league lead with 143 penalties. That has been a point of emphasis for Koetter's staff this offseason, but Martin says the focus on that issue has to come from the players, too.

"It can't just be the coaches," he said. "It's got to be players being accountable for other players and talking to each other. When we see a player step offsides, another player has to tell him, 'That's not cool. We're not doing that this year.' It can't just be the coach yelling at him because sometimes that doesn't work. It has to be a player thing, so that's something we've got to do. We need more of that this year and I want to see that during training camp."

Martin also called for a more energetic camp this year, with another level of competitiveness between the offense and defense. Those, of course, are more subjective concerns, but coupled with the clearly-defined points of emphasis noted above, they may be what the Bucs' offense needs to take another step forward in 2016.

"Overall, the offense, we're confident about what we're going to do this year, and I'm very optimistic on this season," said Martin. "I'm really excited. I'm very anxious to get going, see what this team can do, how we're going to improve, and I just can't wait."

• Jameis Winston rapidly developed into one of the Buccaneers' clear leaders last year, but he let it happen naturally, without trying to usurp the influence of such established front men as Gerald McCoy and Lavonte David. In fact, Winston has urged McCoy to make an even greater impact on his teammates.

"People ask me, 'Gerald, what type of leader are you?' Whatever type my team needs me to be," said McCoy. "Me and Jameis had a private conversation about what he feels like this team needs me to be as a leader. I'm not going to say [what he was asked to do], but I think it will be obvious when it happens.

"[People] are used to seeing me do things a certain way; that's going to change because the face of the franchise came to me and said, 'Hey listen, if we're going to win, we need you to do this.' Okay. My quarterback said this is what he needs, so that's what I'm going to do, because if he feels like that's what our team needs in order for us to win, who am I to say, 'No, I'm not going to do that?' Because I want to win, too. He's an intelligent guy, young or not – very mature, very intelligent. He sits back and he watches and analyzes. And he's seen something that he feels like I can do to help this team be better. It's not hard to do, it's just a matter of me doing it.

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That McCoy, who is heading into his seventh season and has already been to four Pro Bowls, would be so ready to accept a suggestion from a second-year player is an indication of just how thoroughly Winston has been accepted as a leader in the locker room. That influence is only going to grow in the seasons to come.

"When he first got here he was a little quiet, just being a rookie and just listening and learning," said Martin. "Over time, he became that Jameis you see on TV. He's always inspiring and shouting out motivational quotes. He's definitely grown as a leader and I believe this season he'll take [that] to another level."

• As mentioned above, an offense that struggled to put points on the board contributed to last year's season-ending losing streak, but there were other contributing factors as well. There seems to be a very strong feeling among Buccaneer players that the absence of then-rookie linebacker Kwon Alexander for the last four games was one of the most significant issues down the stretch.

"Kwon was missed a lot," said David who formed an impressive playmaking tandem with his rookie teammate. "Kwon was missed a lot, especially by me. You build a bond with a guy on the field, especially a rookie, you want him on the field as much as you can because you guys are going to be working together. I was working with him since the start of training camp. He was one of those guys that brings that energy onto the field. You know you can count on him to play hard. You know you can count on him, whenever a play needs to be made, he'll be able to make a play. That was one thing that was kind of missing. That kind of changed the way those last four games went."

It wasn't just his defensive mates who felt Alexander's absence. Evans brought it up without prompting when asked on Wednesday about the finish to 2015.

"I learned that we needed Kwon Alexander a lot," said Evans. "He's a great player. When he got suspended, we lost every game after that. He was a big piece. And we just didn't make plays offensively as well, myself especially. But this year I think it will be a different story."