I am NOT a FSU fan, but I did watch nearly every game in the 2014 season. Often you would hear commentators talk about how Winston tends to have poor first halves, and much improved second halves of games. They often attributed that to the off the field accusations. He doesn't have these accusations against him anymore, so the question is why does it continue?
2013 first half scoring by FSU
28/17/33/24/21/27/42/21/42/38/42/17/17/10
2014 first half scoring by FSU
17/28/3/21/13/24/10/7/28/10/17/21/28/13
As you can see, his first season with FSU, Winston had 5 games with more than 4 TDs in the first half, and none the second season. He also scored less than 17 only in the National Championship game while it happened 6 times in 2014. I would like to note that in 2013 FSU ranked #22 in rushing, and ranked #80 in 2014.
Now let's look at Winston with the Bucs. We have the same person calling the offensive calls each of his 3 years.
2015 first half scoring
7/10/9/10/20/24/13/9/3/28/12/7/10/3/7/3
As you can see it's pretty bleak. We scored 14 or more in just 3 games. People acting like poor scoring in the first half is a recent problem is kidding themselves. In total we scored 175 points. This is puts us at #16 in the NFL for points scored in the first half. We were #5 in the NFL in rushing offense.
2016 first half scoring
17/0/20/7/6/17/10/14/17/9/14/7/13/6/7/3
At first 2016 seems like an improvement, we scored 14 or more points in 6 games. The truth is that we scored only 167 points dropping us to #22 in 2016 for scoring in the first half. Our rushing offense dropped to #24.
2017 first half scoring, Winston starting
26/3/16/7/0/6/0/3
He had 2 games scoring over 14 points putting him more on the 2015 pace, but the scoring was on pace for almost 3 points less per 1st half compared to the year before. We are currntly #29 in first half scoring this year. This season, our rushing offense ranks #28.
Summary FSU
2013-1st half points 27.1, national rushing rank 22
2014-1st half points 17.1, national rushing rank 80
Summary - NFL ranks
2015-1st half scoring: 16, rushing offense 5
2016-1st half scoring: 22, rushing offense 24
2017-1st half scoring: 29, rushing offense 28
Everyone finds excuses that Winston doesn't perform well in the first half citing off the field issues to being too pumped up at the beggining of games to trying to do too much, but the truth is that his first half play is a direct reflection of his teams rushing attack. Yes, he can't time deep passes with fast receivers, yes he makes poor decisions, but he is no Aaron Rodgers. He can't overcome a below average rushing attack.
Other than this, what else do you think is to blame for the bad first half scoring?