The Dutch-born naturalised Scotland internationalist has played on the winning team against Glasgow Warriors just once, two years ago, when the men from the west held on at Murrayfield to take the trophy on points difference.
That sequence has been down to what seemed like a greater desire on Glasgow's part to come through in these matches and, albeit in slightly back-handed manner, Visser acknowledged the way his club's derby rivals have worked out the way to do what they must.
"Glasgow have won in the past couple of years because they don't necessarily play good-looking rugby, but they are very good in defence and very tough," he said. "They have attacked the breakdown, which is vital and that's something we have concentrated on this week."
That is part of an overall increase of concentration on the area of the game that Visser is not as renowned for, namely defence. "Going into the next two games I honestly couldn't care less about scoring. I would rather just win and take the cup for the first time. That's more important to me right now [than scoring]."
"The 1872 Cup would be a big achievement, but the single most important thing is picking up points in the league and pushing for a much higher finish. We have cranked training up a bit. It has been very physical for the first couple of days this week. That's why I say I'm not too bothered about scoring tries, I just want to win games. Ugly or good rugby doesn't matter; if we pick up two wins we will put ourselves in a good position in the league."
That said, Visser is aware that he is on course for a landmark, particularly now that Tommy Bowe, the Irishman who was the one player ahead of him in the Magners League and Pro12 all-time try-scoring charts, has suffered a serious knee injury when just two short of becoming the first player to score 50 tries in the competition.
Visser is three short of that mark and he admitted that, having scored in every Pro12 match he has played this season, he does want that place in history. "Where I am now with my try-count means the pressure is a little bit off," said the 25-year-old. "This season, I think I'm on 10 tries from seven games, so there is not that much pressure on me to score. I would like to be top try-scorer again, but that is not necessarily one of my big goals this season.
"I've managed to make it in the last three seasons, which I'm really happy about. To get up again this year has been brilliant. One of the biggest things for me now is to be the first to get to 50. That would be great: something to be proud of. Tommy Bowe has one more than me, but he's injured now, so the pressure is a little off. First to 50 would be special."
Given that he scored a hat trick in Edinburgh's opening match this season and was still on the losing side to Munster, there is no guarantee that even if he gets there in the course of the derbies that his team will come through. That said, prolific try-scoring has not been a feature of these encounters, so the chances are that one prize will go a long way towards begetting the other, while there is also the matter of impressing the new Scotland caretaker coach, Scott Johnson.
As he strives to do just that, Visser will be directly up against a major rival for a Test place in Sean Maitland, the Scotland-qualified New Zealander who Glasgow hope will generate greater finishing power. Maitland was generous in his assessment of the man he will confronting tonight. "He's an awesome player and he's quite dangerous, so I've got to keep on him and stop him scoring tries. I'm looking forward to it," he said of Visser.
Once again there was just the hint of a dig when Visser was invited to reciprocate, but that does not mean he is unaware of the danger Glasgow's imports carry. "I don't know much about Sean. There was a bit of hype about him coming, and he has obviously done well in New Zealand, so he is an exciting player for them," he said.
"DTH [van der Merwe] is a different character. He always seems to score, which is fairly annoying for me. He is a good player and a good finisher, which is good to see at the other end of the M8. They have not necessarily been too good at finishing tries, but, whenever he is on the pitch, he seems to do that. He is someone I definitely respect as a player."