———————————————
SPOILER INFO
No spoilers. This article explains a game feature that might easily be perceived as a bug.
———————————————
People keep asking in forum posts why the potions which are supposed to increase your ability to make smithing improvements fail to do so. Every time, a smartass or two replies with the suggestion that the OP make sure the potion's duration hasn't ran out, and when the OP insists he had made sure it hadn't, there are no more replies.
In my previous game, I saw that smithing potions did work. When I consumed one and opened one of the smithing appliances, I saw how I could do a lot more than before. And after a while, those additional opportunities disappeared because the potion's duration period was over. That's exactly what one would expect to happen.
However, in my subsequent test games, I saw that smithing potions had no effect at all, even with the Smithing skill at 100.
Not finding any help on the Web, I kept experimenting. Eventually I succeeded in finding the solution.
As you probably know already, the developers of Skyrim are either arithmetical idiots or pathological liars. For example, when a perk description says it increases something by 60%, it actually increases it only by 14% (from 140 to 160).
Something similar applies to potion descriptions. You are told that a smithing potion increases all smithing improvements by, say, 20%. How is it then possible that without that potion you can improve a weapon by 10 points, and with the potion you can also improve it only by 10 points? That is because they fail to tell you that the 20% improvement is not calculated as 20% of 10, but as 20% of something completely different.
I can imagine how an employee of Bethesda who makes 6000$ a month is being told by his boss that he'll get a 20% raise. To his disappointment, the employee receives only 6400$ the next month, instead of the expected 7200$. When he goes to the bookkeeper pointing out that they have probably made a mistake, the bookkeeper says: "Why, 400$ is precisely 20% of the minimal wage (2000$)." And when the employee still looks dumbfound, the bookkeeper says: "Don't tell me you expected 20% of your current salary," and her colleagues who overhear it burst out laughing.
To cut the long story short, you need Smithing perks. Without them, even the most potent smithing potions will be useless. With appropriate perks, they suddenly begin to take effect. The math behind it, precisely described on one of the Skyrim help websites, is so perverse that I won't bother you with details.
[originally published 2017-02-28]