Dice are the "third party" at a Dungeons & Dragons table. While the DM and the players both contribute to the interactive story-telling, dice determine the outcome of many attempted actions. Extreme rolls can lead to extreme situations like one-shot kills, and that obviously can also lead to memorable situations in the story.

In 5th edition the dice play a bigger role than in 4E for several reasons: There are fewer rolls of dice in a typical combat, because combat is shorter, thus each roll has more importance. The "bounded accuracy" of 5E means that when you roll a d20 for an attack, proficiency check, or saving throw, you add only small numbers to the result; compared to 4E the player's choice of for example being proficient in a skill plays a smaller role in determining the outcome, and the random dice count for a larger part. And finally many spells now deal more dice of damage than in previous editions, while hit points aren't as high than in 4th.

One of the dirty little secrets of Dungeons & Dragons (and other systems) is that a surprisingly large number of DMs cheat by fudging dice. They roll behind the DM screen and then announce the result they want, not the one that the dice said. That is often done with the best of intentions: If the archvillain of the story only gets a few rolls of the dice in combat and ends up rolling low on each of them, he might well end up not being very memorable. The players can't see how dangerous the villain would have been if he had rolled higher, they only see the actual outcome of no damage dealt at all and a boring combat against a harmless villain. On the other hand the DM might also fudge the dice to prevent a total party kill caused by a series of lucky rolls.

Personally I do think that randomness should play a role in the game. I would like to roll my dice openly as much as I can and even got some more easily readable dice for the 5E campaign (in pairs for advantage rolls). But there is at least one exception where I prefer a predictable result over a random result: Character creation.

There are different rules options in 5E on how to create characters. You can take a fixed set of values, you can use a point buy system, or you can roll dice. For my campaign I will use the standard array of fixed values for everybody. My reason for that is that the weight of a random roll on character creation is far too big. A character rolling way above or below average will feel the consequences of that in every attack, every skill check, every damage roll for the whole life of the character. A standard array character putting his best score on his main stat and using a race that gives at least +1 bonus to that stat arrives at a +5 value for his attack roll. If players roll for stats, some might end up with a +4 attack bonus, while others have +6. Over the many, many attack rolls that these characters will make over the course of their career that ends up being a huge difference. I don't want one player being permanently disadvantaged just because he rolled low on character creation.