Alternatives to Dice Modifiers
The following is musings and ideas for ways of working with dice in skirmish games, that are more immersive than relying solely on static modifiers. Way too often I see dice mechanics that are simply meant as a way of calculating statistics. For skirmish games in particular, I think resolution mechanics can provide much more than just math.
First the rant (can be skipped)
The Alternatives
Equals
For opposed rolls, where two players roll off, make equals mean something. There can be a lot of tension in rolling equals. Instead of making an arbitrary rule for who wins equals, use it. An example, in blight equals are partial hits dealing only half damage. It's a small thing, but with a lot of tension, that also helps even out the swingyness of combat.
Example from Blight: Your opponent attacks with a dice pool of 2d6, rolling double 6 (in blight you roll hit and damage in the same roll, so a 6 for hit and 6 for damage). You get lucky and roll a 6 on your defense. Using equals as partial hits, this is no longer just an attack that hit or missed, it is a potentially lethal hit, that althoug it cut deep, could have taken your arm right off. You might say it's just a 3 damage wound, but there is much more tension and narrative in the resolution.
In Blight, other mechanics also work with equals. As an example, shields block arrows on equals, and the Fights Dirty skill allows a free dagger attack on equal defense. If you don't like the idea of partial hits, another narrative way of using equals is for 'advantage'. Say you want to give an attack bonus when a model charges, instead of giving a +1 (which would be very strong on a d6), you could let charging units win equals.
One obvious thing to note about equals is that opposed rolls using dice with less sides produce more equals than systems using say a d20. Blight relies on having lots of equals for small cuts and interactions. If you want effects that are more rare, equal mechanics naturally work better with dice of more sides.
Rerolls
In some parts of the wargame scene rerolls are rather frowned upon. Mostly however, because they are overused (and misused to fix statistical problems). The other issue is more fundamental. Rerolls are essentially introduced to counter randomness and unlucky rolls. Some people however like randomness and luck (as it creates more uncertainty and excitement), others hate it (as a streak of bad luck dice rolls can make you loose a game you where otherwise dominating). Do not let the hate stop you! Just make sure you think it through. Rerolls can have meaning. For skirmish games, allowing a reroll of a certain result signals that the character is skilled enough that this result is unlikely. In Blight, a character that is skilled with a weapon gets to reroll 1's. A character that is sick, is forced to reroll 6's. Another example could be emulating someone drunk; Forcing them to reroll 3's and 4's, really underpinning a feeling of the swingy randomness of someone who looked a bit too deep in the bottle.
You could also let a player reroll the complete roll, or choose the dice they want to reroll. Here things start to become a bit arbitrary again though, also you might end up with a worse roll. This kind of resoloution lends itself better to gambling. For combat, it could be thematic though as a feint mechanic, or other skill where the player takes a risk.

Another thing to note is that many systems make rules for whether or not you may reroll a reroll. Opinions here are many too. Again, do not let that stop you. Just make sure to think through the consequences. If you allow someone to reroll all dice of a roll, and you allow multiple rerolls, they can obviously just reroll until they get the desired result. If you have a system that allows say rerolls of 1's, and you allow multiple rerolls, then what you say is that this model can never get a 1, instead of a 1 being rare.
Last note is on complexity. Be wary of having rules that sometimes allow re-rerolls, and other times not. Players will get confused.
Looking for highest/lowest
This is used as the very foundation of the Blight resolution system (designing the xD6h system). The main idea of rolling multiple dice and picking the highest/lowest value is to add consistency towards one end of the result range.
The pick-highest mechanic could also work well as an alternative to rerolls in a systems that uses a single die, as it prevents the whole "the reroll was worse" issue, and the re-reroll problem.
x of same number
Want models to be able to make critical hits or do special epic actions? As an example: In a system using d6 dice pools, you could let two or three 6's be a critical/special attack. In this way you can avoid unskilled models with 1d pools from running around and making crits, and make models with large pools make more crits. One thing to think about here is that double damage might not be all that fun; Disarming, overrunning, and outmaneuvering people is much more interesting and engaging.
Modifying dice pool instead of result
In Blight, where you have a dice pool and pick the highest dice as your result, there is a big difference between a dice value modifier and a dice pool modifier. As an example, say you have a skill check that requires you to get a 6. A modifier of -1 would means you could never do this. A dice pool modifier of -1 dice, would mean that the roll is hard, but can still succeed. Again, there are situations where both are appropriate, it's all a matter of thinking about the tools at your disposal, and picking the right one.
Modifiers are not bad
It is important to reiterate that I do not think modifiers are in any way bad or should be avoided. If you want to modify the chance of something by x%, modifiers do just that. Also it makes perfect sense to give say a weapon a damage modifier. +x damage is stating that this weapon hurts more, pure and simply. Same way a damage reduction modifier for armor says: "I'm wrapped in all metal, hitting me with a stick simply wont hurt me, no matter how lucky you get". This post is all about remembering to reflect on what the modifier you introduce actually represents and narrates, and to give inspiration for alternative ways of producing the same results in a way that is more thematic. A resolution systems does not need to be only about statistics.