This will be an unpopular opinion in this thread. I'm reading a lot about AD&D sensibilities and how some DMs want to have 5e feel a certain way. That's fine and all, but I think people are overlooking the primary reason why WotC removed the option to interrupt spells in this way: It's not fun for the caster. Wasting your round to cast a single spell that doesn't end up going off is a serious fun-killer.
Something to think about.
I won't presume to know WotC removed it, but I think it really depends on the players, as well as how interesting it is. This system is also used when attempting to cast a spell you are still learning, and also when using counterspell (although that works a little different).
It doesn't happen as often as you might think, but it alters the tactics that the players use in combat. We really enjoy it. More importantly, for folks like us it lets us enjoy AD&D with the more elegant rule system of 5e.
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In my system, if you are interrupted, then you roll on a Wild Magic Surge table. This can be affected by modifiers, bonuses make it less likely to fail and lower rolls get progressively worse.
Wild Magic Surge
d20 Effect
1-2 The spell creates a random effect. Roll on the Wild Magic Surge table (PHB 104).
3-4 The spell backfires and affects the caster instead. If the target is the caster, the spell misfires instead.*
5-6 The spell misfires, roll on the Misfire table.
7-10 The spell fizzles, roll on the Spell Fizzles table.
11-20 The spell functions normally.
*If a backfire is not possible due to the nature of the spell, then roll on the Spell Misfire table and target the caster.
Spell Fizzles
Your Action is used, the energy fizzles and sputters (can cause any harmless visual effect desired); and:
D6 Effect
1 The spell slot is used.
2 The spell slot is not used.
3 You cast the pyrotechnics spell in a random direction in front of you. The spell slot is not used.
4 You cast the pyrotechnics spell in a random direction in front of you. The spell slot is used.
5-6 The spell creates a random effect. Roll on the Wild Magic Surge table (PHB 104).
Spell Misfire
The energy of the spell is catastrophically released.
D6 Effect
1-2 The spell releases its energy as a line 10 ft. long per level of the spell. Roll 1d6:
--1) fire
--2) force
--3) lightning
--4) necrotic
--5) radiant
--6) thunder
--Damage is equal to 2d6 per level of the spell. Creatures that make a successful Dexterity saving throw take half damage.
3-4 The spell violently explodes.
--Creatures in a 30 ft. radius:
--• Take 2d4 damage per level of the spell (no saving throw).
--• Must make a Strength saving throw or be knocked back 10 feet and prone. Creatures immune to force damage do not need to make the saving throw.
5 The spell violently explodes.
--The caster:
--• Takes 2d4 damage per level of the spell (no saving throw).
--• Must make a Strength saving throw or be knocked back 10 feet and prone. Creatures immune to force damage do not need to make the saving throw.
6 The spell creates a random effect. Roll on the Wild Magic Surge table (PHB 104).