Defensive Duelist is strictly better than Medium Armor Master
The math for Medium Armour Master is relatively simple - you have an AC of 20.
Defensive Duelist is slightly more complicated. You effectively have an AC of 22 until the first time an attack rolls well enough to hit AC 19 but not well enough to hit AC 22 - you use your reaction to make that one miss and all subsequent attacks are against AC 19.
This anydice simulates attackers with disadvantage.
The results are:
\begin{array}{r|rr|r}
\text{Hits} & \text{MAM} & \text{DD} & \text{Difference} \\
\hline
0 & 0.6857 & 0.7434 & 0.0577\\
1 & 0.2713 & 0.2322 & -0.0391 \\
2 & 0.0402 & 0.0236 & -0.0166\\
3 & 0.0027 & 0.0008 & -0.0019\\
4 & 0.0001 & 0.0000 & -0.0001 \\
\end{array}
The results are also better for DD without advantage.
However,
With Defensive Duelist you will lose your reaction on your turn with a probability of 0.4780 (i.e. just under half the time) which means no opportunity attacks (or other Reactions) until your next turn. Booming Blade only locks down 1 foe (if you hit), Opportunity Attacks threaten another and you are giving this up half the time.
The Code
MAMAC: 20
DAC: 19
MOD: +5
ATTACKS: 4
DODGEMOD: -3
MAMHIT: [lowest 1 of 2d{0:1, 0:(MAMAC-MOD) - 2, 1: 20 - (MAMAC-MOD), 1:1}]
DHIT: [lowest 1 of 2d{0:1, 0:(DAC-MOD) - 2, 1: 20 - (DAC-MOD), 1:1}]
DODGEHIT: [lowest 1 of 2d{0:1, 0: (DAC-MOD) - 2, -1:-DODGEMOD, 1: 20 - (DAC-MOD-DODGEMOD), 1:1}]
function: N:n dodge D:n {
if N=1 {result: dDHIT}
if D=-1 {result: 0 + d[N-1 dodge DHIT]}
result: D + d[N-1 dodge DODGEHIT]
}
output ATTACKSdMAMHIT named "Medium Armor Master"
output [4 dodge DODGEHIT] named "Defensive Duelist"
The German translation of the Starter Set confuses Chain Shirt with Chain Mail, which is the armor actually used by the Human Fighter and Dwarf Cleric in the Starter Set. Chain Mail is a heavy armor providing 16 AC, Chain Shirt is a medium armor providing 13 + dexterity modifier (up to 2) AC.
Best Answer
Hit your fighter in the NADs1
AC isn't the only way to cause damage to a fighter.
The biggest thing to keep in mind is that AC isn't the end-all-be-all in D&D. Yes, it's important, but there are avenues around it.
1NADs = Non-AC Defenses. In D&D 4e you didn't have saving throws, rather you had static defense values: AC, Fortitude (Str/Con), Reflex (Dex/Int), and Will (Wis/Cha). A common reply to fighters with super-high AC was "hit 'em in the NADs!", meaning that a high AC usually meant a low Reflex and/or Will defense—fighters of course having a high Str or Con meant a good Fortitude defense.