Banner of command (promote) and baron buff. Which minion should be promoted?

What are the final offensive stats of a minion after being promoted by Banner of Command?

What if baron was killed at minute 35 and the minion gets baron buff too?

The reason I ask is because I need to find out:

• which minion would make destruction of towers faster
• and which would be more suitable for clearing minions.

To narrow it down a bit, lets disregard the time they remain alive (so that we can ignore defensive stats).

Note: The links I provide contain the separate stats and it should be fairly trivial to calculate total offensive stats and final dps of a minion. If no one else answers, I ll post an answer myself in the following days, since I don't have enough time now, and I think some people might find this information useful.

TL DR:

Against turrets:

• Cannon minions are the best when promoted+baron, and about equally good as melee when they only have promote.
• Caster minions perform the worse when promoted, or promoted+baron.

Against minions:

• Melee are the best with promote, or promote+baron.
• Cannons with promote+baron are the worse (because baron reduces their attack speed by 50%).

Full answer

[...] it should be fairly trivial to calculate total offensive stats and final dps of a minion.

Not really. It can be quite complex.

Minions get a different bonus from baron and promote based on whether they are melee, casters, or cannons. To check which one deals more damage per second (dps) we will ignore how long they survive (obviously a ranged cannon would take less damage from enemies than a melee minion).

To do so, we multiply their total attack damage by their final attack speed. Then we apply multiplicative bonuses. Minions deal bonus damage to towers, and have a penalty on champions (but champions aren't examined in this answer).

Any damage reductions (e.g. armor, magic resist, etc) are disregarded, so dps values below are unmitigated. Lastly, game time is set to 30.

The results are:

=======================================================================
Minion: caster
----------------------------------------
VS turrets

promote
DPS: 154.2

Baron + promote
DPS: 180.3

----------------------------------------
VS minions

promote
DPS: 102.8

Baron + promote
DPS: 120.2


========================================================================
Minion: melee
----------------------------------------
VS turrets

promote
DPS: 256.5

Baron + promote
DPS: 256.5

----------------------------------------
VS minions

promote
DPS: 171.0

Baron + promote
DPS: 299.2


===========================================================================
Minion: siege
----------------------------------------
VS turrets

promote
DPS: 254.2

Baron + promote
DPS: 329.2

----------------------------------------
VS minions

promote
DPS: 169.5

Baron + promote
DPS: 109.8

This is the Python 3.4 code I wrote and used for above results:

raw_minion_stats = dict(
    caster=dict(
        att_dmg=23,
        att_dmg_per_90_sec=1,
        att_speed=0.670,
        multiplicative_dmg_bonus_vs_turrets=1.5),

melee=dict(
    att_dmg=12,
    att_dmg_per_90_sec=0.5,
    att_speed=1.250,
    multiplicative_dmg_bonus_vs_turrets=1.5),

siege=dict(
    att_dmg=39.5,
    att_dmg_per_90_sec=1.5,
    att_speed=1.000,
    multiplicative_dmg_bonus_vs_turrets=1.5))


promote_buff_stats = dict(
    caster=dict(
        att_dmg=75,
        att_speed_bonus=0.3),

    melee=dict(
        att_dmg=50,
        att_speed_bonus=0.9),

    siege=dict(
        att_dmg=100,
        # Since it would deal aoe dmg, we can assume it would hit 3 minions simultaneously.
        multiplicative_dmg_bonus_vs_minions=3))


baron_buff_stats = dict(
    caster=dict(
        att_dmg=20),

    melee=dict(
        extra_percent_dmg_vs_minions=0.75,
    ),

    siege=dict(
        att_dmg=50,
        att_speed_bonus=-0.5,
        extra_percent_dmg_vs_turrets=1))


def final_att_dmg(minion_name, game_time, buffs_dcts):
    """
    Returns total att_dmg after applying all bonuses.

    :param minion_name: 'caster', 'melee' or 'cannon'
    :param game_time: (int) Game time in minutes.
    :param buffs_dcts: (list) List of buff dicts.
    :return: (float)
    """

    # Base attack damage
    val = raw_minion_stats[minion_name]['att_dmg']

    # Bonus by time
    att_dmg_per_min = raw_minion_stats[minion_name]['att_dmg_per_90_sec'] / 1.5
    val += att_dmg_per_min * game_time

    # Bonus by buffs
    for dct in buffs_dcts:
        minion_buff_dct = dct[minion_name]
        if 'att_dmg' in minion_buff_dct:

            val += minion_buff_dct['att_dmg']

    return val


def final_att_speed(minion_name, buffs_dcts):

    # Base attack damage
    val = raw_minion_stats[minion_name]['att_speed']

    # Bonus by buffs
    bonus_val = 0
    for dct in buffs_dcts:
        minion_buff_dct = dct[minion_name]
        if 'att_speed_bonus' in minion_buff_dct:

            bonus_val += minion_buff_dct['att_speed_bonus']

    return val * (1 + bonus_val)


def unmitigated_dps(minion_name, game_time, buffs_dcts, versus):
    """
    Calculates dmg per second of a minion with given buffs versus selected target,
    without taking into account dmg resistances of target.
    (Champion unmitigated_dps not available yet.)

    DPS is irrelevant of combat duration.

    :param versus: 'minions', or 'turrets'
    :return:
    """

    att_dmg = final_att_dmg(minion_name=minion_name, game_time=game_time, buffs_dcts=buffs_dcts)
    att_speed = final_att_speed(minion_name=minion_name, buffs_dcts=buffs_dcts)

    val = att_dmg * att_speed

    extra_percent_dmg_keyword = 'extra_percent_dmg_vs_' + versus

    for dct in buffs_dcts:
        minion_buff_dct = dct[minion_name]
        if extra_percent_dmg_keyword in minion_buff_dct:

            val *= 1 + minion_buff_dct[extra_percent_dmg_keyword]

    # Minions' final dmg gets a bonus vs turrets and a penalty vs champions.
    multiplicative_bonus_keyword = ''
    if versus == 'turrets':
        multiplicative_bonus_keyword = 'multiplicative_dmg_bonus_vs_' + versus
    elif versus == 'minions':
        multiplicative_bonus_keyword = 'multiplicative_dmg_bonus_vs_' + versus

    if multiplicative_bonus_keyword in raw_minion_stats[minion_name]:
        val *= raw_minion_stats[minion_name][multiplicative_bonus_keyword]

    return val

# =====================================================================================================================
# DISPLAY RESULTS
selected_game_time_in_minutes = 30

# All minions:
for _minion_name in sorted(raw_minion_stats):
    msg = '\n' + '='*60
    msg += '\nMinion: {}'.format(_minion_name)

    for tar_name in ('turrets', 'minions'):
        msg += '\n' + '-'*40
        msg += '\nVS {}\n'.format(tar_name)
        # promote
        msg += '\npromote'
        minion_dps = unmitigated_dps(minion_name=_minion_name,
                                     game_time=selected_game_time_in_minutes,
                                     buffs_dcts=[promote_buff_stats, ],
                                     versus=tar_name)

        msg += '\nDPS: {:.1f}'.format(minion_dps)

        msg += '\n'

        # Baron + promote
        msg += '\nBaron + promote'
        minion_dps = unmitigated_dps(minion_name=_minion_name,
                                     game_time=selected_game_time_in_minutes,
                                     buffs_dcts=[baron_buff_stats, promote_buff_stats],
                                     versus=tar_name)

        msg += '\nDPS: {:.1f}\n'.format(minion_dps)

    print(msg)

Although i did check some of the results (and they seemed reasonable) I have not tested everything. In case you find a mistake, please let me know.

So when looking through the buffs, I came to the conclusion that in a setup where there is no champions involved (except for one that has baron buff, so minions actually have the bonus), just minions, the following would apply (I will get onto champions later):

which minion would make destruction of towers faster

Except for caster minions, baron buff would be more suitable as:

Melee minions

• (Gain +50% movement speed when within 800 units of enemy minions or turrets)
• (Increased size)
• (+75 attack range)
• +75% damage reduction versus champions and minions
• +30% damage reduction versus turrets (similar to cannon minions)

Cannon minions (beyond turret range)

• +600 attack range
• +50 attack damage, but attack speed is halved
• Attacks are now Area of Effect (200 range) and deal double damage to turrets

Quite important to note: Cannon minions actually attack turrets from out of range, so they will shoot infinitely as long as other minions do not kill them.

This does not apply to Caster Minions as they receive similar offensive buffs to the ones of Banner Of Command, but the defensive stats from Banner of Command will make destroying turrets easier as the minions survive longer:

• • 400 Health.
• • 40 Armor and Magic Resist

and which would be more suitable for clearing minions

Cannon minions (beyond turret range)

• Attacks are now Area of Effect (200 range) (and deal double damage to turrets)

The AoE will clear minions faster, considering they will stand in standard 3-1-3 or 3-0-3 formation (melee-cannon-caster)

Meelee minions (in a 1v1-scenario) empowered with Banner Of Command should overcome minions that have Hand Of Baron as they do not receive major offensive boosts from Hand of Baron in contrast to Banner Of Command granting:

• +50 Attack Damage
• +90% bonus Attack Speed

The defensive boost are comparable. While Hand of Baron gives +75% damage reduction versus minions, Banner Of Command gives

• +600 Health
• +40 Armor and Magic Resist

Caster minions (again, in a 1v1-scenario) should overcome with Banner of Command as the offensive statistics of both buffs are comparable, but Banner of Command gives bonus health and resistances.

DISCLAIMER: In my eyes, this is rather hard to theorycraft, as the circumstances under which you apply the buffs decide the outcome. Questions as:

Do the minions come in waves or are they single-handedly going onto towers?

Are their champions with waveclear or which turrets (Outer or Inner Turrets) are attacked?

Context: While baron gives resistance to slow effects, 75% damage reduction versus area of effect, damage over time, and persistent effects, Banner of Command gives a permanent Black Shield which grants total immunity to magic damage and Tower Shield (reduced turret damage). Turrets prioritize minions that have been promoted over other minions. So it is important to notice that there is a lot of factors to be considered.

Personal opinion should not be included, but considering that Hand Of Baron gives the buff to all nearby minions and not just one unit, I would personally prefer it over Banner of Command. In a scenario where a Baron-empowered wave faces a wave with a single Banner of Command-empowered minion (choose whichever), I am certain the wave with baron will push.

I suggest you refine your question and/or play a custom game and try out your idea yourself. ;)