Author Topic: Initiative math and matchups discussion  (Read 1939 times)

Offline Jackinthegreen

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Initiative math and matchups discussion
« on: January 05, 2014, 03:48:57 PM »
This is the discussion thread for http://www.minmaxboards.com/index.php?topic=12239.0

Offline Garryl

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Re: Initiative math and matchups discussion
« Reply #1 on: January 07, 2014, 01:48:50 AM »
The tiebreaker going to the character with highest Dex is only for 3.0. In 3.5, the combatants who are tied act in order of total initiative modifier (highest first), just like an opposed check. As a result, ties are meaningless with unequal modifiers. With equal modifiers, ties result in a reroll, which has equal chances of winning or losing and the same chance of a reroll as before, resulting in even odds for going either direction.

The end result for attempting to beat a single opponent is as follows:
(click to show/hide)

Since initiative checks usually involve multiple characters on each side, there are numerous possible permutations of both the modifiers involved on each side, and the final order of actions. Depending on what you're looking for, it's not always as easy as multiplying probabilities, like it is with a series of consecutive, independent checks, as each character only has one roll against which all rolls from the opposing sides are compared.
« Last Edit: January 07, 2014, 01:56:43 AM by Garryl »

Offline phaedrusxy

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Re: Initiative math and matchups discussion
« Reply #2 on: January 08, 2014, 09:19:31 AM »
You might want to put in a mention of how rerolls can affect this. Having a reroll can tip the scales in your favor dramatically, and may cost less than spending the money to boost your initiative by an amount to give you the same advantage without the reroll. For example, if you have a +5 advantage (higher bonus) over your opponent, you have about a 70% chance to win initiative. However, if you have a reroll available, this gets boosted up to about 90%, which requires the equivalent of a +6 or +7 boost in initiative without a reroll.
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Offline LudicSavant

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Re: Initiative math and matchups discussion
« Reply #3 on: May 08, 2014, 11:54:51 AM »
First off, this is a lovely idea for a handbook.  Being able to figure out how much initiative is enough at a glance would be very handy.

Now this may be nitpicking about math and wording, but this handbook has math in the title, so I'm just going to go ahead.  "Diminishing Returns" here are slight, if they diminish at all.
 
If you have 50% win rate on initiative, you lose 1/2.  Increasing 50 percentage points here cuts your losses in half.
If you have 75% win rate, you lose 1/4.  Increasing 25 percentage points here cuts your losses in half. 
If you have 87.5% win rate, you lose 1/8.  Increasing 12.5 percentage points here cuts your losses in half.

The thing about percentages is that higher percentages are worth more.  Moving from 50% to 75% is generally worth as much as moving from 0% to 50%.  To put it another way, consider if you had % damage reduction.  If you had 50% DR, you effectively have 2x health.  If you have 75% DR, you effectively have 4x health, NOT 3x.  This is why, for instance the armor formula for League of Legends (100 / (110+armor)) has perfectly linear returns.  A character with a 50% initiative win rate wins 1/2 initiative rolls, while a character with 100% wins *all* of them.  That's increasing returns for the same number of percentage points.  In order to have merely even returns, you need to be earning less percentage points with each bonus.

Also, with the popularity of solutions like Ring of Anticipation, it would probably be good to include data on how rerolls affect probability.  Without such figures, the handbook can't really help you much with figuring out how much initiative is enough.

You could also combine this with optimization by the numbers and add in the expected initiative (average to max) for different CRs
« Last Edit: May 08, 2014, 12:26:21 PM by LudicSavant »