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Formula for exp award for same CR in different levels

Discussion in 'Icewind Dale 2' started by Sir Rechet, Sep 26, 2012.

  1. Sir Rechet

    Sir Rechet I speak maths and logic, not stupid Veteran

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    [​IMG] I finally discovered a closed formula on how to calculate the exp award for kills for any given average party level (APL) based on the amount you receive currently. Alas, it's not really all that simple since it's a recursive function, ie. you need a separate calculation for every level difference rather than being able to calculate large spans directly. That's because exp awards go up by an alternating 3/2 or 4/3 multiplier across increasing CR values, and the current exp value contains the average party level as a multiplier. Hence, you end up with a double multiplier situation, where the second one is a conditional one to complicate things even more.

    Definitions:
    CAPL = Current APL

    For every level BELOW your current average (for example, by adding mules) will net you a following multiplier:
    (CAPL - 1)/CAPL times 4/3 (for even CAPL) or 2/3 (for odd CAPL).

    For every level ABOVE your current average (by taking a level-up) will net you a following multiplier:
    (CAPL + 1)/CAPL multiplied by 3/4 (for odd CAPL) or 2/3 (for even CAPL).

    In the standard IWD2 rules table, the following bounds hold:
    1) APL 1 = APL 2 = APL 3
    2) For any kill where CAPL => enemy CR + 8, zero exp is awarded.
    3) Low levels vs low CR values are inflated such that you keep receiving the same amount of exp until quite high levels, all the way up to APL 6 for CR between 0.25 and 1.

    For example, a level 10 party is to meet a Crystal Golems (CR 11). They decide to add a new mule to bring the average to 8. Hence, the current award 2250 is taken through the first formula twice: 9/10*4/3 and 8/9*3/2. Combining and simplifying, we get 8/10*2 = 16/10 (+60% increase) for a total value of 3600.

    However, if that same party levels up to 11, they'll only receive 11/10*2/3 for a multiplier of 22/30 and a total exp value of 1650 for any subsequent golems nearby.

    ---------- Added 0 hours, 37 minutes and 27 seconds later... ----------

    Now that I think of it, it's rather straightforward to approximate large spans. Since the multipliers 4/3 and 2/3 combine into exactly 2 after every two CR, all you really need is the ratio of TARGET_APL/CAPL and multiply it with sqrt(2)**(CAPL-TARGET_APL). Might be useful if you want to calculate exp awards for level squatters and the like.
     
    Sir Rechet, Sep 26, 2012
    #1
    JT, coineineagh and spmdw45 like this.
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