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The Quadratic Problem—Speculations on 4e
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<blockquote data-quote="mmadsen" data-source="post: 3753242" data-attributes="member: 1645"><p>I thought I'd expand on this a bit, because it plays a large, but hidden, role in the game, and it could play a larger role in a new design.</p><p></p><p>If attack bonuses and defense bonuses increase in lock step, then character will find themselves hitting and being hit "reasonably often" at every level. Large differences in bonuses cause inordinate differences in outcome though -- in one direction, but not the other.</p><p></p><p>If your attack bonus outclasses your opponent's defense bonus, it's no big deal. Instead of hitting 50 percent of the time, you might hit 55, 60, 65, ..., up to 95 percent of the time. That is, if you totally outclass your opponent, you'll hit twice as often as against an equal.</p><p></p><p>If your defense bonus outclasses your opponent's attack bonus though, you'll defend not just 50 percent of attacks, but 55, 60, 65, ..., up to 95 of attacks. That seems parallel, but it's not. Instead of getting hit by one attack in two, you get hit by one attack in <em>20</em>, or one <em>tenth</em> as many attacks. In fact, just going from defending 90 percent to 95 percent of attacks, an additional +1 bonus, <em>doubles</em> your expected lifespan.</p><p></p><p>Once you have a decent defense bonus, each additional point is tremendously valuable. Again, if your chance of defending is 50 percent, then you expect to get hit once per <em>two</em> rounds. If your chance of defending is 75 percent, then you expect to get hit once per <em>four</em> rounds -- doubling your defense, but still reasonable. If your chance of defending is 95 percent, then you expect to get hit once per <em>20</em> rounds -- which is a lot like having 10 times as many hit points as someone who gets hit every other round:</p><p></p><p>50% -- 02.00 [expected rounds between hits]</p><p>55% -- 02.22</p><p>60% -- 02.50</p><p>65% -- 02.86</p><p>70% -- 03.33</p><p>75% -- 04.00</p><p>80% -- 05.00</p><p>85% -- 06.67</p><p>90% -- 10.00</p><p>95% -- 20.00</p></blockquote><p></p>
[QUOTE="mmadsen, post: 3753242, member: 1645"] I thought I'd expand on this a bit, because it plays a large, but hidden, role in the game, and it could play a larger role in a new design. If attack bonuses and defense bonuses increase in lock step, then character will find themselves hitting and being hit "reasonably often" at every level. Large differences in bonuses cause inordinate differences in outcome though -- in one direction, but not the other. If your attack bonus outclasses your opponent's defense bonus, it's no big deal. Instead of hitting 50 percent of the time, you might hit 55, 60, 65, ..., up to 95 percent of the time. That is, if you totally outclass your opponent, you'll hit twice as often as against an equal. If your defense bonus outclasses your opponent's attack bonus though, you'll defend not just 50 percent of attacks, but 55, 60, 65, ..., up to 95 of attacks. That seems parallel, but it's not. Instead of getting hit by one attack in two, you get hit by one attack in [i]20[/i], or one [i]tenth[/i] as many attacks. In fact, just going from defending 90 percent to 95 percent of attacks, an additional +1 bonus, [i]doubles[/i] your expected lifespan. Once you have a decent defense bonus, each additional point is tremendously valuable. Again, if your chance of defending is 50 percent, then you expect to get hit once per [i]two[/i] rounds. If your chance of defending is 75 percent, then you expect to get hit once per [i]four[/i] rounds -- doubling your defense, but still reasonable. If your chance of defending is 95 percent, then you expect to get hit once per [i]20[/i] rounds -- which is a lot like having 10 times as many hit points as someone who gets hit every other round: 50% -- 02.00 [expected rounds between hits] 55% -- 02.22 60% -- 02.50 65% -- 02.86 70% -- 03.33 75% -- 04.00 80% -- 05.00 85% -- 06.67 90% -- 10.00 95% -- 20.00 [/QUOTE]
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