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<blockquote data-quote="Zimbel" data-source="post: 2728145" data-attributes="member: 29912">Analysis of CR for Astral ConstructsThe last several posts I made form the foundation for this one. Assuming that no speicial abilities are chosen that affect their combat stats, what is the approparite CR for the astral contructs?Conclusion:The CRs should be:[CODE]Construct level 1&nbsp; &nbsp; 2&nbsp; &nbsp; 3&nbsp; &nbsp; 4&nbsp; &nbsp; 5&nbsp; &nbsp; 6&nbsp; &nbsp; 7&nbsp; &nbsp; 8&nbsp; &nbsp; 9 Listed CR&nbsp; &nbsp; &nbsp;&nbsp; 0.5&nbsp; 1&nbsp; &nbsp; 2&nbsp; &nbsp; 3&nbsp; &nbsp; 5&nbsp; &nbsp; 7&nbsp; &nbsp; 8&nbsp; &nbsp; 9&nbsp;&nbsp; 10&nbsp; &nbsp; Correct CR&nbsp; &nbsp; &nbsp; 1&nbsp; &nbsp; 2&nbsp; &nbsp; 3&nbsp; &nbsp; 4&nbsp; &nbsp; 6&nbsp; &nbsp; 7&nbsp; &nbsp; 8&nbsp; &nbsp; 9&nbsp;&nbsp; 10[/CODE]Note that the CR for the Following constructs is built on incomplete data: 4th level, 5th level.Analysis:Of the data in prior posts, the most useful comparitive data appears to be stadard deviations away from the mean. a value that's too large is strongly indicative of a creature being at an incorrect CR; a value that's too small is indicative that the CR is wrong if and only if the creature is a front-line battler whose primary effect is melee damage. Since it's nice to collate the information into a single number, I propose the following formula to be a CR tester; i.e. a determiner if the listed CR is too low for a front-line battler:(SD = Standard Deviations from mean(signed), after the &quot;battler&quot; filter)If SD(HP) + SD(AC) + SD(Damage)&nbsp; &gt; 3, then the listed CR is too low.The reasons I choose 3 instead of a lower value are 1) There should be quite a bit of variation within each CR, and 2) even with the &quot;battler&quot; filter, a number of creatures in the sample are not optimized for these stats for their CR.Most of the curvevs in question are not normal distributions, so it would be hasty to draw precise mathematical conclusions from the above, but given the above forumla, very few creatures in our entire sample should indicate that their CR is too low. Noting 6 deviations from this among all the CRs in our sample, I conclude that this is likely a reasonable determiner (after all, I assume that some of the creatures in the sample are not at their correct CRs).Now let's apply this to the astral constructs:[CODE]LV SD(HP) SD(AC) SD(Damage)&nbsp; &nbsp;&nbsp; Sum1&nbsp;&nbsp; 2.6&nbsp; &nbsp; &nbsp; 2.9&nbsp; &nbsp; &nbsp; 0.2&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 5.62&nbsp;&nbsp; 3.4&nbsp; &nbsp; &nbsp; 2.0&nbsp; &nbsp; &nbsp; 0.3&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 5.73&nbsp;&nbsp; 1.6&nbsp; &nbsp; &nbsp; 2.2&nbsp; &nbsp; &nbsp; 0.2&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 4.04&nbsp;&nbsp; 1.9&nbsp; &nbsp; &nbsp; 2.8&nbsp; &nbsp; &nbsp; 0.3&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 4.95&nbsp;&nbsp; 0.3&nbsp; &nbsp; &nbsp; 1.8&nbsp; &nbsp; &nbsp; 1.1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 3.26&nbsp; -0.4&nbsp; &nbsp; &nbsp; 2.4&nbsp; &nbsp; &nbsp; 0.2&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 2.2 7&nbsp; -0.1&nbsp; &nbsp; &nbsp; 2.2&nbsp; &nbsp; &nbsp; 0.2&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 2.28&nbsp; -0.6&nbsp; &nbsp; &nbsp; 2.6&nbsp; &nbsp; &nbsp; 0.1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 2.09&nbsp;&nbsp; 0.0&nbsp; &nbsp; &nbsp; 2.6&nbsp; &nbsp; &nbsp; 0.1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 2.6[/CODE]Now, if we increase the CRs for the LV 1-3 constructs, we get:[CODE]LV SD(HP) SD(AC) SD(Damage)&nbsp; &nbsp;&nbsp; Sum1&nbsp;&nbsp; 0.4&nbsp; &nbsp; &nbsp; 2.0&nbsp; &nbsp;&nbsp; -0.1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 2.32&nbsp;&nbsp; 1.1&nbsp; &nbsp; &nbsp; 1.2&nbsp; &nbsp;&nbsp; -0.4&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 1.93&nbsp;&nbsp; 1.1&nbsp; &nbsp; &nbsp; 1.2&nbsp; &nbsp;&nbsp; -0.4&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 1.9[/CODE]As a quick double-check, if we pumped up the CR of the LV 1 construct to 2 (and LV4-&gt; cr5 and LV5-&gt;CR7), we get:[CODE]LV SD(HP) SD(AC) SD(Damage)&nbsp; &nbsp;&nbsp; Sum1&nbsp;&nbsp; -0.7&nbsp; &nbsp; &nbsp; 1.2&nbsp; &nbsp;&nbsp; -0.6&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; -0.14&nbsp;&nbsp; -0.9&nbsp; &nbsp; &nbsp; 1.5&nbsp; &nbsp;&nbsp; -1.1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; -0.55&nbsp;&nbsp; -0.9&nbsp; &nbsp; &nbsp; 1.6&nbsp; &nbsp;&nbsp; -0.5&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 0.2[/CODE]These number are low for a battler, which suggests that they all should be one CR lower than we tested for.Not yet started:Astral Constructs w/ special abilities.</blockquote>

[QUOTE="Zimbel, post: 2728145, member: 29912"] [b]Analysis of CR for Astral Constructs[/b] The last several posts I made form the foundation for this one. Assuming that no speicial abilities are chosen that affect their combat stats, what is the approparite CR for the astral contructs? Conclusion: The CRs should be: [CODE] Construct level 1 2 3 4 5 6 7 8 9 Listed CR 0.5 1 2 3 5 7 8 9 10 Correct CR 1 2 3 4 6 7 8 9 10 [/CODE] Note that the CR for the Following constructs is built on incomplete data: 4th level, 5th level. Analysis: Of the data in prior posts, the most useful comparitive data appears to be stadard deviations away from the mean. a value that's too large is strongly indicative of a creature being at an incorrect CR; a value that's too small is indicative that the CR is wrong if and only if the creature is a front-line battler whose primary effect is melee damage. Since it's nice to collate the information into a single number, I propose the following formula to be a CR tester; i.e. a determiner if the listed CR is too low for a front-line battler: (SD = Standard Deviations from mean(signed), after the "battler" filter) If SD(HP) + SD(AC) + SD(Damage) > 3, then the listed CR is too low. The reasons I choose 3 instead of a lower value are 1) There should be quite a bit of variation within each CR, and 2) even with the "battler" filter, a number of creatures in the sample are not optimized for these stats for their CR. Most of the curvevs in question are not normal distributions, so it would be hasty to draw precise mathematical conclusions from the above, but given the above forumla, very few creatures in our entire sample should indicate that their CR is too low. Noting 6 deviations from this among all the CRs in our sample, I conclude that this is likely a reasonable determiner (after all, I assume that some of the creatures in the sample are not at their correct CRs). Now let's apply this to the astral constructs: [CODE] LV SD(HP) SD(AC) SD(Damage) Sum 1 2.6 2.9 0.2 5.6 2 3.4 2.0 0.3 5.7 3 1.6 2.2 0.2 4.0 4 1.9 2.8 0.3 4.9 5 0.3 1.8 1.1 3.2 6 -0.4 2.4 0.2 2.2 7 -0.1 2.2 0.2 2.2 8 -0.6 2.6 0.1 2.0 9 0.0 2.6 0.1 2.6 [/CODE] Now, if we increase the CRs for the LV 1-3 constructs, we get: [CODE] LV SD(HP) SD(AC) SD(Damage) Sum 1 0.4 2.0 -0.1 2.3 2 1.1 1.2 -0.4 1.9 3 1.1 1.2 -0.4 1.9 [/CODE] As a quick double-check, if we pumped up the CR of the LV 1 construct to 2 (and LV4-> cr5 and LV5->CR7), we get: [CODE] LV SD(HP) SD(AC) SD(Damage) Sum 1 -0.7 1.2 -0.6 -0.1 4 -0.9 1.5 -1.1 -0.5 5 -0.9 1.6 -0.5 0.2 [/CODE] These number are low for a battler, which suggests that they all should be one CR lower than we tested for. Not yet started: Astral Constructs w/ special abilities. [/QUOTE]

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