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<blockquote data-quote="ichabod" data-source="post: 770872" data-attributes="member: 1257">Hey y'all,Seasong's point buy system inadvertently inspired me to create the following point buy system. Now, the reasoning is perhaps even more convoluted than Seasong's, but it all starts with a very basic concept: design a point buy system that models the distribution of the standard rolling mechanism in the PHB. So, I started with the distribution of the standard PHB (this was done by John Kim, and can be found&nbsp; <a href="http://www.darkshire.org/~jhkim/rpg/dnd/abilities.html" target="_blank">here</a>). This is sorted, so the '1st' column is the probability for your highest ability, the '2nd' column for your 2nd highest ability, and so on. AFAICT, this table just leaves off any probabilities less than 0.01. More than sufficient for my purposes.[code][color=white]&nbsp; &nbsp; &nbsp; 1st&nbsp; &nbsp; 2nd&nbsp; &nbsp; 3rd&nbsp; &nbsp; 4th&nbsp; &nbsp; 5th&nbsp; &nbsp; 6th18&nbsp;&nbsp; 10.6&nbsp; &nbsp; 0.4&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 17&nbsp;&nbsp; 23.2&nbsp; &nbsp; 4.5&nbsp; &nbsp; 0.4&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 16&nbsp;&nbsp; 29.6&nbsp;&nbsp; 15.5&nbsp; &nbsp; 3.4&nbsp; &nbsp; 0.4&nbsp; &nbsp; &nbsp; 15&nbsp;&nbsp; 23.6&nbsp;&nbsp; 27.5&nbsp;&nbsp; 12.4&nbsp; &nbsp; 2.9&nbsp; &nbsp; 0.4&nbsp;&nbsp; 14&nbsp;&nbsp; 13&nbsp; &nbsp;&nbsp; 30.0&nbsp;&nbsp; 25.4&nbsp;&nbsp; 10.8&nbsp; &nbsp; 2.4&nbsp; &nbsp; 0.213&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 16.5&nbsp;&nbsp; 29.6&nbsp;&nbsp; 22.5&nbsp; &nbsp; 8.5&nbsp; &nbsp; 1.312&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 5.0&nbsp;&nbsp; 20.2&nbsp;&nbsp; 28.1&nbsp;&nbsp; 18.2&nbsp; &nbsp; 4.711&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 0.5&nbsp; &nbsp; 7.2&nbsp;&nbsp; 21.7&nbsp;&nbsp; 24.8&nbsp;&nbsp; 10.910&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1.5&nbsp;&nbsp; 10.9&nbsp;&nbsp; 23.6&nbsp;&nbsp; 17.79&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 2.3&nbsp;&nbsp; 14.3&nbsp;&nbsp; 21.08&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 0.4&nbsp; &nbsp; 6.1&nbsp;&nbsp; 19.17&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 1.4&nbsp;&nbsp; 12.86&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 0.3&nbsp; &nbsp; 7.55&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 3.24&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1.33&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 0.3[/color][/code]Note that the median ability vector is [16, 14, 13, 12, 11, 9]. Also note that the median overall ability is 12.5.Now it's time for the over-analyzing. I started by arbitrarily setting the standard point buy at 30 points. This is a nice round figure that is divisible by the number of abilities. I also set the cost for the lowest probability in each column to 1. This leads to some oddness, but I think it works out. Next I stipulated that you should be able to buy the median ability vector with the standard point buy. Third, I stipulated that you should be able to buy six of the median ability with the standard point buy. Given that the median is 12.5, I set the cost of three 13's and three 12's to 30 (for this I dropped the minimum on the highest roll to 13). Finally, it seemed reasonable to make cost differentials at least one and non-decreasing (that is, the difference in cost between two abilities will be at least that of the next two lowest abilities). That gave me the lower parts of the table below. I finished it off using an increasing cost scheme similar to WotC's point buy. You use the first column to buy your highest ability, the second column to buy your second highest ability, and so on.[code][color=white]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 1st&nbsp;&nbsp; 2nd&nbsp;&nbsp; 3rd&nbsp;&nbsp; 4th&nbsp;&nbsp; 5th&nbsp;&nbsp; 6th18&nbsp; &nbsp; 10&nbsp; &nbsp; 16&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a17&nbsp; &nbsp;&nbsp; 7&nbsp; &nbsp; 13&nbsp; &nbsp; 16&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a16&nbsp; &nbsp;&nbsp; 5&nbsp; &nbsp; 10&nbsp; &nbsp; 13&nbsp; &nbsp; 15&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a15&nbsp; &nbsp;&nbsp; 3&nbsp; &nbsp;&nbsp; 7&nbsp; &nbsp; 10&nbsp; &nbsp; 12&nbsp; &nbsp; 15&nbsp;&nbsp; n/a14&nbsp; &nbsp;&nbsp; 2&nbsp; &nbsp;&nbsp; 5&nbsp; &nbsp;&nbsp; 7&nbsp; &nbsp;&nbsp; 9&nbsp; &nbsp; 12&nbsp; &nbsp; 1413&nbsp; &nbsp;&nbsp; 1&nbsp; &nbsp;&nbsp; 3&nbsp; &nbsp;&nbsp; 5&nbsp; &nbsp;&nbsp; 7&nbsp; &nbsp;&nbsp; 9&nbsp; &nbsp; 1112&nbsp; &nbsp;&nbsp; 0&nbsp; &nbsp;&nbsp; 2&nbsp; &nbsp;&nbsp; 3&nbsp; &nbsp;&nbsp; 5&nbsp; &nbsp;&nbsp; 7&nbsp; &nbsp;&nbsp; 911&nbsp;&nbsp; n/a&nbsp; &nbsp;&nbsp; 1&nbsp; &nbsp;&nbsp; 2&nbsp; &nbsp;&nbsp; 4&nbsp; &nbsp;&nbsp; 5&nbsp; &nbsp;&nbsp; 710&nbsp;&nbsp; n/a&nbsp; &nbsp;&nbsp; 0&nbsp; &nbsp;&nbsp; 1&nbsp; &nbsp;&nbsp; 3&nbsp; &nbsp;&nbsp; 4&nbsp; &nbsp;&nbsp; 69&nbsp; &nbsp; n/a&nbsp;&nbsp; n/a&nbsp; &nbsp;&nbsp; 0&nbsp; &nbsp;&nbsp; 2&nbsp; &nbsp;&nbsp; 3&nbsp; &nbsp;&nbsp; 58&nbsp; &nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a&nbsp; &nbsp;&nbsp; 1&nbsp; &nbsp;&nbsp; 2&nbsp; &nbsp;&nbsp; 47&nbsp; &nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a&nbsp; &nbsp;&nbsp; 0&nbsp; &nbsp;&nbsp; 1&nbsp; &nbsp;&nbsp; 36&nbsp; &nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a&nbsp; &nbsp;&nbsp; 0&nbsp; &nbsp;&nbsp; 25&nbsp; &nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a&nbsp; &nbsp;&nbsp; 14&nbsp; &nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a&nbsp; &nbsp;&nbsp; 03&nbsp; &nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a[/color][/code]Now, as I said there is some oddness. Because I wanted the flat median available, it's possible to get things with 30 points that you can't with a standard roll. I'm not too worried about that, since a player can?t really screw themselves that way. To keep the costs differing by at least one, I had to remove the ability to buy a 3 for your lowest ability. I'm not too worried about that, because if you really want a 3 that badly, it?s easier to indulge your need for angst by rolling one of those twenty siders numbered 1-10 instead of a d20 for checks. Besides, in the end I knew it wouldn't match perfectly, and if you?re willing to use a six-column table for ability generation, you should be able to deal with a little oddness (more on that later).To emphasize some things I like about this point buy, let's look at high stats. If you want an 18, you can still get 14, 12, 10, 10, 9. If you want two 16's, you can still get 12, 10, 10, 9. So you can take a slight hit to get a couple decent stats. If you want three decent stats, you'll need to take a bigger hit. Now some may say I?m just a power gamer whining for bigger scores, but I think this better represents a character made with standard rolls. 1 in 8 characters is going to have two 16's or better with standard rolling.If you want different power levels, I suggest the following: low-powered = 15 (about equivalent to WotC's low-powered), challenging = 22, tougher = 40 (allows median vector +1), and high powered = 55 (median vector +2).As noted before, this does require using a six-column table to generate abilities. However, my intention was always to look at the table generated, and try to work from there to a simpler system (no, really, honest!). To that end, I present two steps down from the above system. I don't think you lose much stepping down, but I haven't analyzed it that much.In the next table, there are three columns. Any player can use the &quot;Avg&quot; column all they want. Each time they make use of the &quot;Good&quot; column, they must make use of the &quot;Bad&quot; column. If you wanted, you could even limit it to two uses of the &quot;Good&quot; column.[code][color=white]&nbsp; &nbsp; Good&nbsp;&nbsp; Avg&nbsp;&nbsp; Bad18&nbsp; &nbsp; 13&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a17&nbsp; &nbsp; 10&nbsp; &nbsp; 17&nbsp;&nbsp; n/a16&nbsp; &nbsp;&nbsp; 7&nbsp; &nbsp; 14&nbsp;&nbsp; n/a15&nbsp; &nbsp;&nbsp; 5&nbsp; &nbsp; 11&nbsp; &nbsp; 1614&nbsp; &nbsp;&nbsp; 3&nbsp; &nbsp;&nbsp; 8&nbsp; &nbsp; 1313&nbsp; &nbsp;&nbsp; 2&nbsp; &nbsp;&nbsp; 6&nbsp; &nbsp; 1012&nbsp; &nbsp;&nbsp; 1&nbsp; &nbsp;&nbsp; 4&nbsp; &nbsp;&nbsp; 811&nbsp; &nbsp;&nbsp; 0&nbsp; &nbsp;&nbsp; 3&nbsp; &nbsp;&nbsp; 610&nbsp;&nbsp; n/a&nbsp; &nbsp;&nbsp; 2&nbsp; &nbsp;&nbsp; 59&nbsp; &nbsp; n/a&nbsp; &nbsp;&nbsp; 1&nbsp; &nbsp;&nbsp; 48&nbsp; &nbsp; n/a&nbsp; &nbsp;&nbsp; 0&nbsp; &nbsp;&nbsp; 37&nbsp; &nbsp; n/a&nbsp;&nbsp; n/a&nbsp; &nbsp;&nbsp; 26&nbsp; &nbsp; n/a&nbsp;&nbsp; n/a&nbsp; &nbsp;&nbsp; 15&nbsp; &nbsp; n/a&nbsp;&nbsp; n/a&nbsp; &nbsp;&nbsp; 04&nbsp; &nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a3&nbsp; &nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a[/color][/code]Again, the median vector and the flat median value can be bought for 30 points. Getting a couple good stats is close in difficulty to the six-column system.If this is not simple enough for you, pick any one of the collumns in the six-column table (except the first). The cost of 5 gets you the appropriate ability from the median vector. Moving the ability up or down one moves the cost up or down one. In other words, you start with 16, 14, 13, 12, 11, 9. For each ability, you pay the cost below to modify it (use one and only one column, maximum 18):[code][color=white]&nbsp; &nbsp; &nbsp; A&nbsp; &nbsp;&nbsp; B&nbsp; &nbsp;&nbsp; C+5&nbsp;&nbsp; n/a&nbsp;&nbsp; n/a&nbsp;&nbsp; 14+4&nbsp; &nbsp; 16&nbsp; &nbsp; 15&nbsp;&nbsp; 11+3&nbsp; &nbsp; 13&nbsp; &nbsp; 12&nbsp; &nbsp; 9+2&nbsp; &nbsp; 10&nbsp; &nbsp;&nbsp; 9&nbsp; &nbsp; 7+1&nbsp; &nbsp;&nbsp; 7&nbsp; &nbsp;&nbsp; 7&nbsp; &nbsp; 6+0&nbsp; &nbsp;&nbsp; 5&nbsp; &nbsp;&nbsp; 5&nbsp; &nbsp; 5-1&nbsp; &nbsp;&nbsp; 3&nbsp; &nbsp;&nbsp; 4&nbsp; &nbsp; 4-2&nbsp; &nbsp;&nbsp; 2&nbsp; &nbsp;&nbsp; 3&nbsp; &nbsp; 3-3&nbsp; &nbsp;&nbsp; 1&nbsp; &nbsp;&nbsp; 2&nbsp; &nbsp; 2-4&nbsp; &nbsp;&nbsp; 0&nbsp; &nbsp;&nbsp; 1&nbsp; &nbsp; 1-5&nbsp;&nbsp; n/a&nbsp; &nbsp;&nbsp; 0&nbsp; &nbsp; 0[/color][/code]I haven't analyzed these yet, but my guess is that column A will be slightly worse than the standard roll, column B will be slightly better, and column C will be enough better that I wouldn't recommed using it.So, do any of the two or three people who bothered to read this whole thing have any comments, criticisms, or shiny glass beads I can use to impress my fellow villagers?</blockquote>

[QUOTE="ichabod, post: 770872, member: 1257"] Hey y'all, Seasong's point buy system inadvertently inspired me to create the following point buy system. Now, the reasoning is perhaps even more convoluted than Seasong's, but it all starts with a very basic concept: design a point buy system that models the distribution of the standard rolling mechanism in the PHB. So, I started with the distribution of the standard PHB (this was done by John Kim, and can be found [url=http://www.darkshire.org/~jhkim/rpg/dnd/abilities.html]here[/url]). This is sorted, so the '1st' column is the probability for your highest ability, the '2nd' column for your 2nd highest ability, and so on. AFAICT, this table just leaves off any probabilities less than 0.01. More than sufficient for my purposes. [code][color=white] 1st 2nd 3rd 4th 5th 6th 18 10.6 0.4 17 23.2 4.5 0.4 16 29.6 15.5 3.4 0.4 15 23.6 27.5 12.4 2.9 0.4 14 13 30.0 25.4 10.8 2.4 0.2 13 16.5 29.6 22.5 8.5 1.3 12 5.0 20.2 28.1 18.2 4.7 11 0.5 7.2 21.7 24.8 10.9 10 1.5 10.9 23.6 17.7 9 2.3 14.3 21.0 8 0.4 6.1 19.1 7 1.4 12.8 6 0.3 7.5 5 3.2 4 1.3 3 0.3 [/color][/code] Note that the median ability vector is [16, 14, 13, 12, 11, 9]. Also note that the median overall ability is 12.5. Now it's time for the over-analyzing. I started by arbitrarily setting the standard point buy at 30 points. This is a nice round figure that is divisible by the number of abilities. I also set the cost for the lowest probability in each column to 1. This leads to some oddness, but I think it works out. Next I stipulated that you should be able to buy the median ability vector with the standard point buy. Third, I stipulated that you should be able to buy six of the median ability with the standard point buy. Given that the median is 12.5, I set the cost of three 13's and three 12's to 30 (for this I dropped the minimum on the highest roll to 13). Finally, it seemed reasonable to make cost differentials at least one and non-decreasing (that is, the difference in cost between two abilities will be at least that of the next two lowest abilities). That gave me the lower parts of the table below. I finished it off using an increasing cost scheme similar to WotC's point buy. You use the first column to buy your highest ability, the second column to buy your second highest ability, and so on. [code][color=white] 1st 2nd 3rd 4th 5th 6th 18 10 16 n/a n/a n/a n/a 17 7 13 16 n/a n/a n/a 16 5 10 13 15 n/a n/a 15 3 7 10 12 15 n/a 14 2 5 7 9 12 14 13 1 3 5 7 9 11 12 0 2 3 5 7 9 11 n/a 1 2 4 5 7 10 n/a 0 1 3 4 6 9 n/a n/a 0 2 3 5 8 n/a n/a n/a 1 2 4 7 n/a n/a n/a 0 1 3 6 n/a n/a n/a n/a 0 2 5 n/a n/a n/a n/a n/a 1 4 n/a n/a n/a n/a n/a 0 3 n/a n/a n/a n/a n/a n/a [/color][/code] Now, as I said there is some oddness. Because I wanted the flat median available, it's possible to get things with 30 points that you can't with a standard roll. I'm not too worried about that, since a player can?t really screw themselves that way. To keep the costs differing by at least one, I had to remove the ability to buy a 3 for your lowest ability. I'm not too worried about that, because if you really want a 3 that badly, it?s easier to indulge your need for angst by rolling one of those twenty siders numbered 1-10 instead of a d20 for checks. Besides, in the end I knew it wouldn't match perfectly, and if you?re willing to use a six-column table for ability generation, you should be able to deal with a little oddness (more on that later). To emphasize some things I like about this point buy, let's look at high stats. If you want an 18, you can still get 14, 12, 10, 10, 9. If you want two 16's, you can still get 12, 10, 10, 9. So you can take a slight hit to get a couple decent stats. If you want three decent stats, you'll need to take a bigger hit. Now some may say I?m just a power gamer whining for bigger scores, but I think this better represents a character made with standard rolls. 1 in 8 characters is going to have two 16's or better with standard rolling. If you want different power levels, I suggest the following: low-powered = 15 (about equivalent to WotC's low-powered), challenging = 22, tougher = 40 (allows median vector +1), and high powered = 55 (median vector +2). As noted before, this does require using a six-column table to generate abilities. However, my intention was always to look at the table generated, and try to work from there to a simpler system (no, really, honest!). To that end, I present two steps down from the above system. I don't think you lose much stepping down, but I haven't analyzed it [b]that[/b] much. In the next table, there are three columns. Any player can use the "Avg" column all they want. Each time they make use of the "Good" column, they must make use of the "Bad" column. If you wanted, you could even limit it to two uses of the "Good" column. [code][color=white] Good Avg Bad 18 13 n/a n/a 17 10 17 n/a 16 7 14 n/a 15 5 11 16 14 3 8 13 13 2 6 10 12 1 4 8 11 0 3 6 10 n/a 2 5 9 n/a 1 4 8 n/a 0 3 7 n/a n/a 2 6 n/a n/a 1 5 n/a n/a 0 4 n/a n/a n/a 3 n/a n/a n/a [/color][/code] Again, the median vector and the flat median value can be bought for 30 points. Getting a couple good stats is close in difficulty to the six-column system. If this is not simple enough for you, pick any one of the collumns in the six-column table (except the first). The cost of 5 gets you the appropriate ability from the median vector. Moving the ability up or down one moves the cost up or down one. In other words, you start with 16, 14, 13, 12, 11, 9. For each ability, you pay the cost below to modify it (use one and only one column, maximum 18): [code][color=white] A B C +5 n/a n/a 14 +4 16 15 11 +3 13 12 9 +2 10 9 7 +1 7 7 6 +0 5 5 5 -1 3 4 4 -2 2 3 3 -3 1 2 2 -4 0 1 1 -5 n/a 0 0 [/color][/code] I haven't analyzed these yet, but my guess is that column A will be slightly worse than the standard roll, column B will be slightly better, and column C will be enough better that I wouldn't recommed using it. So, do any of the two or three people who bothered to read this whole thing have any comments, criticisms, or shiny glass beads I can use to impress my fellow villagers? [/QUOTE]

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