Expertise
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The Mathematics of Expertise
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Tom is a proficient user, Kira is an expert user.
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Primary Skill: High ability modifier. We arbitrary choose a progression of 3,4,5,5,5
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Tertiary Skill: Low ability modifier. We arbitrary choose a progression of 1,2,2,2,2
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Proficiency:2Odds of Tom beating Kira48%
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Odds of Tom's successOdds of Kira's successRelative increase of Kira over TomOdds of Tom beating Kira, conditioned by Tom's successThe weighs I chose are supposed to reflect how often certain DCs are set by the DMs. They are also somewhat inspired by the evolutions of DCs in the MM. Of course, those choices are necessiraly arbitrary, lacking the necessary data to not make it so.
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Weight
DC/Mod
-1012345-1012345-1012345-1012345
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1.001055%60%65%70%75%80%85%65%70%75%80%85%90%95%18%17%15%14%13%13%12%68%65%62%59%56%53%50%
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2.001150%55%60%65%70%75%80%60%65%70%75%80%85%90%20%18%17%15%14%13%13%72%68%65%62%59%56%53%
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3.001245%50%55%60%65%70%75%55%60%65%70%75%80%85%22%20%18%17%15%14%13%75%72%68%65%62%59%56%
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5.001340%45%50%55%60%65%70%50%55%60%65%70%75%80%25%22%20%18%17%15%14%79%75%72%68%65%62%59%
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3.001435%40%45%50%55%60%65%45%50%55%60%65%70%75%29%25%22%20%18%17%15%83%79%75%72%68%65%62%
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2.001530%35%40%45%50%55%60%40%45%50%55%60%65%70%33%29%25%22%20%18%17%88%83%79%75%72%68%65%
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1.001625%30%35%40%45%50%55%35%40%45%50%55%60%65%40%33%29%25%22%20%18%93%88%83%79%75%72%68%
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0.501720%25%30%35%40%45%50%30%35%40%45%50%55%60%50%40%33%29%25%22%20%100%93%88%83%79%75%72%
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0.501815%20%25%30%35%40%45%25%30%35%40%45%50%55%67%50%40%33%29%25%22%100%100%93%88%83%79%75%
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0.251910%15%20%25%30%35%40%20%25%30%35%40%45%50%100%67%50%40%33%29%25%100%100%100%93%88%83%79%
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0.25205%10%15%20%25%30%35%15%20%25%30%35%40%45%200%100%67%50%40%33%29%100%100%100%100%93%88%83%
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0.00210%5%10%15%20%25%30%10%15%20%25%30%35%40%200%100%67%50%40%33%0%100%100%100%100%93%88%
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0.00220%0%5%10%15%20%25%5%10%15%20%25%30%35%200%100%67%50%40%0%0%100%100%100%100%93%
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0.00230%0%0%5%10%15%20%0%5%10%15%20%25%30%N/A200%100%67%50%0%0%0%100%100%100%100%
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0.00240%0%0%0%5%10%15%0%0%5%10%15%20%25%N/AN/A200%100%67%0%0%0%0%100%100%100%
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0.00250%0%0%0%0%5%10%0%0%0%5%10%15%20%N/AN/AN/A200%100%0%0%0%0%0%100%100%
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0.00260%0%0%0%0%0%5%0%0%0%0%5%10%15%N/AN/AN/AN/A200%0%0%0%0%0%0%100%
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0.00270%0%0%0%0%0%0%0%0%0%0%0%5%10%N/AN/AN/AN/AN/A0%0%0%0%0%0%0%
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0.00280%0%0%0%0%0%0%0%0%0%0%0%0%5%N/AN/AN/AN/AN/AN/A0%0%0%0%0%0%0%
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0.00290%0%0%0%0%0%0%0%0%0%0%0%0%0%N/AN/AN/AN/AN/AN/AN/A0%0%0%0%0%0%0%
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0.00300%0%0%0%0%0%0%0%0%0%0%0%0%0%N/AN/AN/AN/AN/AN/AN/A0%0%0%0%0%0%0%
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Averages:10%10%10%10%10%10%10%31%26%22%20%18%16%15%25%10101010101010
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50%10101010101010
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75%10101010101010
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Proficiency:3Odds of Tom beating Kira43%
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Odds of Tom's successOdds of Exp. SuccessRelative increase of Kira over TomOdds of Tom beating Kira, conditioned by Tom's success
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Weight
DC/Mod
-1012345-1012345-1012345-1012345
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0.501060%65%70%75%80%85%90%75%80%85%90%95%100%100%25%23%21%20%19%18%11%60%57%54%51%48%45%43%0.0000.33333333330
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1.001155%60%65%70%75%80%85%70%75%80%85%90%95%100%27%25%23%21%20%19%18%63%60%57%54%51%48%45%0.0000.42857142860
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1.001250%55%60%65%70%75%80%65%70%75%80%85%90%95%30%27%25%23%21%20%19%66%63%60%57%54%51%48%0.0000.46153846150
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2.001345%50%55%60%65%70%75%60%65%70%75%80%85%90%33%30%27%25%23%21%20%69%66%63%60%57%54%51%0.10100.520
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3.001440%45%50%55%60%65%70%55%60%65%70%75%80%85%38%33%30%27%25%23%21%73%69%66%63%60%57%54%0.2540.54545454557.333333333
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5.001535%40%45%50%55%60%65%50%55%60%65%70%75%80%43%38%33%30%27%25%23%77%73%69%66%63%60%57%0.5020.63.333333333
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3.001630%35%40%45%50%55%60%45%50%55%60%65%70%75%50%43%38%33%30%27%25%82%77%73%69%66%63%60%1.0010.66666666671.5
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2.001725%30%35%40%45%50%55%40%45%50%55%60%65%70%60%50%43%38%33%30%27%87%82%77%73%69%66%63%1.0010.751.333333333
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1.001820%25%30%35%40%45%50%35%40%45%50%55%60%65%75%60%50%43%38%33%30%94%87%82%77%73%69%66%2.000.50.85714285710.5833333333
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0.501915%20%25%30%35%40%45%30%35%40%45%50%55%60%100%75%60%50%43%38%33%100%94%87%82%77%73%69%3.000.333333333310.3333333333
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0.502010%15%20%25%30%35%40%25%30%35%40%45%50%55%150%100%75%60%50%43%38%100%100%94%87%82%77%73%5.000.21.20.1666666667
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0.25215%10%15%20%25%30%35%20%25%30%35%40%45%50%300%150%100%75%60%50%43%100%100%100%94%87%82%77%3.000.33333333331.50.2222222222
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0.00220%5%10%15%20%25%30%15%20%25%30%35%40%45%300%150%100%75%60%50%0%100%100%100%94%87%82%2.000.520.25
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0.00230%0%5%10%15%20%25%10%15%20%25%30%35%40%300%150%100%75%60%0%0%100%100%100%94%87%1.00130.3333333333
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0.00240%0%0%5%10%15%20%5%10%15%20%25%30%35%300%150%100%75%0%0%0%100%100%100%94%1.00160.1666666667
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0.00250%0%0%0%5%10%15%0%5%10%15%20%25%30%N/A300%150%100%0%0%0%0%100%100%100%1.0010
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0.00260%0%0%0%0%5%10%0%0%5%10%15%20%25%N/AN/A300%150%0%0%0%0%0%100%100%0.5020
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0.00270%0%0%0%0%0%5%0%0%0%5%10%15%20%N/AN/AN/A300%0%0%0%0%0%0%100%0.5020
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0.00280%0%0%0%0%0%0%0%0%0%0%5%10%15%N/AN/AN/AN/A0%0%0%0%0%0%0%0.2540
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0.00290%0%0%0%0%0%0%0%0%0%0%0%5%10%N/AN/AN/AN/AN/A0%0%0%0%0%0%0%0.2540
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0.00300%0%0%0%0%0%0%0%0%0%0%0%0%5%N/AN/AN/AN/AN/AN/A0%0%0%0%0%0%0%0.2540
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Averages:15%15%15%15%15%15%15%51%42%36%32%29%26%24%25%10101010101010109%
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50%10101010111213
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75%10101010111213
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Proficiency:4Odds of Tom beating Kira38%
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Odds of Tom's successOdds of Exp. SuccessRelative increase of Kira over TomOdds of Tom beating Kira, conditioned by Tom's success
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Weight
DC/Mod
-1012345-1012345-1012345-1012345
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0.101065%70%75%80%85%90%95%85%90%95%100%100%100%100%31%29%27%25%18%11%5%51%48%45%43%40%38%36%
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0.251160%65%70%75%80%85%90%80%85%90%95%100%100%100%33%31%29%27%25%18%11%54%51%48%45%43%40%38%
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0.501255%60%65%70%75%80%85%75%80%85%90%95%100%100%36%33%31%29%27%25%18%57%54%51%48%45%43%40%
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1.001350%55%60%65%70%75%80%70%75%80%85%90%95%100%40%36%33%31%29%27%25%61%57%54%51%48%45%43%
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1.001445%50%55%60%65%70%75%65%70%75%80%85%90%95%44%40%36%33%31%29%27%64%61%57%54%51%48%45%
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2.001540%45%50%55%60%65%70%60%65%70%75%80%85%90%50%44%40%36%33%31%29%68%64%61%57%54%51%48%
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3.001635%40%45%50%55%60%65%55%60%65%70%75%80%85%57%50%44%40%36%33%31%71%68%64%61%57%54%51%
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5.001730%35%40%45%50%55%60%50%55%60%65%70%75%80%67%57%50%44%40%36%33%76%71%68%64%61%57%54%
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3.001825%30%35%40%45%50%55%45%50%55%60%65%70%75%80%67%57%50%44%40%36%81%76%71%68%64%61%57%
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2.001920%25%30%35%40%45%50%40%45%50%55%60%65%70%100%80%67%57%50%44%40%88%81%76%71%68%64%61%
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1.002015%20%25%30%35%40%45%35%40%45%50%55%60%65%133%100%80%67%57%50%44%97%88%81%76%71%68%64%
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0.502110%15%20%25%30%35%40%30%35%40%45%50%55%60%200%133%100%80%67%57%50%100%97%88%81%76%71%68%
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0.25225%10%15%20%25%30%35%25%30%35%40%45%50%55%400%200%133%100%80%67%57%100%100%97%88%81%76%71%
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0.00230%5%10%15%20%25%30%20%25%30%35%40%45%50%400%200%133%100%80%67%0%100%100%97%88%81%76%
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0.00240%0%5%10%15%20%25%15%20%25%30%35%40%45%400%200%133%100%80%0%0%100%100%97%88%81%
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0.00250%0%0%5%10%15%20%10%15%20%25%30%35%40%400%200%133%100%0%0%0%100%100%97%88%
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0.00260%0%0%0%5%10%15%5%10%15%20%25%30%35%400%200%133%0%0%0%0%100%100%97%
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0.00270%0%0%0%0%5%10%0%5%10%15%20%25%30%N/A400%200%0%0%0%0%0%100%100%
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0.00280%0%0%0%0%0%5%0%0%5%10%15%20%25%N/AN/A400%0%0%0%0%0%0%100%
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0.00290%0%0%0%0%0%0%0%0%0%5%10%15%20%N/AN/AN/A0%0%0%0%0%0%0%
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0.00300%0%0%0%0%0%0%0%0%0%0%5%10%15%N/AN/AN/AN/A0%0%0%0%0%0%0%
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Averages:20%20%20%20%20%20%20%76%61%52%46%41%37%33%25%10101010101010
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50%10111213141516
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