The choice of allele-sharing statistics can have a great impact on the power of robust affected relative methods. Similarly, when allele-sharing statistics from several pedigrees are combined, the weight applied to each pedigree's statistic can affect power. Here we describe the direct connection between the affected relative methods and traditional parametric linkage analysis, and we use this connection to give explicit formulae for the optimal sharing statistics and weights, applicable to all pedigree types. One surprising consequence is that under any single gene model, the value of the optimal allele-sharing statistic does not depend on whether observed sharing is between more closely or more distantly related affected relatives. This result also holds for any multigene model with loci unlinked, additivity between loci, and all loci having small effect. For specific classes of two-allele models, we give the most powerful statistics and optimal weights for arbitrary pedigrees. When the effect size is small, these also extend to multigene models with additivity between loci. We propose a useful new statistic, S(rob dom), which performs well for dominant and additive models with varying phenocopy rates and varying predisposing allele frequency. We find that the statistic S(_#alleles), performs well for recessive models with varying phenocopy rates and varying redisposing allele frequency. We also find that for models with large deviation from null sharing, the correspondence between allele-sharing statistics and the models for which they are optimal may also depend on which method is used to test for linkage.