In Perennial ryegrass breeding, F2's derived from parental crosses are sown in plots and phenotypes and genotypes are obtained as single measurements for the whole F2 family pool. For genotypes this means that quantitative assays must be used to obtain allele frequencies. For this purpose a sequencing approach to obtain Single Nucleotide Polymorphisms (SNPs) frequencies is considered here. In this work we develop the theoretical framework to perform association studies using allele frequencies from such F2 family pools. We show that expected allele frequencies in the F2 families will have distinct values of 0, 1/4, 1/2, 3/4, and 1, and that a regression of phenotypes on these frequencies will estimate twice the allele substitution effect at the SNP. We further derive that the efficiency of this association mapping is half that of an approach where genotypes would be available on single individuals. This effect is caused by extreme families (homozygote x homozygote) being less frequent than extreme (homozygote) individuals. We finally consider the effects of using sequencing to obtain allele frequencies, which will cause inaccuracy in the frequency estimate due to obtaining a limited number of sequencing reads. We evaluated that with a fixed sequencing capacity it is advantageous to use low coverage and maximize the number of samples, because the value of additional samples is larger than that of additional coverage.