Rank Analysis of Incomplete Block Designs

Understanding baseball team standings and streaks

“…Our starting point to account for the win/loss records of all baseball teams is the BT model [12,13] that incorporates the heterogeneity in team strengths in a natural and simple manner. We assume that each team has an intrinsic strength x i that is fixed for each season.…”

“…One of our goals is to understand the rank dependence of this win fraction. An important outcome of our study is that the Bradley-Terry (BT) competition model [12,13] provides an excellent account of the team win/loss records. This agreement between the data and theory is predicated on using a specific form for the distribution of team strengths.…”

Monte Carlo Analysis of Incomplete Paired-Comparison Experiments

“…There are some alternative models with a similar function to Thurstone's model such as the Gaussian model 8 , the logistic Bradley-Terry model [9][10][11][12][13] , Angular However, when the complete matrix of comparisons is carried out the work required becomes prohibitive for large numbers n of stimuli [18][19] . Thus, the investigator most likely conducts an incomplete pairedcomparison experiment with a high number of stimuli 20 .…”

“…We note, however, that use of blocks to separate the stimuli into two of more groups is an alternative method of effectively reducing the number of paired comparisons when the number of samples is large. 12 Durbin, for example, suggested using balanced incomplete block (BIB) designs for incomplete paired comparisons 22 . The block sizes were suggested to be more than two 12 .…”

“…12 Durbin, for example, suggested using balanced incomplete block (BIB) designs for incomplete paired comparisons 22 . The block sizes were suggested to be more than two 12 . Within each block the rank orders of objects are obtained [23][24][25][26][27][28][29] .…”