Index
aggregated list, 211
Ali, I., et al., 225
Amoako-Adu, B., et al, 225
Analytic Hierarchy Process (AHP), 223
anchor text, 163
Anderson, Jeff, 17
Anderson, L.B., 225
Annis, David H., et al., 225
antitrust and BCS, 19
AOL data, 221
aperiodic, 73
archaeological dig, 192
arithmetic mean, 220
Arrow’s Impossibility Theorem, 4, 160–163, 231
Ashburn, James R., 53
Ask.com, 92
Atlantic Coast Conference, 19
attendance, college football, 8
Avatar, 28
average dominance, 223
back button, 74
Ball, Barbara, xv
Basabe, Ibai, xv
basketball, 143
Bassett, Gilbert W., 225
BCS, 6, 9, 21, 136, 162, 204, 211
BCS rankings, 17
beating the spread, 115
BelKor, 134
Berman, Chris, 19
Bethany, v
betting
methods, 113
over/under, 115
by spread, 114
Big East Conference, 19
Big 12 Conference, 19
Billingsley, Richard, 17
binary integer linear program, 185
Bing, number of Web pages, 182
bipartite graph, 202
black hole, 202
Borda, Jean-Charles de, 3
Borda count, BCS, 17
Bowl Championship Series, 6, 9, 231
brackets, number of, 154
Bradley, R. A. and Terry, M. E., 225
Bradley–Terry model, 18
Brin, Sergey, 51
Brown, Dr. Emmett, 48
bubble sort, 204
Bhlmann, Hans and Huber, Peter J., 226
Callaghan, Thomas, et al., 226
Caritat, Marie Jean Antoine Nicolas, 3
Carnegie classification, 78
Cassady, C. R., et al., 226
casualties, college football, 112
Cauchy–Schwarz (or CBS) inequality, 119
centroid method, 231
centroid ratings, 120
centroid ratings and Markov chains, 132
Chartier, Timothy, xv
Chebotarev P.Y., and Shamis, E., 226
chess ratings, highest ever, 66
Cholesky decomposition, 23
cityplot, 100
Cleveland vs. NY Giants, 156
Coaches football poll, 17
cocktails, highest rated, 230
college football, attendance, 8
college football, casualties, 112
College Rankings, 6
Colley and LRMC, 224
Colley method, 21–27, 162, 231
algorithm, 24
connection to Massey method, 24
linear system, 22
main idea, 21
notation for, 24
properties of, 24
for ranking movies, 25
rank-one update, 155
running example, 23
sensitivity, 155
strength of schedule, 22
summary of, 24
weighting by time, 150
Colleyized Massey method, 25, 231
Colvery, Paul M., 53
comparison ratings
direct, 129
optimal, 129
computer-generated list, 181
concordant pair, 232
Condorcet winner, 160, 166, 232
conformity, 183
Conner, G. R., and Grant, C. P., 226
conservation property, 24
constraints in Keener’s method, 35
convex combination, 73
Cook, W., et al., 226
correlation coefficient, 47
Department of Justice, 19
deviation between two ranked lists, 201
diagonals in a matrix, 88
differential matrices
Differential methods
weighting by time, 151
direct comparison ratings, 129
discordant pair, 232
distance measure, 201
doubly stochastic matrix, 88
Douglas, Emmie, xv
Dovidio, Nick, 153
drinks, highest rated, 230
Eastwood, Clint, 222
Eaton, Morris L., 226
eBay, 135
Eduardo Saverin, 64
Elo method, 232
ties, 139
Elo’s system
for the NFL, 57
K factor, 55
rating formulas, 54
the idea, 53
weighting by time, 150
Emmert, Mark, 19
Ensemble team, 134
ESPN, 151
ESPN Tournament Challenge, 213
Eugene Onegin, 67
evolutionary algorithm, 110
Q-bert matrix, 101
evolutionary approach, 194
evolutionary optimization, 104, 232
Facebook, 64
Facemash, 64
Fahrmeir, L. and Tutz, G., 226
Farmer, Christopher J., 226
FBI, 216
FIDE, 53
Fiesta Bowl, 19
final four, lowest seeded winner, 200
Fischer, Bobby, 66
Fluek, John A. and Korsh, James F., 226
Ford, L. R., Jr., 226
Frobenius, Georg, 51
full ranked list, 166, 204, 232
fundamental form, 108
fundamental rank-differential matrix, 98
Gauss–Markov theorem, 47
Gaussian elimination, 23
geometric mean, 220
George Mason, 151
Georgetown, 200
girls, rating and ranking, 64
Glickman, Mark E., 226
Goddard, S., 226
Goodson, Neil, xiv, xvi, 151, 213
Google, 51
Google, number of Web pages, 182
Google, revenue, 52
Google bombs, 163
Gore, Al, 160
Govan, Anjela, 67, 92, 94, 219
and OD ratings, 94
Grafton, Clive, 226
graph isomorphism, 107
graph theory method of aggregation, 172
Grays Sports Almanac, 48
Gupta, Shanti S. and Sobel, Milton, 227
Harris college football poll, 17
Harvard’s hot girls, 64
Harville, David, 227
HDI, 6
Hepburn, Katharine, 222
Hessian matrix, 119
Hester, Chris, 17
highest grossing movies, 28
hindsight win accuracy, 123
and OD ratings, 92
hockey, 141
home-field advantage, 121
hot girls, ratings and rankings, 64
Houston Rockets, 46
Huang, Huang, Weng, and Lin, 227
Huber, Peter J., 227
Human Development Index, 6
human-generated list, 181
identity property, 201
IMDb, 6
independence of irrelevant alternatives, 4, 160, 170, 232
Ingram, Luke, xiv, 67, 83, 149, 151, 165
irreducibility
forcing it, 39
irreducibility in Keener’s method, 35
irreducible Markov chain, 73
James, Bill, 45
Jech, Thomas, 227
Justice Department, 19
Karlin, Samuel, 227
Kasparov, Gary, 66
constraints, 35
irreducibility, 35
keystone equation, 34
least squares, 47
nonnegativity, 35
normalization, 32
point spreads, 49
primitivity, 36
strength
absolute, 33
relative, 33
ties, 139
traveling fan, 50
weighting by time, 150
Kendall, Maurice, 51, 201, 203
Kendall tau, 203
formula for, 206
full lists, 204
measure, 233
partial lists, 205
keystone equation, Keener’s method, 34
Kleinberg, Jon, 92
Knopp, Paul, 89
Knorr-Held, L., 227
Krylov methods, 23
Kvam, Paul, 224
Laplace’s rule of succession, 22, 30
Leake, R. J., 227
leaves in the river, 51
Lebovic J. H. and Sigelman L., 227
Line Makers, 96
linear program, 186
link farms, 163
Llull, Ramon, 166
Llull count, 166
Llull winners, 166
local Kemenization, 175
logistic function, 54
Logistic parameter, 56
Louisville, 200
LRMC, 224
connection to Colley, 224
connection to Markov, 224
connection to Massey, 224
LSU, 200
March Madness, xiv, 181, 197, 202
March Madness, number of brackets, 154
Markov, A. A., 67
Markov chains and centroid ratings, 132
Markov chains and LRMC, 224
Markov chains and preference ratings, 130
Markov method, 67–78, 107, 233
algorithm, 75
connection to Massey, 76
fair weather fan, 68
main idea, 67
notation for, 75
properties of, 75
running example, 67
summary of, 74
ties, 138
voting
with losses, 68
with other statistics, 71
with point differentials, 69, 76
with points, 70
weighting by time, 150
yardage, 71
Markov voting matrix, 99
Martinich, Joseph, 227
Massey
NFL 2001–2010 ratings, 122
Massey and LRMC, 224
Massey matrix M
properties of, 10
advanced features of, 11
algorithm, 14
linear system, 10
main idea, 9
notation for, 13
point spreads, 12
properties of, 14
for ranking movies, 25
for ranking webpages, 14
summary of, 13
ties, 137
weighting by time, 149
Massey website, 9
Masseyized Colley method, 25
McFarland, William N, 228
McFly, Marty, 48
McNeil, Charles K., 114
mean absolute deviation, 45
Mease, David, 228
Menke, J. and Martinez, T., 228
meta-list, 171
meta-search engine, 159, 163, 173
methods of comparison
yardsticks for success, 211–215
Meyer, Bethany B., v
Miller, John J., 112
miserable failure, 164
Moran, Patrick, xv
Morey, Daryl, 46
Morris, Ryan K., xvi
MovieLens, 141
movies, highest grossing, 28
multiple optimal solutions, 187
Mundfrom D. J., et al., 228
mutually reinforcing rating system, 93
Nader, Ralph, 160
national championship game, BCS, 18
National Science and Technology Medals Foundation, xvi
National Science Foundation, 179
NCAA brackets, number of, 154
NCAA mens basketball, lowest seeded winner, 200
NCAA mens basketball, total wagers, 216
Netflix, 6, 25, 95, 135, 140, 220, 221
Netflix prize, 134
Newman, M. E. J., 224
NFL, 143
NFL 2009–2010
Elo ratings, 58
game-by-game analysis, 62
hindsight and foresight, 62
variable K factors, 60
hindsight win accuracy, 123
home-field advantage, 121
Massey ratings, 122
OD ratings, 84
Pythagorean theorem, 45
Sagarin ratings, 122
scoring data, 42
spread (or centroid) ratings, 120
spread errors, 123
Vegas line comparisons, 123
NFL spread, largest ever, 126
NFL ties, most, 146
NHL, 141
NHL ties, most and fewest, 146
non-dictatorship, 4, 160, 163, 171, 233
nonnegativity in Keener’s method, 35
normalization, Keener’s method, 32
Notre Dame rule, 18
NPR, 152
number line representation, 11, 202
Obama, Barack, 19
running example, 82
ties, 138
weighting by time, 151
OD ratings
aggregation, 82
alternating refinement, 81
convergence theorem, 90
definition, 80
forcing convergence, 91
and HITS, 92
mathematical analysis, 87
NFL 2009–2010, 84
scoring vs. yardage, 83
Okoniewski, Michael, xvi
optimization over a permutation space, 99
Orange Bowl, 19
Oscars, most won, 222
outliers, 211
overtime, 142
Page, Larry, 51
PageRank, 6, 14, 51, 67, 68, 77, 172, 233
pair-wise comparisons, 124, 135, 220
Pareto principle, 4, 160, 162, 171, 233
Park, J. and Newman, M. E. J., 228
Park, Juyong, 224
Park-Newman method, 224
Pedings, Kathryn, xiv, xvi, 104, 110, 153, 214
Perron, Oscar, 51
Perron
value, 36
vector, 36
Perron–Frobenius
connection with PageRank, 51
theorem, 36
perturbation analysis, 139, 155
point spread, 233
point spread, largest NFL, 126
beating the spread, 115
to build ratings, 117
definition, 113
Keener’s method, 49
in the NFL, 117
odds, 114
over/under betting, 115
spread betting, 114
spread ratings, 120
vig (or juice), 114
possession, 219
power method, 38
predictive scoring, 142
preference graph, 130
preference ratings, 127
primitivity
forcing it, 39
in Keener’s method, 36
privacy, 221
Pushkin, A. S., 67
Pythagorean theorem
baseball, 45
football, 45
optimal exponent, 46
Q-bert matrix, 101
qualitative deviation between two ranked lists, 201
quantitative deviation between two ranked lists Kendall tau, 203
formula for, 206
partial lists, 205
Spearman footrule, 206
unweighted formula for full lists, 206
weighted formula for full lists, 206
weighted formula for partial lists, 207–211
random surfer, 77
random walk, 69
rank aggregation, 136, 159–182, 201, 233
definition, 159
method
simulated game data, 167
methods, 163–176
average rank, 166
Borda count, 165
graph theory, 172
simulated game data, 170
multiple optimal solutions, 187
OD, 159
by optimization, 183–199
notation for, 193
properties of, 193
summary of, 193
refinement, 175
summary of, 181
rank-differential matrix, 98
rank-differential method, 98–107
advanced model, 105
algorithm, 106
notation for, 106
optimization, 101
running example, 99
summary of, 106
ranked list, 233
ranking, definition, 5
ranking girls, 64
ranking U.S. colleges, 77
rating aggregation, 176–182
summary of, 181
rating, definition, 5
rating girls, 64
rating list, 234
rating systems
aggregated, 176
centroid, 120
Colley, 21
derived from spreads, 120
direct comparison, 129
Elo, 53
HITS, 92
Keener, 29
Massey, 9
offense-defense (OD), 79
user preference, 127
weighted, 147
rating-aggregation method, 211
rating-differential matrix, 107, 118
rating-differential method, 107–112, 194
algorithm, 111
fundamental form, 108
hillside form, 108
notation for, 111
optimization, 110
properties of, 111
running example, 109
summary of, 111
reciprocal pairwise comparison matrix, 223
Redmond, Charles, 223
Redmond method, 223
refinement after rank aggregation, 175
Reid, M. B., 228
retrodictive scoring, 142, 234
Rodgers, Clare, xv
Roosevelt, Theodore, 112
Rose Bowl, 19
rule of succession, 30
Runyan, Bob, 53
Saaty, T. L., 51
Saaty, Thomas, 223
NFL 2001–2010 ratings, 122
SALSA, 172
Saverin, Eduardo, 64
scalability, 16
score-differential matrix, 118
scraping data, 218
seed, lowest final four, 200
seed, lowest to win, 200
sensitivity, 155–158
Cleveland vs. NY Giants, 156
Sex on the Beach #2, 230
SIAM, 77
simulated game data, 167
properties of, 170
Singh, J. and Thompson W. A. Jr., 228
Sinkhorn, Richard, 89
Sinkhorn–Knopp theorem, 89
Sinuany-Stern, Z, 228
skew-symmetric, 220
skewing function, 31
smart ranking method, 214, 234
Smith, M. H., 227
Smith, Warren D., 228
soccer, 142
Social Network, the movie, 64
Sokol, Joel, 224
Southeastern Conference, 19, 20
Spearman footrule, 206
unweighted formula for full lists, 206
weighted formula for full lists, 206
weighted formula for partial lists, 207
Spearman, Charles, 201
sports wagers, 96
spread errors for NFL, 123
spread ratings, 117
based on win-loss, 124
and home-field advantage, 121
for NFL 2001–2010, 120
from point spreads, 120
total absolute error, 121
spread, largest NFL, 126
Srivastava, M.S. and Ogilvie, J., 228
star rated products, 128
Stefani, Raymond T., 228
Stephenson, Colin, xiv, xvi, 151, 213
Stern, Hal., et al., 228
stochastic matrix, 88
Stone, Daniel F., 229
strength
absolute in Keener’s method, 33
relative in Keener’s method, 33
strength of schedule, 22
Sugar Bowl, 19
super game, 220
symmetric reordering, 98
symmetry property, 201
Tannen, Biff, 48
teleportation matrix, 73
Thomas, I.B., 229
Thompson, Mark., 229
tie-breaking, 167
ties, 26, 135–145, 166, 205, 220
ties, most in NFL and NHL, 146
time weighting, 147–153
Titanic, 28
Tong, Y. L., 229
total absolute-spread error, 121
traveling fan, 50
traveling salesman problem, 104
triangle inequality, 201
Trono, John A., 229
Tsukuba University, 110
United Nations, 6
United States Chess Federation (USCF), 53
unrestricted domain, 4, 160, 234
upsets, biggest ever, 158
U.S. Department of Justice, 19
US News, 77
US News College Rankings, 6
USCF, 53
Varney, Christine, 19
Vegas lines, NFL 2009–2010, 123
vig, 234
Vigna, Sebastiano, 52
Villanova, 200
voting, 67
wagers on sports, 96
wagers, NCAA mens basketball, 216
Web pages, Google, Yahoo, Bing, 182
webpage traffic, 14
Wei, T. H., 51
weighted adjacency matrix, 16
weighted least squares, 150
weighted normal equations, 150
weighting away wins, 147
weighting by time, 147–153
Colley method, 150
Differential methods, 151
Elo’s system, 150
exponential, 148
Keener’s method, 150
linear, 148
logarithmic, 148
Markov method, 150
Massey method, 149
OD method, 151
step function, 148
weighting rivalry wins, 147
Weis, Charlie, 19
Wessell, Charles D., xv
West, B. T. and Lamsal, M., 229
what if . . . , 155–158
White Russian, 230
whydomath?, 77
wiggle room, none for BCS, 18
Wikipedia, 93
Wilkins, R., 229
Wilson, David, 225
Wilson, R. L, 229
win-loss spread ratings, 124
Winston, Wayne, 45
Wolfe, Peter, 17
World Chess Federation (FIDE), 53
wrestling, 162
Yahoo, 93
Yahoo, number of Web pages, 182
Yamamoto, Yoshitsugu, xvi, 153, 183
yardage, 71
yardsticks for success, 211–215
Zermelo, E., 226
Zuber, R. A., et al., 229
Zuckerberg, Mark, 64