1996 Low-Key Hillclimbs: Regression


The Results

Key

week    :  week number
rider   :  rider number
#       :  approximate degrees of freedom contributing to the data.
           These are non-integral because degrees of freedom for riders
           are reduced for the degrees of freedom lost in determining
           the weekly normalizations.  The degrees of freedom for weeks
           are reduced for the degrees of freedom lost in determining
           the rider scores.  The calculation is iterative.
rating  :  for riders, the natural log of the rider's expected ratio
           to the average speed.
           for weeks, the natural log of the time in seconds for the
           average rider.
           Thus, the predicted time for a given rider in a given week
           is exp(rating_rider + rating_week) seconds.
sigma   :  the standard error associated with a rating

Weeks

week #       rating  sigma       climb
1    31.647  7.75363 0.0398593   Montebello
2    44.4949 7.98183 0.0356381   Page Mill Road
3    45.3847 8.3447  0.02699     Mt Diablo
4    54.5015 7.48581 0.0295556   Kings Mountain
5    53.6109 8.07969 0.0443287   West 84 & W OLH
6    39.1248 7.76355 0.0395436   Bohlman-On Orbit-Bohlman
7    42.7838 6.91905 0.0341594   Alpine & Juaquin
8    37.4537 7.93937 0.0296849   Hick's & Loma Almaden
9    44.1999 8.70311 0.0289379   Mt Hamilton Road
X    21.4496 7.32499 0.0810513   Old La Honda Road

These raw ranking can be converted into hill conversion factors, represented in the following matrix:

                           t o   w e e k
    
  -     1     2     3     4     5     6     7     8     9     X

f 1     1.000 1.256 1.806 0.765 1.385 1.010 0.434 1.204 2.584 0.651

r 2     0.796 1.000 1.437 0.609 1.103 0.804 0.345 0.958 2.057 0.518

o 3     0.554 0.696 1.000 0.424 0.767 0.559 0.240 0.667 1.431 0.361

m 4     1.307 1.642 2.361 1.000 1.811 1.320 0.567 1.574 3.378 0.851

  5     0.722 0.907 1.303 0.552 1.000 0.729 0.313 0.869 1.865 0.470

w 6     0.990 1.244 1.788 0.757 1.372 1.000 0.430 1.192 2.559 0.645

e 7     2.304 2.894 4.161 1.763 3.192 2.327 1.000 2.774 5.954 1.501

e 8     0.830 1.043 1.500 0.635 1.151 0.839 0.360 1.000 2.146 0.541

k 9     0.387 0.486 0.699 0.296 0.536 0.391 0.168 0.466 1.000 0.252

  X     1.535 1.929 2.772 1.174 2.127 1.550 0.666 1.849 3.967 1.000

Riders

rider #        rating      sigma
14    0.984074 -0.750676   0
123   0.988922 -0.745592   0
200   0.988244 -0.682599   0
218   0.988623 -0.611946   0
15    0.984074 -0.58744    0
217   0.988623 -0.500624   0
214   0.988623 -0.500422   0
195   0.987138 -0.471075   0
185   1.97777  -0.438934   0.0758477
137   0.988922 -0.412395   0
138   0.988922 -0.412395   0
228   0.976412 -0.409311   0
63    3.95232  -0.385065   0.129368
71    0.984074 -0.328921   0
142   1.97734  -0.320458   0.008018
126   0.988922 -0.28925    0
56    7.89887  -0.287188   0.06064
32    1.973    -0.256515   0.0124924
80    5.9359   -0.253942   0.0407013
182   1.97777  -0.235325   0.0414138
196   0.987138 -0.233994   0
191   0.987138 -0.223821   0
174   0.990784 -0.219989   0
192   0.987138 -0.21492    0
13    0.984074 -0.197291   0
40    0.984074 -0.184484   0
84    5.92819  -0.176916   0.0611196
129   0.988922 -0.176742   0
177   1.97887  -0.175985   0.0186729
81    5.92153  -0.171566   0.0368434
97    0.988699 -0.169285   0
49    0.984074 -0.166784   0
103   0.988699 -0.164935   0
64    8.89367  -0.160514   0.0227901
194   0.987138 -0.160508   0
76    0.984074 -0.160203   0
68    0.984074 -0.157632   0
210   0.988623 -0.15022    0
225   0.988623 -0.145189   0
10    1.97719  -0.140036   0.0261499
197   2.96194  -0.13865    0.0675284
173   0.990784 -0.138138   0
17    0.984074 -0.136445   0
58    8.88116  -0.131178   0.0576084
86    0.988699 -0.128836   0
73    0.984074 -0.121305   0
25    0.984074 -0.120542   0
119   0.988922 -0.113654   0
79    6.91998  -0.111508   0.0076885
136   0.988922 -0.111311   0
205   0.98656  -0.108179   0
59    9.87009  -0.105103   0.0484398
16    1.9747   -0.101795   0.0357074
207   0.98656  -0.0988288  0
66    0.984074 -0.0958113  0
85    8.88601  -0.0946885  0.0309075
202   1.97687  -0.0920767  0.00898471
21    1.97277  -0.0854065  0.0121905
55    4.92605  -0.0831742  0.0535985
100   6.91053  -0.0770808  0.046833
118   5.92045  -0.0750928  0.0567755
106   0.988699 -0.0737142  0
107   1.97948  -0.0730018  0.00277274
38    7.90505  -0.066382   0.027467
89    4.94766  -0.0631822  0.0254037
47    7.8906   -0.0588127  0.0321898
190   2.96194  -0.0565618  0.0506294
183   0.99063  -0.0556763  0
121   2.96262  -0.0552238  0.0257693
9     3.94996  -0.0531579  0.032044
75    1.9727   -0.0515168  0.0437369
208   0.98656  -0.0493581  0
213   0.988623 -0.0479608  0
159   2.96765  -0.0395697  0.0282118
48    5.92959  -0.0383228  0.0239397
19    0.984074 -0.0374093  0
67    0.984074 -0.0365795  0
155   0.990784 -0.0344097  0
39    2.96162  -0.0286113  0.016978
131   2.96817  -0.0212069  0.0211312
204   0.98656  -0.0210511  0
115   0.988922 -0.0179186  0
102   0.988699 -0.0177349  0
227   0.976412 -0.0158454  0
151   3.95828  -0.015802   0.0138969
152   3.95828  -0.015802   0.0138969
44    7.89483  -0.0138222  0.0537359
232   0.976412 -0.00997264 0
236   0.976412 -0.00997264 0
184   0.99063  -0.00472331 0
135   0.988922 -0.00447972 0
62    3.95248  -0.00440555 0.0229056
30    1.9747   -0.00364245 0.00829667
146   3.94439  0.00165159  0.0527561
95    1.97948  0.00463461  0.0176936
122   2.97034  0.00499541  0.0301333
220   0.988623 0.00653884  0
42    0.984074 0.0114638   0
221   0.988623 0.0161438   0
128   0.988922 0.0180848   0
171   1.97941  0.0202143   0.00312445
165   1.98141  0.0207741   0.00405197
92    6.90847  0.0224632   0.0442421
222   0.988623 0.0256709   0
105   3.95903  0.0265655   0.0343722
150   2.96966  0.0281093   0.0181596
203   0.988244 0.0313138   0
53    6.91829  0.0329005   0.022054
34    0.984074 0.0339267   0
167   0.990784 0.0342337   0
206   0.98656  0.0347489   0
23    8.89367  0.0390259   0.0385895
170   1.98141  0.0419923   0.00593128
109   5.93206  0.0430454   0.046531
124   0.988922 0.0496534   0
153   1.97903  0.0498533   0.00582125
12    6.91633  0.0517648   0.0282747
156   0.990784 0.0524534   0
164   2.96654  0.0544596   0.0524685
8     6.91681  0.0552699   0.0289824
178   0.99063  0.0627683   0
161   0.990784 0.063187    0
231   0.976412 0.0633302   0
27    2.96356  0.0666457   0.0154091
108   4.94766  0.068528    0.0174084
72    0.984074 0.0734504   0
41    0.984074 0.07577     0
188   0.987138 0.0778188   0
78    0.984074 0.0794927   0
215   1.97725  0.0812552   0.0640234
172   2.96855  0.0818263   0.0190334
61    2.96378  0.0819327   0.0325556
219   0.988623 0.0828293   0
125   1.97971  0.0829355   0.00297025
93    5.93019  0.0838583   0.0263485
179   2.96543  0.0861482   0.00623828
52    9.87009  0.0883234   0.0404602
134   0.988922 0.0890044   0
112   2.96624  0.0909975   0.0375779
180   1.96704  0.0911934   0.0280273
35    1.9747   0.0919104   0.00770484
24    8.89367  0.0956702   0.0271279
199   0.987138 0.0959546   0
114   5.93228  0.0977282   0.0270777
69    0.984074 0.098792    0
82    0.988699 0.100048    0
90    0.988699 0.102323    0
74    0.984074 0.102601    0
145   0.990784 0.102935    0
233   0.976412 0.104299    0
50    0.984074 0.108343    0
193   1.9737   0.111503    0.0159071
37    1.97277  0.111519    0.0173242
198   0.987138 0.113947    0
169   0.990784 0.114228    0
132   3.95642  0.115831    0.00444312
91    6.92304  0.116247    0.0281384
154   4.94336  0.118675    0.0245562
28    1.97486  0.120727    0.00270629
77    2.96169  0.121107    0.0224311
176   0.990784 0.1231      0
110   1.97948  0.127079    0.00388746
157   0.990784 0.13398     0
22    0.984074 0.136075    0
229   0.976412 0.136355    0
235   0.976412 0.136355    0
163   1.97941  0.136801    0.00334122
33    0.984074 0.141517    0
149   3.95828  0.145565    0.0218166
148   1.98141  0.146678    0.021887
43    5.91774  0.151034    0.0417444
6     4.9411   0.154099    0.0208203
209   1.96503  0.155171    0.0569649
45    4.93725  0.155433    0.0268866
46    7.8906   0.158148    0.0431735
88    0.988699 0.158544    0
212   0.988623 0.164442    0
99    2.97011  0.166966    0.0378676
26    1.97277  0.171456    0.00357809
29    0.984074 0.172242    0
87    8.88601  0.173728    0.0303258
117   2.95396  0.176579    0.0560572
127   4.94572  0.176668    0.0390158
70    6.91226  0.178509    0.0175664
0     4.94105  0.179756    0.0274114
113   4.94313  0.181492    0.0187196
234   0.976412 0.184464    0
20    9.87009  0.189009    0.0335662
83    4.93994  0.190728    0.0311907
130   0.988922 0.195031    0
223   0.988623 0.197991    0
147   0.990784 0.201182    0
160   0.990784 0.202559    0
158   0.990784 0.212255    0
116   0.988922 0.212276    0
54    0.984074 0.212957    0
96    1.96511  0.215793    0.0475268
187   2.96401  0.21889     0.0491922
101   2.9624   0.221618    0.0302988
120   0.988922 0.228323    0
94    0.988699 0.23358     0
166   1.97941  0.237474    0.035549
1     7.89739  0.238551    0.0597298
133   2.97034  0.241172    0.0468569
230   0.976412 0.243401    0
104   1.97948  0.244297    0.0367161
168   4.94336  0.249947    0.0421082
224   0.988623 0.257398    0
139   6.90653  0.260411    0.0418354
36    0.984074 0.263774    0
162   2.96654  0.268084    0.00929699
189   0.987138 0.269214    0
31    0.984074 0.278455    0
11    0.984074 0.337624    0
18    0.984074 0.35774     0
98    6.90676  0.366107    0.0494707

The Details

A regression scheme was implemented to rank riders and weeks. This was done for the determination of "most improved" rider awards, for which it was important to determine the relative performance of the winners of each week, so the winner-normalized scores could be converted into a globally-normalized score. Weeks in which riders exhibited anamolously low normalized scores were pruned from the data and then scores reiterated. For example, weeks in which riders punctured were typically noted and eliminated from the data in this way.

A shell script called weeks_to_regression was used to initiate the analysis:

#! /bin/tcsh -f set fnet = "weeks.dat" cat $fnet | nawk -f weeks_to_regression.nawk

weeks_to_regression.nawk was as follows:

BEGIN{ # team data name_col = 0; num_col = 0; # rider data name_col = 0; cat_col = 0l num_col = 0; sex_col = 0; url_col = 0; if (getline s < "riders.dat"){ n = split(s,a); for (i=0; i++<n;) if (a[i]=="name") name_col = i; else if (a[i] == "#") num_col = i; else if (substr(toupper(a[i]),1,3) == "SEX") sex_col = i; else if (substr(toupper(a[i]),1,3) == "CAT") cat_col = i; else if (substr(toupper(a[i]),1,3) == "URL") url_col = i; } if ((!name_col)||(!cat_col)||(!num_col)||(!url_col)||(!sex_col)){ print "ERROR -- Rider data file not found"; exit; } while (getline s < "riders.dat") if (n = split(s,a)){ rider_name[a[num_col]] = convert_string(a[name_col]); if (a[url_col] != "-") rider_name[a[num_col]] = "<a href=\"" a[url_col] "\">" rider_name[a[num_col]] "</a>" rider_sex[a[num_col]] = toupper(a[sex_col]); if ((rider_cat[a[num_col]] = a[cat_col]) > cat_max) cat_max = a[cat_col]; cat_count[a[cat_col]]++; } } (NF==0){ NR--; next; } (NR==1){ rider_col = 0; time_col = 0; team_col = 0; week_col = 0; for (i=0; i++<NF;) if ($i == "rider") rider_col = i; else if ($i == "time") time_col = i; else if ($i == "team") team_col = i; else if ($i == "week") week_col = i; if (rider_col == 0){ print "ERROR : column rider not found."; exit; } if (time_col == 0){ print "ERROR : column time not found."; exit; } if (team_col == 0){ print "ERROR : column team not found."; exit; } if (week_col == 0){ print "ERROR : column week not found."; exit; } next; n=0; } { # tabulate results if ((w=$week_col) > week_max) week_max = w; if (($time_col != "*")&&((s = 1*time_to_sec($time_col)) > 0)&&($rider_col != "-")){ week_sum_0[w] ++; week_sum_1[w] += (res = result[n] = log(s)); rider_sum_0[$rider_col] ++; rider_sum_1[$rider_col] += res; sum_1 += res; week[n] = w; rider[n++] = $rider_col; } avg = sum_1/n; } END{ do { prune_count = 0; iter=0; do { # calculate dof factors for (w in week_sum_0) if (week_sum_0[w] <= 1) week_dof_factor[w] = 0; else week_dof_factor[w] = sqrt(1 - 1/week_sum_0[w]); for (r in rider_sum_0) if (rider_sum_0[r] <= 1) rider_dof_factor[r] = 0; else rider_dof_factor[r] = sqrt(1 - 1/rider_sum_0[r]); for (w in week_sum_0){ week_sum_old_0[w] = week_sum_0[w]; week_sum_0[w] = 0; } for (r in rider_sum_0){ rider_sum_old_0[r] = rider_sum_0[r]; rider_sum_0[r] = 0; } ssr = 0; # sum of the square of the residuals for (i=0; i<n; i++) if ((r = rider[i]) != "-"){ w = week[i]; week_sum_0[w] += rider_dof_factor[r]; rider_sum_0[r] += week_dof_factor[w]; } sdsrs = 0; for (r in rider_sum_0) if (rider_sum_0[r] == 0){ delete rider_sum_0[r]; system("echo_stderr deleting rider " r); } else sdsrs += (rider_sum_0[r] - rider_sum_old_0[r])^2; sdsws = 0; for (w in week_sum_0) if (week_sum_0[w] == 0){ delete week_sum_0[w]; system("echo_stderr deleting week " w); } else sdsws += (week_sum_0[w] - week_sum_old_0[w])^2; print "iteration of dof : " ++iter ", " sdsrs ", " sdsws; } while (sdsws + sdsrs > 1e-5); if (prune_count == 0){ # first guess for week ratings for (w in week_sum_0) week_rating[w] = week_sum_1[w]/week_sum_0[w]; # first guess for rider ratings for (r in rider_sum_0) rider_rating[r] = rider_sum_1[w]/rider_sum_0[w] - avg; } # iterate iter = 0; do{ system("echo_stderr -n iteration " iter " : "); for (w in week_sum_0){ week_sum_old_1[w] = week_sum_1[w]; week_sum_1[w] = week_ssr_1[w] = week_ssr_0[w] = 0; } for (r in rider_sum_0){ rider_sum_old_1[r] = rider_sum_1[r]; rider_sum_1[r] = rider_ssr_1[r] = rider_ssr_0[r] = 0; } for (i=0; i<n; i++) if ((r = rider[i]) != "-"){ w = week[i]; week_sum_1[w] += (rider_dof_factor[r]) * (res - rider_rating[r]); rider_sum_1[r] += (week_dof_factor[w]) * ((res = result[i]) - week_rating[w]); } # assertion : sum of all rider ratings is zero # this should be dof-weighted, but it isn't important rr_sum_0 = rr_sum_1 =0; for (r in rider_sum_0){ rr_sum_0 ++; rr_sum_1 += rider_sum_1[r] / rider_sum_0[r]; } delta = rr_sum_1 / rr_sum_0; sdsrs = 0; for (r in rider_sum_0){ rider_rating[r] =\ 0.2 * rider_rating[r] +\ 0.8 * (rider_sum_1[r]/rider_sum_0[r] - delta); sdsrs += (rider_sum_1[r] - rider_sum_old_1[r])^2; } sdsws = 0; for (w in week_sum_0){ week_rating[w] =\ 0.2 * week_rating[w] +\ 0.8 * (week_sum_1[w]/week_sum_0[w] + delta); sdsws += (week_sum_1[w] - week_sum_old_1[w])^2; } # calculate ssr ssr_0 = ssr_1 = 0; for (i=0; i<n; i++) if ((r = rider[i]) != "-"){ w = week[i]; ssr_1 +=\ (residual_squared[i] =\ sr =\ ((result[i] - rider_rating[r] - week_rating[w]) *\ (dof = rider_dof_factor[r] * week_dof_factor[w]))^2); ssr_0 += dof; rider_ssr_1[r] += sr; rider_ssr_0[r] += dof; week_ssr_1[w] += sr; week_ssr_0[w] += dof; } sigma = sqrt(var = ssr_1/ssr_0); system("echo_stderr rms residual = " sigma); system("echo_stderr delta = " delta); print "ratings:",++iter,sdsrs,sdsws; } while (sdsrs + sdsws > 1e-4); # prune underliers, indicating punctures, etc for (i=0; i<n; i++) if (((r = rider[i]) != "-")&&(rider_ssr_0[r] > 0)){ w = week[i]; threshold = week_rating[w] + rider_rating[r] + (dt = sqrt(2*var + 2*rider_ssr_1[r]/rider_ssr_0[r])); if (result[i] > threshold){ prune_count++; rider[i] = "-"; print "rider " r ", week " w ", delta "\ result[i] - threshold ", delta_t = " dt ", was pruned."; print "rider " r ", week " w ", delta "\ result[i] - threshold ", delta_t = " dt ", was pruned." > "/tmp/prunes"; } } } while (prune_count > 0); print "week","#","rating","sigma" > "/tmp/weeks"; for (w in week_sum_0){ if (week_ssr_0[w] > 0) sigma = sqrt(week_ssr_1[w]/week_ssr_0[w]); else sigma = 0; print w,week_sum_0[w],week_rating[w],sigma > "/tmp/weeks"; } print "rider","#","rating","sigma" > "/tmp/riders"; for (r in rider_sum_0){ if (rider_ssr_0[r] > 0) sigma = sqrt(rider_ssr_1[r]/rider_ssr_0[r]); else sigma = 0; print r,rider_sum_0[r],-rider_rating[r],sigma > "/tmp/riders"; } print "rider","week","result","residual" > "/tmp/residuals"; for (i=0; i<n; i++) print rider[i], week[i], result[i],(result[i]-week_rating[week[i]]-rider_rating[rider[i]]) > "/tmp/residuals"; } function convert_string(s) { gsub("<","<",s); gsub(">",">",s); gsub("&","&",s); gsub("_"," ",s); return s; } function print_header(){ print "<tr>" >> fout; printf " <th>\n rider\n </th>\n" >> fout; printf " <th>\n team\n </th>\n" >> fout; printf " <th>\n cat\n </th>\n" >> fout; printf " <th>\n %cSpeed\n </th>\n","%" >> fout; print "</tr>" >> fout; } function time_to_sec(s,n){ n = split (s,a,":"); if (n==1) return a[1]; if (n==2) return 60*a[1] + a[2]; if (n==3) return a[3] + 60*(a[2] + 60*a[1]); return 0; }

The rider data file is the following:

# sex cat name - - - - 0 M 2 Winterfield,Kevin 1 M 4 Connelly,Daniel 2 M 0 Schmidt,Todd 3 M 0 Stanley,Clarke 4 M 0 Hernandez,Ken 5 M 0 Whipple,Rich 6 M 3 Good,Gordan 7 M 0 Caragio,Mark 8 F 47 Benishin,Liz 9 M 47 Smith,Wayne 10 F 10 Curran,Lisa 11 M 2 Leman,Steve 12 M 18 Miller,Ed 13 M 0 Farkas,Greg 14 M 46 Fernandez,Rauel 15 M 46 Kinell,Don 16 M 5 Hirsch,Bennett 17 F 11 Osmon,Cindy 18 M 5 Johansson,Henrik 19 M 6 Schwappach,Jim 20 M 4 Hawley,Lorin 21 F 11 Jaremizuh,Connie 22 M 6 Chung,Mark 23 M 6 Pereira,Lucas 24 M 6 Alafouzos,John 25 F 10 Hackell,Stella 26 M 5 Axelrad,Valery 27 M 5 Begley,Brian 28 M 6 Coale,David 29 M 5 Glueck,Brian 30 M 6 Harding,Maynard 31 M 37 Wyandt,David 32 M 6 Dumouchel,Jean 33 M 6 Pravetz,Jim 34 M 4 Motta,Neal 35 M 4 Buchanan,Mike 36 M 3 Lindberg,Craig 37 M 6 Jackson,Dale 38 M 17 Herman,Gary 39 M 6 Baltz,Jim 40 M 18 McMahan,Mike 41 M 6 Bonachita,Joe 42 M 16 Haughey,Jim 43 M 6 Bushnell,Bill 44 M 6 Maslen,Thomas 45 M 37 Bloom,Greg 46 M 16 Herms,Richard 47 F 27 Herms,Cheryl 48 M 17 Rodemaker,Mark 49 M 6 Cavalieni,Jeff 50 M 6 Custodio,Tony 52 M 6 Stephens,Duane 53 M 16 Pugh,Luther 54 M 6 Palmer,Jim 55 M 17 McCoy,Jim 56 M 17 Vogel,John 58 F 47 Baenen,Pat 59 M 6 Weston,Mike 61 M 16 Blair,Steve 62 M 48 Hurkmans,Henry 63 M 49 Flynn,Mark 64 M 6 Morris,Stephen 65 F 49 Goodman,Cris 66 M 6 Ranekketti,Scott 67 M 16 Hogenson,Brent 68 M 37 Emmons,Russ 69 M 6 Lawrence,Tom 70 M 4 Studenicka,Todd 71 M 5 Campbell,Bob 72 M 16 Barth,Scott 73 M 3 Kretschmann,John 74 M 16 Brokeshoulder,Darrel 75 M 5 Jessen,Mike 76 M 5 Lau,Garrett 77 M 6 Imacseng,Mac 78 M 6 Ryan,Patrick 79 M 6 Nelson,Randy 80 F 28 Robinson,Roxanne 81 F 27 Jung-Ames,Julia 82 M 16 Goldbeck,Steve 83 M 6 Cosentino,Giorgio 84 M 17 Ames,Roy 85 M 17 Robinson,Dick 86 M 17 Haugner,James 87 M 16 Wilkinson,Jim 88 M 6 Wong,Leo 89 M 18 Lowman,Tom 90 M 2 Tapscott,Peter 91 M 4 Schott,Rob 92 M 6 Rescorla,Eric 93 M 18 McDermand,Bob 94 M 6 Clifford,Mark 95 M 6 Begley,Al 96 M 4 Kendall,Lee 97 M 6 Bennett,Derek 98 M 6 Colwell,Tracy 99 M 4 Long,Richard 100 F 28 Olrich,Phyllis 101 M 37 Dickie,Brock 102 M 6 Bone,Richard 103 M 6 Cuevas,Marc 104 M 6 Lund,Thomas 105 M 6 Siehl,Dan 106 M 6 Spencer,Garth 107 M 6 Johnson,Eric 108 M 17 Calhoon,Stuart 109 M 6 Martinez,Jonathan 110 F 27 Stern,Laura 111 M 16 Halverson,Robin 112 M 16 Stanley,Hal 113 M 6 Rienhardt,Scott 114 M 6 Anderson,Rich 115 F 27 Forbes,Donamarie 116 M 16 Roberts,Scott 117 M 3 Crannell,Loren 118 F 11 Colwell,Julie 119 F 11 Chamness,Kim 120 M 4 Hsu,Brian 121 M 37 Hardy,Robert 122 M 48 Fenzi,Millo 123 F 28 Edwards,Sandra 124 M 17 Faulhaber,Bob 125 M 6 Beschle,John 126 M 6 Keagy,Tyler 127 M 6 Preas,Chris 128 M 6 Prewett,Woody 129 M 6 Clarke,Kevin 130 M 6 Johnson,Mark 131 M 17 Fulton,Dick 132 M 4 Anderson,Mark 133 M 6 Crawford,Chris 134 M 6 Holland,Ben 135 M 6 Wilson,Charles 136 M 6 Sebastiani,Marco 137 F 51 Anderson,Ann 138 M 51 Anderson,Richard 139 M 5 Podgorski,Mike 140 M 0 Rocha,Paul 141 M 0 Young,Peter 142 F 53 Colwell,Judy 145 M 6 Parker,Brian 146 M 16 Evitt,Eric 147 M 16 Smith,Bradford 148 M 16 Jaworkski,Ted 149 M 6 Straub,Ken 150 F 11 Antonino,Lisa 151 F 51 Jacobson,Charlotte 152 M 51 Trowbridge,Mike 153 M 6 Mostats,Mike 154 M 55 Boos.Freddy 155 M 16 Pflasterer,Jim 156 M 17 Bolander,Larry 157 M 16 King,Archie 158 M 6 Allen,Eric 159 M 16 Yorston,Karl 160 M 0 Hossack,John 161 M 16 Hargrove,Val 162 M 0 Denardi,Michael 163 M 56 Heller,Pete 164 M 17 Lebard,Ron 165 M 17 Sienna,Phil 166 M 0 Brunner,Ruedi 167 M 0 Mathews,Alex 168 M 5 Chadwick,Glenn 169 M 16 Sutton,Ken 170 M 57 Weiler,Chris 171 M 5 Spata,Robert 172 F 11 Neubauer,Kristen 173 M 5 Love,Wyland 174 F 11 Saibuya,Kana 175 M 0 Burnett,Damien 176 M 58 Goebel,Patrick 177 M 59 Carry,Mark 178 M 37 Cardwell,J. 179 M 0 Emmel,John 180 M 5 Carmichael,Rick 182 M 0 Watson,Andrew 183 M 0 Hansen,Bill 184 M 5 Grote,Mike 185 M 0 Spurling,James 186 M 4 Reddy,Achut 187 M 2 Johnston,Jim 188 M 0 Herman,James 189 M 0 Hutcheson,Charles 190 M 0 Nix,Marc 191 M 0 Johnson,Barry 192 M 0 Schmidt,William 193 M 4 Wilder,Michael 194 M 0 Wagner,Jered 195 M 0 Tanner,Jim 196 M 37 Jones,David 197 M 5 Simpkinson,Doug 198 M 39 Gellin,Gary 199 F 10 Harris,Holly 200 F 0 Lopez,Julie 201 M 0 Johnston,Jim 202 M 60 Schermer,Mark 203 M 0 Patterson,Jim 204 M 0 Salehi 205 M 0 Rautenberg 206 M 0 Rider_206 207 M 0 Cady,S 208 M 0 Wolfert,Randy 209 M 0 Snyder,David 210 f 0 Nasen,Dea 211 m 16 Moore,Greg 212 m 16 Martin,Scott 213 m 6 Zaharis,Tom 214 m 6 Mircik,Paul 215 m 16 Barsh,Greg 216 m 6 Morris,Simon 217 m 6 Ralph,Robert 218 m 61 Pereira,Patrick 219 m 18 Turner,Jim 220 m 4 Wong,Patrick 221 m 16 Moore,Bill 222 m 17 Williams,Al 223 m 17 Elgart,John 224 m 62 Hlady,Mark 225 m 15 Kelly,Mathew 226 m 63 Claus,Santa 227 M 37 Park,Tim 228 F 0 Cliff,Susie 229 M 51 Trail,Mark 230 M 0 Pietrofesa,Mark 231 M 37 Schmidt,Todd 232 M 51 Taylor,Paul 233 M 0 Pufahl,Randy 234 M 0 Harrison,Dave 235 F 51 Trail,Lisa 236 F 51 Taylor,Jane


Last modified: Sun Aug 24 15:57:19 PDT 1997