Overview

Six models are used to forecast each major age class of sockeye salmon in the major rivers of Bristol Bay. Five of these models are linear regressions and the sixth is a 5-year running average of the age class under consideration.

Forecast models

This document covers output from five linnear regression models run against four major age classes in this river. Three regressions are variations of the sibling relationship with the age being forecast (Table 1). The first regression (sibling) uses observed forecast age and the brood year younger sibling return. The second regression (ln.sibling) uses a natural log transformation of both the forecasted age and the sibling return. The third regression (lnY.sibling) uses the sibling age return and a natural log transformation of the forecasted age. Two linnear regression models based on forecasted age return and total spawning escapment. The first of these (lnS.lnR) is the natural log of the forecasted age class regressed against the natural log of the spawning escapement. The second forecast method that relies on the relationship between the forecasted age and the spawning escapement is a linnear transformation of the Ricker relationship.

Table 1. Forecast ages and the sibling age class used for forecasting.

Forecast Age Sibling
Age.12 Age.11
Age.22 Age.21
Age.13 Age.12
Age.23 Age.22

Output

Each model output consists of a table and two graphs. The table shows the most recent 10 years of observed returns for the age being forecast (‘Observed Return’) and the relevant sibling return (‘Sibling Return’) shown in bold black text. Brood and return years are shown in blue text. Two regression model statistics (R-squared and P-value of the slope) are shown in red. Model forecasted returns are shown in bold black text with a yellow highlight. Error measurements are shown in green text. Error measurements shown are absolute deviation (AD), absolute percent error (APE), percent error (PE) and arc tan percent error (AAPE).

After the table summarizing the model output for the most recenet ten years, two graphs are shown for each of the linnear regression models. The first graph is a scatter plot of the data with a linnear regression superimposed. The second graph is a plot of the residuals of the regression analysis.

Absolute deviation (AD) is defined as

\[\ AD = O - F\] where

O = Observed Return

F = Forecasted Return

Percent error (PE) is defined as

\[\ PE = (F - O)/O\] Absolute Percent error (APE) is defined as

\[\ APE = |(F - O)/O|\]

Arctangent percent error (AAPE) is defined (Kim and Kim, 2016) as \[\ AAPE = arctan(|((O - F)/O)|)\]

At the end of the model output section for each age class, a performance table is presented that contains the mean absolute deviation (MAD), neam absolute percent error (MAPE), mean percent error (MPE) and mean arctanget percent error (MAAPE). These performance metrics are calculated and presented across the most recent three and five years. Color bars show the relative size of each metric.

age.12

Below are model outputs using data from 1972

lnS.lnR

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2008 125,488 205,680 -0.025 0.697 113,501 11,987 0.11 -0.11 0.10
2013 2009 88,287 313,946 -0.024 0.694 108,122 19,835 0.18 0.18 0.22
2014 2010 130,232 188,298 -0.022 0.645 114,552 15,680 0.14 -0.14 0.12
2015 2011 166,292 190,970 -0.021 0.637 114,717 51,575 0.45 -0.45 0.30
2016 2012 176,979 203,148 -0.020 0.625 114,791 62,188 0.54 -0.54 0.34
2017 2013 298,803 128,118 -0.019 0.624 123,844 174,959 1.41 -1.41 0.53
2018 2014 583,074 151,934 -0.011 0.465 125,726 457,348 3.64 -3.64 0.67
2019 2015 292,933 218,700 -0.003 0.350 119,872 173,061 1.44 -1.44 0.53
2020 2016 191,935 200,046 -0.005 0.379 125,434 66,501 0.53 -0.53 0.33
2021 2017 NA 190,098 -0.005 0.377 128,339 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2008 125,488 205,680 0.284 0 123,193 2,295 0.02 -0.02 0.02
2013 2009 88,287 313,946 0.285 0 106,293 18,006 0.17 0.17 0.20
2014 2010 130,232 188,298 0.299 0 123,300 6,932 0.06 -0.06 0.05
2015 2011 166,292 190,970 0.300 0 123,468 42,824 0.35 -0.35 0.25
2016 2012 176,979 203,148 0.302 0 124,024 52,955 0.43 -0.43 0.29
2017 2013 298,803 128,118 0.302 0 118,218 180,585 1.53 -1.53 0.54
2018 2014 583,074 151,934 0.321 0 128,230 454,844 3.55 -3.55 0.66
2019 2015 292,933 218,700 0.322 0 130,682 162,251 1.24 -1.24 0.51
2020 2016 191,935 200,046 0.314 0 136,089 55,846 0.41 -0.41 0.28
2021 2017 NA 190,098 0.314 0 138,317 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2008 125,488 195,572 70,084 0.36 0.36 0.51
2013 2009 88,287 171,720 83,433 0.49 0.49 0.76
2014 2010 130,232 168,118 37,886 0.23 0.23 0.28
2015 2011 166,292 133,689 32,603 0.24 -0.24 0.19
2016 2012 176,979 134,807 42,172 0.31 -0.31 0.23
2017 2013 298,803 137,456 161,347 1.17 -1.17 0.50
2018 2014 583,074 172,119 410,955 2.39 -2.39 0.61
2019 2015 292,933 271,076 21,857 0.08 -0.08 0.07
2020 2016 191,935 303,616 111,681 0.37 0.37 0.53
2021 2017 NA 308,745 NA NA NA NA

Performance summary

This age class has not fluctuated much so the running average is more convincing than the spawner relationship so we pick this for a forecast of 308,000.

model range MAD MAPE MPE MAAPE
sibling 5 years 139,858 81.18% -81.18% 0.33
sibling 3 years 184,129 103.71% -103.71% 0.39
ln.sibling 5 years 141,271 83.12% -83.12% 0.33
ln.sibling 3 years 184,866 106.72% -106.72% 0.38
lnY.sibling 5 years 164,797 111.51% -111.51% 0.41
lnY.sibling 3 years 211,879 138.97% -138.97% 0.48
lnS.lnR 5 years 186,811 151.32% -151.32% 0.48
lnS.lnR 3 years 232,303 187.05% -187.05% 0.51
ricker 5 years 181,296 143.07% -143.07% 0.46
ricker 3 years 224,313 173.30% -173.30% 0.48
average 5 years 149,603 86.45% -71.74% 0.39
average 3 years 181,498 94.54% -70.01% 0.41

age.22

Below are model outputs using data from 1972

lnS.lnR

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 38,261 269,646 -0.020 0.576 27,338 10,923 0.40 -0.40 0.28
2013 2008 3,072 205,680 -0.018 0.537 25,858 22,786 0.88 0.88 1.44
2014 2009 25,841 313,946 -0.019 0.577 27,110 1,269 0.05 0.05 0.05
2015 2010 9,047 188,298 -0.018 0.570 23,848 14,801 0.62 0.62 1.02
2016 2011 16,663 190,970 -0.017 0.551 23,328 6,665 0.29 0.29 0.38
2017 2012 9,337 203,148 -0.016 0.541 23,504 14,167 0.60 0.60 0.99
2018 2013 4,547 128,118 -0.016 0.543 20,401 15,854 0.78 0.78 1.29
2019 2014 4,843 151,934 -0.005 0.378 19,940 15,097 0.76 0.76 1.26
2020 2015 3,175 218,700 0.002 0.305 22,252 19,077 0.86 0.86 1.41
2021 2016 NA 200,046 -0.003 0.356 20,467 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 38,261 269,646 0.062 0.081 28,446 9,815 0.35 -0.35 0.25
2013 2008 3,072 205,680 0.060 0.080 27,272 24,200 0.89 0.89 1.44
2014 2009 25,841 313,946 0.048 0.103 27,370 1,529 0.06 0.06 0.06
2015 2010 9,047 188,298 0.052 0.090 24,899 15,852 0.64 0.64 1.05
2016 2011 16,663 190,970 0.047 0.100 24,324 7,661 0.31 0.31 0.43
2017 2012 9,337 203,148 0.046 0.099 24,630 15,293 0.62 0.62 1.02
2018 2013 4,547 128,118 0.043 0.102 19,227 14,680 0.76 0.76 1.27
2019 2014 4,843 151,934 0.026 0.156 19,898 15,055 0.76 0.76 1.26
2020 2015 3,175 218,700 0.015 0.207 23,144 19,969 0.86 0.86 1.41
2021 2016 NA 200,046 0.014 0.212 21,189 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2007 38,261 38,256 5 0.00 0.00 0.00
2013 2008 3,072 40,818 37,746 0.92 0.92 1.49
2014 2009 25,841 39,810 13,969 0.35 0.35 0.50
2015 2010 9,047 35,514 26,467 0.75 0.75 1.24
2016 2011 16,663 24,243 7,580 0.31 0.31 0.43
2017 2012 9,337 18,577 9,240 0.50 0.50 0.78
2018 2013 4,547 12,792 8,245 0.64 0.64 1.07
2019 2014 4,843 13,087 8,244 0.63 0.63 1.04
2020 2015 3,175 8,887 5,712 0.64 0.64 1.06
2021 2016 NA 7,713 NA NA NA NA

Performance summary

No significant regression exists so we take the 5-year average for a forecast of 8,000.

model range MAD MAPE MPE MAAPE
sibling 5 years 27,694 78.53% 78.53% 1.28
sibling 3 years 30,552 87.97% 87.97% 1.43
ln.sibling 5 years 14,704 66.23% 66.23% 1.07
ln.sibling 3 years 17,645 80.88% 80.88% 1.34
lnY.sibling 5 years 14,704 66.23% 66.23% 1.07
lnY.sibling 3 years 17,645 80.88% 80.88% 1.34
lnS.lnR 5 years 14,172 65.60% 65.60% 1.07
lnS.lnR 3 years 16,676 79.72% 79.72% 1.32
ricker 5 years 14,531 66.38% 66.38% 1.08
ricker 3 years 16,568 79.43% 79.43% 1.31
average 5 years 7,804 54.55% 54.55% 0.88
average 3 years 7,400 63.91% 63.91% 1.06

age.13

Below are model outputs using data from 1972

sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 654,989 163,735 0.305 0 482,842 172,147 0.36 -0.36 0.26
2013 2008 469,887 125,488 0.306 0 427,193 42,694 0.10 -0.10 0.09
2014 2009 364,308 88,287 0.305 0 369,385 5,077 0.01 0.01 0.01
2015 2010 338,788 130,232 0.308 0 435,766 96,978 0.22 0.22 0.28
2016 2011 538,658 166,292 0.308 0 490,593 48,065 0.10 -0.10 0.09
2017 2012 357,182 176,979 0.311 0 508,962 151,780 0.30 0.30 0.40
2018 2013 756,364 298,803 0.303 0 696,373 59,991 0.09 -0.09 0.08
2019 2014 983,763 583,074 0.331 0 1,159,142 175,379 0.15 0.15 0.18
2020 2015 418,533 292,933 0.398 0 667,679 249,146 0.37 0.37 0.54
2021 2016 NA 191,935 0.375 0 513,222 NA NA NA NA

ln.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 654,989 163,735 0.418 0 468,309 186,680 0.40 -0.40 0.28
2013 2008 469,887 125,488 0.423 0 410,370 59,517 0.15 -0.15 0.13
2014 2009 364,308 88,287 0.424 0 340,469 23,839 0.07 -0.07 0.07
2015 2010 338,788 130,232 0.424 0 420,959 82,171 0.20 0.20 0.24
2016 2011 538,658 166,292 0.421 0 477,471 61,187 0.13 -0.13 0.11
2017 2012 357,182 176,979 0.426 0 495,804 138,622 0.28 0.28 0.37
2018 2013 756,364 298,803 0.417 0 648,413 107,951 0.17 -0.17 0.14
2019 2014 983,763 583,074 0.436 0 941,193 42,570 0.05 -0.05 0.04
2020 2015 418,533 292,933 0.471 0 650,852 232,319 0.36 0.36 0.51
2021 2016 NA 191,935 0.457 0 508,145 NA NA NA NA

lnY.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 654,989 163,735 0.330 0 419,351 235,638 0.56 -0.56 0.35
2013 2008 469,887 125,488 0.329 0 366,149 103,738 0.28 -0.28 0.22
2014 2009 364,308 88,287 0.326 0 319,171 45,137 0.14 -0.14 0.12
2015 2010 338,788 130,232 0.326 0 376,953 38,165 0.10 0.10 0.11
2016 2011 538,658 166,292 0.326 0 432,001 106,657 0.25 -0.25 0.20
2017 2012 357,182 176,979 0.328 0 453,029 95,847 0.21 0.21 0.26
2018 2013 756,364 298,803 0.325 0 718,843 37,521 0.05 -0.05 0.05
2019 2014 983,763 583,074 0.348 0 2,173,242 1,189,479 0.55 0.55 0.88
2020 2015 418,533 292,933 0.359 0 629,497 210,964 0.34 0.34 0.47
2021 2016 NA 191,935 0.347 0 451,049 NA NA NA NA

lnS.lnR

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 654,989 269,646 -0.016 0.493 405,483 249,506 0.62 -0.62 0.36
2013 2008 469,887 205,680 -0.010 0.423 392,096 77,791 0.20 -0.20 0.16
2014 2009 364,308 313,946 -0.009 0.414 429,699 65,391 0.15 0.15 0.18
2015 2010 338,788 188,298 -0.010 0.430 385,641 46,853 0.12 0.12 0.14
2016 2011 538,658 190,970 -0.009 0.420 385,370 153,288 0.40 -0.40 0.28
2017 2012 357,182 203,148 -0.009 0.423 393,266 36,084 0.09 0.09 0.10
2018 2013 756,364 128,118 -0.008 0.418 359,454 396,910 1.10 -1.10 0.48
2019 2014 983,763 151,934 -0.017 0.567 383,798 599,965 1.56 -1.56 0.55
2020 2015 418,533 218,700 -0.021 0.702 409,944 8,589 0.02 -0.02 0.02
2021 2016 NA 200,046 -0.020 0.698 406,865 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 654,989 269,646 0.286 0.001 413,669 241,320 0.58 -0.58 0.35
2013 2008 469,887 205,680 0.275 0.001 416,736 53,151 0.13 -0.13 0.11
2014 2009 364,308 313,946 0.275 0.001 410,770 46,462 0.11 0.11 0.13
2015 2010 338,788 188,298 0.288 0.000 410,028 71,240 0.17 0.17 0.21
2016 2011 538,658 190,970 0.286 0.000 409,097 129,561 0.32 -0.32 0.24
2017 2012 357,182 203,148 0.288 0.000 417,007 59,825 0.14 0.14 0.17
2018 2013 756,364 128,118 0.288 0.000 356,627 399,737 1.12 -1.12 0.49
2019 2014 983,763 151,934 0.307 0.000 395,830 587,933 1.49 -1.49 0.54
2020 2015 418,533 218,700 0.314 0.000 435,070 16,537 0.04 0.04 0.04
2021 2016 NA 200,046 0.314 0.000 432,648 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2007 654,989 584,401 70,588 0.12 -0.12 0.11
2013 2008 469,887 569,904 100,017 0.18 0.18 0.21
2014 2009 364,308 519,166 154,858 0.30 0.30 0.40
2015 2010 338,788 495,365 156,577 0.32 0.32 0.43
2016 2011 538,658 488,699 49,959 0.10 -0.10 0.09
2017 2012 357,182 473,326 116,144 0.25 0.25 0.31
2018 2013 756,364 413,765 342,599 0.83 -0.83 0.43
2019 2014 983,763 471,060 512,703 1.09 -1.09 0.48
2020 2015 418,533 594,951 176,418 0.30 0.30 0.40
2021 2016 NA 610,900 NA NA NA NA

Performance summary

The sibling models perform best and are similar so we recommend a basket of sibling models for a forecast of 496,000.

model range MAD MAPE MPE MAAPE
sibling 5 years 136,872 20.14% 12.77% 0.26
sibling 3 years 161,505 20.35% 14.61% 0.26
ln.sibling 5 years 116,530 19.53% 5.93% 0.24
ln.sibling 3 years 127,613 18.96% 4.84% 0.23
lnY.sibling 5 years 328,094 27.86% 15.90% 0.37
lnY.sibling 3 years 479,321 31.16% 27.68% 0.47
lnS.lnR 5 years 238,968 63.56% -59.89% 0.29
lnS.lnR 3 years 335,155 89.61% -89.61% 0.35
ricker 5 years 238,719 62.09% -54.83% 0.29
ricker 3 years 334,736 88.14% -85.61% 0.35
average 5 years 239,565 51.21% -29.53% 0.34
average 3 years 343,907 73.76% -54.00% 0.43

age.23

Below are model outputs using data from 1972

sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2006 11,470 44,996 0.508 0 52,590 41,120 0.78 0.78 1.30
2013 2007 27,737 38,261 0.489 0 46,094 18,357 0.40 0.40 0.58
2014 2008 8,282 3,072 0.486 0 17,972 9,690 0.54 0.54 0.86
2015 2009 8,630 25,841 0.497 0 35,490 26,860 0.76 0.76 1.26
2016 2010 2,908 9,047 0.497 0 21,290 18,382 0.86 0.86 1.41
2017 2011 3,523 16,663 0.505 0 26,685 23,162 0.87 0.87 1.42
2018 2012 9,653 9,337 0.509 0 19,916 10,263 0.52 0.52 0.82
2019 2013 2,776 4,547 0.516 0 15,568 12,792 0.82 0.82 1.36
2020 2014 559 4,843 0.525 0 15,269 14,710 0.96 0.96 1.53
2021 2015 NA 3,175 0.533 0 13,270 NA NA NA NA

ln.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2006 11,470 44,996 0.321 0.000 46,346 34,876 0.75 0.75 1.25
2013 2007 27,737 38,261 0.274 0.001 40,698 12,961 0.32 0.32 0.44
2014 2008 8,282 3,072 0.270 0.001 12,531 4,249 0.34 0.34 0.47
2015 2009 8,630 25,841 0.319 0.000 33,201 24,571 0.74 0.74 1.23
2016 2010 2,908 9,047 0.295 0.000 19,296 16,388 0.85 0.85 1.40
2017 2011 3,523 16,663 0.306 0.000 24,276 20,753 0.85 0.85 1.40
2018 2012 9,653 9,337 0.288 0.000 16,730 7,077 0.42 0.42 0.63
2019 2013 2,776 4,547 0.301 0.000 10,892 8,116 0.75 0.75 1.24
2020 2014 559 4,843 0.343 0.000 10,086 9,527 0.94 0.94 1.51
2021 2015 NA 3,175 0.368 0.000 6,026 NA NA NA NA

lnY.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2006 11,470 44,996 0.361 0 37,947 26,477 0.70 0.70 1.16
2013 2007 27,737 38,261 0.333 0 33,405 5,668 0.17 0.17 0.20
2014 2008 8,282 3,072 0.333 0 20,525 12,243 0.60 0.60 0.98
2015 2009 8,630 25,841 0.352 0 27,134 18,504 0.68 0.68 1.13
2016 2010 2,908 9,047 0.344 0 20,510 17,602 0.86 0.86 1.41
2017 2011 3,523 16,663 0.339 0 21,316 17,793 0.83 0.83 1.38
2018 2012 9,653 9,337 0.331 0 17,787 8,134 0.46 0.46 0.70
2019 2013 2,776 4,547 0.341 0 16,019 13,243 0.83 0.83 1.36
2020 2014 559 4,843 0.348 0 14,946 14,387 0.96 0.96 1.53
2021 2015 NA 3,175 0.326 0 12,656 NA NA NA NA

lnS.lnR

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2006 11,470 312,126 -0.031 0.982 34,794 23,324 0.67 0.67 1.11
2013 2007 27,737 269,646 -0.028 0.811 32,660 4,923 0.15 0.15 0.18
2014 2008 8,282 205,680 -0.027 0.787 33,296 25,014 0.75 0.75 1.25
2015 2009 8,630 313,946 -0.026 0.775 30,644 22,014 0.72 0.72 1.20
2016 2010 2,908 188,298 -0.019 0.575 31,521 28,613 0.91 0.91 1.47
2017 2011 3,523 190,970 -0.021 0.655 29,521 25,998 0.88 0.88 1.44
2018 2012 9,653 203,148 -0.022 0.705 27,690 18,037 0.65 0.65 1.08
2019 2013 2,776 128,118 -0.022 0.702 29,074 26,298 0.90 0.90 1.47
2020 2014 559 151,934 -0.025 0.965 25,474 24,915 0.98 0.98 1.55
2021 2015 NA 218,700 -0.021 0.697 23,887 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2006 11,470 312,126 0.141 0.016 35,873 24,403 0.68 0.68 1.13
2013 2007 27,737 269,646 0.170 0.008 35,089 7,352 0.21 0.21 0.26
2014 2008 8,282 205,680 0.175 0.006 35,952 27,670 0.77 0.77 1.28
2015 2009 8,630 313,946 0.160 0.008 31,656 23,026 0.73 0.73 1.21
2016 2010 2,908 188,298 0.187 0.004 33,604 30,696 0.91 0.91 1.48
2017 2011 3,523 190,970 0.143 0.010 31,375 27,852 0.89 0.89 1.44
2018 2012 9,653 203,148 0.116 0.018 29,689 20,036 0.67 0.67 1.12
2019 2013 2,776 128,118 0.110 0.019 25,875 23,099 0.89 0.89 1.45
2020 2014 559 151,934 0.071 0.049 24,981 24,422 0.98 0.98 1.55
2021 2015 NA 218,700 0.025 0.155 25,324 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2006 11,470 33,130 21,660 0.65 0.65 1.08
2013 2007 27,737 23,001 4,736 0.21 -0.21 0.17
2014 2008 8,282 24,815 16,533 0.67 0.67 1.11
2015 2009 8,630 23,799 15,169 0.64 0.64 1.05
2016 2010 2,908 17,599 14,691 0.83 0.83 1.38
2017 2011 3,523 11,805 8,282 0.70 0.70 1.17
2018 2012 9,653 10,216 563 0.06 0.06 0.06
2019 2013 2,776 6,599 3,823 0.58 0.58 0.94
2020 2014 559 5,498 4,939 0.90 0.90 1.46
2021 2015 NA 3,884 NA NA NA NA

Performance summary

The running average is clearly the high performer so we recommend it here for a forecast of 816,000.

model range MAD MAPE MPE MAAPE
sibling 5 years 15,862 80.64% 80.64% 1.31
sibling 3 years 12,588 76.68% 76.68% 1.24
ln.sibling 5 years 12,372 76.34% 76.34% 1.24
ln.sibling 3 years 8,240 70.42% 70.42% 1.13
lnY.sibling 5 years 14,232 78.79% 78.79% 1.28
lnY.sibling 3 years 11,922 74.89% 74.89% 1.20
lnS.lnR 5 years 24,772 86.45% 86.45% 1.40
lnS.lnR 3 years 23,083 84.47% 84.47% 1.36
ricker 5 years 25,221 86.93% 86.93% 1.41
ricker 3 years 22,519 84.84% 84.84% 1.37
average 5 years 6,460 61.38% 61.38% 1.00
average 3 years 3,108 51.09% 51.09% 0.82