This package generates Marcel projections, using data from the Lahman package.
Marcels describes a projection system for baseball, first developed by Tom Tango. It is often described as the most basic projection system. It weights a players last three seasons, regresses this to the mean, and applies an age adjustment.
Since this is not on CRAN, it needs to be installed from github,
> library(devtools)
> install_github('bdilday/marcelR')
> library(marcelR)
As of this writing the Lahman package has not been updated to include the 2017+ seasons. I created an updated version, however, that can be used for generating projections for the 2018-2020 seasons. It can be installed from github as well,
> install_github('bdilday/Lahman')
> max(Lahman::Batting$yearID)
[1] 2019
This package includes the marcels as a set of data frames.
> data(marcels)
> names(marcels)
[1] "Pitching" "Batting" "Teams"
> nrow(marcels$Batting)
[1] 56622
> nrow(marcels$Pitching)
[1] 42777
> nrow(marcels$Teams)
[1] 2877
Here's an example of a projection, illustrated with Carlos Beltran for 2004.
> library(dplyr)
> marcels$Batting %>%
filter(yearID==2004, playerID=='beltrca01') %>%
print.data.frame()
playerID yearID proj_pa X1B X2B X3B HR BB HBP SB
1 beltrca01 2004 573.2 93.154 25.37286 7.483096 22.70545 58.44974 3.351604 29.40546
CS SO SH SF
1 3.721516 92.3098 1.338349 5.604223
The highest projected HR,
> marcels$Batting %>% arrange(-HR) %>% select(playerID, yearID, HR)
# A tibble: 54,730 × 3
playerID yearID HR
<fctr> <dbl> <dbl>
1 mcgwima01 1999 52.27053
2 mcgwima01 2000 51.93934
3 bondsba01 2002 49.70076
4 sosasa01 2002 48.08998
5 mcgwima01 1998 47.17453
6 sosasa01 2001 46.87696
7 sosasa01 2000 46.38852
8 griffke02 1999 45.72925
9 bondsba01 2003 45.71398
10 sosasa01 2003 43.79848
# ... with 54,720 more rows
Lowest projected RA9 since 1950.
> marcels$Pitching %>%
mutate(RA9=27*R/proj_pt) %>%
arrange(RA9) %>%
filter(yearID>=1950) %>%
select(playerID, yearID, RA9)
# A tibble: 29,054 × 3
playerID yearID RA9
<fctr> <dbl> <dbl>
1 gibsobo01 1970 2.409111
2 goodedw01 1986 2.417237
3 gibsobo01 1969 2.439491
4 koufasa01 1965 2.451923
5 koufasa01 1967 2.473709
6 kershcl01 2015 2.480347
7 koufasa01 1966 2.525069
8 kershcl01 2016 2.525205
9 kimbrcr01 2014 2.529273
10 maddugr01 1996 2.530020
# ... with 28,830 more rows
Highest projected winning percentage since 1913,
> marcels$Teams %>% filter(yearID>=1913) %>% arrange(-wpct) %>% select(yearID, teamID, wpct)
# A tibble: 2,290 × 3
yearID teamID wpct
<dbl> <fctr> <dbl>
1 1940 NYA 0.6175461
2 1928 NYA 0.6119175
3 1952 NY1 0.6096779
4 1913 NY1 0.6089000
5 1953 BRO 0.6082399
6 1934 CHN 0.6039637
7 2017 CHN 0.6039189
8 2004 BOS 0.6038871
9 1921 NYA 0.6037286
10 1941 NYA 0.6033883
# ... with 2,280 more rows
As of this writing, the Batting and Pitching stats have been updated to 2019, but the team projectison have not (waiting on creation of updated rosters).
The marcel data is exported in the marcel_data_exporter.R script. The low-level functions to compute the marcels are also included, however. Examples are given below.
For batting stats, the weights given to the previous three seasons are 5, 4, and 3, and the amount of regression is 100 PA.
An example of computing marcels for batting stats,
> a <- get_batting_stats()
> b <- dplyr::tbl_df(marcelR:::append_previous_years(a %>% filter(POS!="P"),
get_seasonal_averages_batting,
previous_years = 3))
> mcl <- dplyr::tbl_df(apply_marcel_batting(b, "HR", marcelR:::age_adjustment))
> mcl %>% filter(projectedYearID==2004, playerID=='beltrca01') %>% print.data.frame()
playerID yearID projectedYearID age_adj x_metric x_pa x_av proj_pa metric_target
1 beltrca01 2003 2004 1.012 318 7938 0.02867754 573.2 0.02868739
num denom proj_rate_raw proj_rate proj_value metric_agg proj_value_floating
1 352.413 9138 0.03856566 0.03902845 22.70545 0.02826497 22.37111
metric_multiplier
1 1.014945
For pitching stats, the weights given to the previous three seasons are 3, 2, and 1, and the amount of regression is 134 Outs, or about 44.2 innings.
An example of computing marcels for pitching stats,
> a <- get_pitching_stats()
> b <- dplyr::tbl_df(marcelR:::append_previous_years(a %>% filter(POS=="P"),
get_seasonal_averages_pitching,
previous_years=3))
> mcl <- dplyr::tbl_df(apply_marcel_pitching(b, "R", marcelR:::age_adjustment_reciprocal))
> mcl %>% filter(projectedYearID==2017) %>% mutate(RA9=27*proj_value/proj_pt) %>% arrange(RA9) %>% head(4) %>% print.data.frame()
playerID yearID projectedYearID age_adj x_metric x_pt x_lgav proj_pt metric_target
1 kershcl01 2016 2017 1.000 259 3332 0.1607082 473.3 0.1616625
2 brittza01 2016 2017 1.003 70 1226 0.1614394 195.2 0.1616625
3 daviswa01 2016 2017 1.009 51 1010 0.1602990 160.2 0.1616625
4 millean01 2016 2017 1.009 87 1226 0.1621735 205.0 0.1616625
num denom proj_rate_raw proj_rate proj_value metric_agg proj_value_floating
1 388.2094 4136 0.09386108 0.09386108 44.42786 0.1616501 44.42445
2 199.7973 2030 0.09842229 0.09871756 19.27115 0.1616501 19.26967
3 179.8804 1814 0.09916231 0.10005477 16.03000 0.1616501 16.02877
4 217.3875 2030 0.10708744 0.10805123 22.15220 0.1616501 22.15050
metric_multiplier RA9
1 1.000077 2.534444
2 1.000077 2.665579
3 1.000077 2.701686
4 1.000077 2.917607
Team win projections aren't strictly a part of the marcel specification. In this package, marcels are used in the following way to project wins.
-
Specify a roster of batters and pitchers. In practice this comes from the players that actually played in the subsequent season, based on
Lahmandata. -
Given the assumed roster, aggregate batting and pitching stats based on projected playing time.
-
Apply Base Runs to estimate the number of runs scored on offense.
-
Use estimated RA9 from the pitching projections directly for estimating runs allowed.
-
Adjust the estimated runs and runs-allowed to a common number of PA.
-
Apply the Pythagorean win formula to these adjusted runs estimates.