library(tidyverse)
.
.
# data preparation steps
.
.
# create position alternatives
soccer <- mutate(
soccer,
# fielder vs goalkeeper
position_fld_vs_gk = if_else(position == "Goalkeeper",
"Goalkeeper", "Fielder"),
# grouping into 4 groups
position_group = forcats::fct_collapse(
position,
Forward = c("Center Forward", "Right Winger", "Left Winger"),
Midfielder = c("Defensive Midfielder", "Attacking Midfielder",
"Right Midfielder", "Center Midfielder",
"Left Midfielder"),
Defender = c("Center Back", "Right Fullback", "Left Fullback"),
Goalkeeper = c("Goalkeeper")
)
)
# specify variable inclusion and exclusion
model_1 <- formula(redCards ~ skintone)
model_2 <- formula(redCards ~ skintone + position)
model_3 <- formula(redCards ~ skintone + position_fld_vs_gk)
model_4 <- formula(redCards ~ skintone + position_group)
model_5 <- formula(redCards ~ skintone +
weight)
model_6 <- formula(redCards ~ skintone + position +
weight)
model_7 <- formula(redCards ~ skintone + position_fld_vs_gk +
weight)
model_8 <- formula(redCards ~ skintone + position_group +
weight)
model_9 <- formula(redCards ~ skintone +
height)
model_10 <- formula(redCards ~ skintone + position +
height)
model_11 <- formula(redCards ~ skintone + position_fld_vs_gk +
height)
model_12 <- formula(redCards ~ skintone + position_group +
height)
model_13 <- formula(redCards ~ skintone + weight +
height)
model_14 <- formula(redCards ~ skintone + position +
weight + height)
model_15 <- formula(redCards ~ skintone + position_fld_vs_gk +
weight + height)
model_16 <- formula(redCards ~ skintone + position_group +
weight + height)
model_17 <- formula(redCards ~ skintone +
leagueCountry)
model_18 <- formula(redCards ~ skintone + position +
leagueCountry)
model_19 <- formula(redCards ~ skintone + position_fld_vs_gk +
leagueCountry)
model_20 <- formula(redCards ~ skintone + position_group +
leagueCountry)
model_21 <- formula(redCards ~ skintone +
weight + leagueCountry)
model_22 <- formula(redCards ~ skintone + position +
weight + leagueCountry)
model_23 <- formula(redCards ~ skintone + position_fld_vs_gk +
weight + leagueCountry)
model_24 <- formula(redCards ~ skintone + position_group +
weight + leagueCountry)
model_25 <- formula(redCards ~ skintone +
height + leagueCountry)
model_26 <- formula(redCards ~ skintone + position +
height + leagueCountry)
model_27 <- formula(redCards ~ skintone + position_fld_vs_gk +
height + leagueCountry)
model_28 <- formula(redCards ~ skintone + position_group +
height + leagueCountry)
model_29 <- formula(redCards ~ skintone +
weight + height + leagueCountry)
model_30 <- formula(redCards ~ skintone + position +
weight + height + leagueCountry)
model_31 <- formula(redCards ~ skintone + position_fld_vs_gk +
weight + height + leagueCountry)
model_32 <- formula(redCards ~ skintone + position_group +
weight + height + leagueCountry)
# bring the multiverse together and fit
models <- list(
model_1, model_2, model_3, model_4,
model_5, model_6, model_7, model_8,
model_9, model_10, model_11, model_12,
model_13, model_14, model_15, model_16,
model_17, model_18, model_19, model_20,
model_21, model_22, model_23, model_24,
model_25, model_26, model_27, model_28,
model_29, model_30, model_31, model_32
)
multiverse_fit <- lapply(
models, glm, family = binomial, data = soccer)mverse: How the R package is designed to help students explore the multiverse
CANSSI Ontario Statistical Software Conference
Michael Jongho Moon
PhD Student, DoSS, University of Toronto
November 10, 2022
Multiverse
analysis
Example
Are darker-skinnedsoccer players
more likely
to receive a red card?
Data1
- Card counts received by 2,053 soccer players who played in the first male divisions of England, France, and Spain in the 2012-2013 season throughout their careers
- Contains skin tone information along with other player information
- Which attributes are important to take into account as covariates?
1Silberzahn, R., Uhlmann, E.L., …, & Nosek, B.A. (2018). Many Analysts, One Data Set: Making Transparent How Variations in Analytic Choices Affect Results. Advances in Methods and Practices in Psychological Science, 1(3), 337-356. https://doi.org/10.1177/2515245917747646
Position
As-is
Fielder vs. goalkeeper
Fielder groups
Position
Which groupings should we use?
Size
Should we use height, weight, or both to represent size?
League country
Should we take the league country into account?
- Reporting results from a single analysis doesn’t reveal the full scholarship involved in the analysis
Multiverse analysis2
involves performing and reporting all analyses across the whole set of reasonable alternatives
- There are at least 29 unique analytic approaches with the same data set1
- A multiverse analysis would consider all reasonable combinations of alternatives for each analytic decision
2Steegen, S., Tuerlinckx, F., Gelman, A., & Vanpaemel, W. (2016).
Increasing Transparency Through a Multiverse Analysis.
Perspectives on Psychological Science, 11(5), 702–712.
https://doi.org/10.1177/1745691616658637
1Silberzahn, R., Uhlmann, E.L., …, & Nosek, B.A. (2018).
Many Analysts, One Data Set: Making Transparent How Variations in Analytic Choices Affect Results.
Advances in Methods and Practices in Psychological Science, 1(3), 337-356.
https://doi.org/10.1177/2515245917747646
3Figure by Richie King, Aug 19, 2015, Science Sin’t Broken.
FiveThirtyEight. https://fivethirtyeight.com/features/science-isnt-broken/
Exploring a multiverse
is complex and difficult,
especially for students
with limited technical competency
mverse
An R package for tidy multiverse analysis
Collaborators
Haoda Li,
Mingwei Xu,
Nathan Taback, PhD, &
Fanny Chevalier, PhD
How we approached the design
- Systematic syntax
- Familiar syntax
- Interactive exploration tool
Some of the features presented are in the experimental stage.
Systematic syntax
Multiverse definition to execution
Without mverse
Systematic syntax
Designed around analytical decision points
With mverse
library(mverse)
.
.
# data preparation steps
.
.
# create position alternatives
position_alternative <- mutate_branch(
as_is = position, # use position as is
# fielder vs goalkeeper
position_fld_vs_gk = if_else(position == "Goalkeeper",
"Goalkeeper", "Fielder"),
# grouping into 4 groups
`Fielder Grouping` = forcats::fct_collapse(
position,
Forward = c("Center Forward", "Right Winger", "Left Winger"),
Midfielder = c("Defensive Midfielder", "Attacking Midfielder",
"Right Midfielder", "Center Midfielder",
"Left Midfielder"),
Defender = c("Center Back", "Right Fullback", "Left Fullback"),
Goalkeeper = c("Goalkeeper")
)
)
# create size alternatives
size <- mutate_branch(height, weight)
# specify variable inclusion and exclusion
frmls <- formula_branch(
`No Covariate` = redCards ~ skintone,
`Position` = redCards ~ skintone + position_alternative,
`Position + Size` = redCards ~ skintone + position_alternative + size,
`Position + Weight + Height` = redCards ~ skintone + position_alternative + weight + height,
`Size` = redCards ~ skintone + size,
`Weight + Height` = redCards ~ skintone + weight + height,
`Country` = redCards ~ skintone + leagueCountry,
`Position + Country` = redCards ~ skintone + position_alternative + leagueCountry,
`Position + Size + Country` = redCards ~ skintone + position_alternative + size + leagueCountry,
`Position + Weight + Height + Country` = redCards ~ skintone + position_alternative + weight + height + leagueCountry,
`Size + Country` = redCards ~ skintone + size + leagueCountry,
`Weight + Height + Country` = redCards ~ skintone + weight + height + leagueCountry,
)
# remove unnecessary branch combinations
condition_position_1 <- branch_condition(
redCards ~ skintone, position)
condition_position_2 <- branch_condition(
redCards ~ skintone + size, position)
condition_position_3 <- branch_condition(
redCards ~ skintone + size + leagueCountry, position)
condition_position_4 <- branch_condition(
redCards ~ skintone + leagueCountry, position)
condition_position_5 <- branch_condition(
redCards ~ skintone + weight + height, position)
condition_position_6 <- branch_condition(
redCards ~ skintone + weight + height + leagueCountry, position)
# bring the multiverse together and fit
mv <- mverse(soccer) %>%
add_mutate_branch(position_alternative, size) %>%
add_formula_branch(frmls) %>%
add_family_branch(
family_branch(logistic = binomial, name = "fam")
) %>%
add_branch_condition(
condition_position_1, condition_position_2, condition_position_3,
condition_position_4, condition_position_5, condition_position_6
)
glm_mverse(mv)
Systematic syntax
Requires a fewer lines of codes
With mverse
.
.
.
# specify variable inclusion and exclusion
frmls <- formula_branch(
`No Covariate` = redCards ~ skintone,
`Position` = redCards ~ skintone + position_alternative,
`Position + Size` = redCards ~ skintone + position_alternative + size,
`Position + Weight + Height` = redCards ~ skintone + position_alternative + weight + height,
`Size` = redCards ~ skintone + size,
`Weight + Height` = redCards ~ skintone + weight + height,
`Country` = redCards ~ skintone + leagueCountry,
`Position + Country` = redCards ~ skintone + position_alternative + leagueCountry,
`Position + Size + Country` = redCards ~ skintone + position_alternative + size + leagueCountry,
`Position + Weight + Height + Country` = redCards ~ skintone + position_alternative + weight + height + leagueCountry,
`Size + Country` = redCards ~ skintone + size + leagueCountry,
`Weight + Height + Country` = redCards ~ skintone + weight + height + leagueCountry,
)
# remove unnecessary branch combinations
condition_position_1 <- branch_condition(
redCards ~ skintone, position)
condition_position_2 <- branch_condition(
redCards ~ skintone + size, position)
condition_position_3 <- branch_condition(
redCards ~ skintone + size + leagueCountry, position)
condition_position_4 <- branch_condition(
redCards ~ skintone + leagueCountry, position)
condition_position_5 <- branch_condition(
redCards ~ skintone + weight + height, position)
condition_position_6 <- branch_condition(
redCards ~ skintone + weight + height + leagueCountry, position)
# bring the multiverse together and fit
mv <- mverse(soccer) %>%
add_mutate_branch(position_alternative, size) %>%
add_formula_branch(frmls) %>%
add_family_branch(
family_branch(logistic = binomial, name = "fam")
) %>%
add_branch_condition(
condition_position_1, condition_position_2, condition_position_3,
condition_position_4, condition_position_5, condition_position_6
)
glm_mverse(mv)Without mverse
.
.
.
# specify variable inclusion and exclusion
model_1 <- formula(redCards ~ skintone)
model_2 <- formula(redCards ~ skintone + position)
model_3 <- formula(redCards ~ skintone + position_fld_vs_gk)
model_4 <- formula(redCards ~ skintone + position_group)
model_5 <- formula(redCards ~ skintone +
weight)
model_6 <- formula(redCards ~ skintone + position +
weight)
model_7 <- formula(redCards ~ skintone + position_fld_vs_gk +
weight)
model_8 <- formula(redCards ~ skintone + position_group +
weight)
model_9 <- formula(redCards ~ skintone +
height)
model_10 <- formula(redCards ~ skintone + position +
height)
model_11 <- formula(redCards ~ skintone + position_fld_vs_gk +
height)
model_12 <- formula(redCards ~ skintone + position_group +
height)
model_13 <- formula(redCards ~ skintone + weight +
height)
model_14 <- formula(redCards ~ skintone + position +
weight + height)
model_15 <- formula(redCards ~ skintone + position_fld_vs_gk +
weight + height)
model_16 <- formula(redCards ~ skintone + position_group +
weight + height)
model_17 <- formula(redCards ~ skintone +
leagueCountry)
model_18 <- formula(redCards ~ skintone + position +
leagueCountry)
model_19 <- formula(redCards ~ skintone + position_fld_vs_gk +
leagueCountry)
model_20 <- formula(redCards ~ skintone + position_group +
leagueCountry)
model_21 <- formula(redCards ~ skintone +
weight + leagueCountry)
model_22 <- formula(redCards ~ skintone + position +
weight + leagueCountry)
model_23 <- formula(redCards ~ skintone + position_fld_vs_gk +
weight + leagueCountry)
model_24 <- formula(redCards ~ skintone + position_group +
weight + leagueCountry)
model_25 <- formula(redCards ~ skintone +
height + leagueCountry)
model_26 <- formula(redCards ~ skintone + position +
height + leagueCountry)
model_27 <- formula(redCards ~ skintone + position_fld_vs_gk +
height + leagueCountry)
model_28 <- formula(redCards ~ skintone + position_group +
height + leagueCountry)
model_29 <- formula(redCards ~ skintone +
weight + height + leagueCountry)
model_30 <- formula(redCards ~ skintone + position +
weight + height + leagueCountry)
model_31 <- formula(redCards ~ skintone + position_fld_vs_gk +
weight + height + leagueCountry)
model_32 <- formula(redCards ~ skintone + position_group +
weight + height + leagueCountry)
# bring the multiverse together and fit
models <- list(
model_1, model_2, model_3, model_4,
model_5, model_6, model_7, model_8,
model_9, model_10, model_11, model_12,
model_13, model_14, model_15, model_16,
model_17, model_18, model_19, model_20,
model_21, model_22, model_23, model_24,
model_25, model_26, model_27, model_28,
model_29, model_30, model_31, model_32
)
multiverse_fit <- lapply(
models, glm, family = binomial(), data = soccer)Systematic syntax
Automates multiplexing
With mverse
.
.
.
# bring the multiverse together and fit
mv <- mverse(soccer) %>%
add_mutate_branch(position_alternative, size) %>%
add_formula_branch(frmls) %>%
add_family_branch(
family_branch(logistic = binomial, name = "fam")
) %>%
add_branch_condition(
condition_position_1, condition_position_2,
condition_position_3, condition_position_4,
condition_position_5, condition_position_6
)
glm_mverse(mv)Without mverse
.
.
.
# bring the multiverse together and fit
models <- list(
model_1, model_2, model_3, model_4,
model_5, model_6, model_7, model_8,
model_9, model_10, model_11, model_12,
model_13, model_14, model_15, model_16,
model_17, model_18, model_19, model_20,
model_21, model_22, model_23, model_24,
model_25, model_26, model_27, model_28,
model_29, model_30, model_31, model_32
)
multiverse_fit <- lapply(
models, glm, family = binomial, data = soccer)Systematic syntax
library(mverse)
.
.
# data preparation steps
.
.
# create position alternatives
position_alternative <- mutate_branch(
as_is = position, # use position as is
# fielder vs goalkeeper
position_fld_vs_gk = if_else(position == "Goalkeeper",
"Goalkeeper", "Fielder"),
# grouping into 4 groups
`Fielder Grouping` = forcats::fct_collapse(
position,
Forward = c("Center Forward", "Right Winger", "Left Winger"),
Midfielder = c("Defensive Midfielder", "Attacking Midfielder",
"Right Midfielder", "Center Midfielder",
"Left Midfielder"),
Defender = c("Center Back", "Right Fullback", "Left Fullback"),
Goalkeeper = c("Goalkeeper")
)
)
# create size alternatives
size <- mutate_branch(height, weight)
# specify variable inclusion and exclusion
frmls <- formula_branch(
`No Covariate` = redCards ~ skintone,
`Position` = redCards ~ skintone + position_alternative,
`Position + Size` = redCards ~ skintone + position_alternative + size,
`Position + Weight + Height` = redCards ~ skintone + position_alternative + weight + height,
`Size` = redCards ~ skintone + size,
`Weight + Height` = redCards ~ skintone + weight + height,
`Country` = redCards ~ skintone + leagueCountry,
`Position + Country` = redCards ~ skintone + position_alternative + leagueCountry,
`Position + Size + Country` = redCards ~ skintone + position_alternative + size + leagueCountry,
`Position + Weight + Height + Country` = redCards ~ skintone + position_alternative + weight + height + leagueCountry,
`Size + Country` = redCards ~ skintone + size + leagueCountry,
`Weight + Height + Country` = redCards ~ skintone + weight + height + leagueCountry,
)
# remove unnecessary branch combinations
condition_position_1 <- branch_condition(
redCards ~ skintone, position)
condition_position_2 <- branch_condition(
redCards ~ skintone + size, position)
condition_position_3 <- branch_condition(
redCards ~ skintone + size + leagueCountry, position)
condition_position_4 <- branch_condition(
redCards ~ skintone + leagueCountry, position)
condition_position_5 <- branch_condition(
redCards ~ skintone + weight + height, position)
condition_position_6 <- branch_condition(
redCards ~ skintone + weight + height + leagueCountry, position)
# bring the multiverse together and fit
mv <- mverse(soccer) %>%
add_mutate_branch(position_alternative, size) %>%
add_formula_branch(frmls) %>%
add_family_branch(
family_branch(logistic = binomial, name = "fam")
) %>%
add_branch_condition(
condition_position_1, condition_position_2, condition_position_3,
condition_position_4, condition_position_5, condition_position_6
)
glm_mverse(mv)Less prone to errors
compared to copy-and-paste approach
Familiar syntax
Defining alternative options for a variable
With mverse
# create position alternatives
position_alternative <- mutate_branch(
as_is = position, # use position as is
# fielder vs goalkeeper
position_fld_vs_gk = if_else(position == "Goalkeeper",
"Goalkeeper", "Fielder"),
# grouping into 4 groups
`Fielder Grouping` = forcats::fct_collapse(
position,
Forward = c("Center Forward", "Right Winger", "Left Winger"),
Midfielder = c("Defensive Midfielder", "Attacking Midfielder",
"Right Midfielder", "Center Midfielder",
"Left Midfielder"),
Defender = c("Center Back", "Right Fullback", "Left Fullback"),
Goalkeeper = c("Goalkeeper")
)
)
# create size alternatives
size <- mutate_branch(height, weight)Without mverse
# create position alternatives
soccer <- mutate(
soccer,
# fielder vs goalkeeper
position_fld_vs_gk = if_else(position == "Goalkeeper",
"Goalkeeper", "Fielder"),
# grouping into 4 groups
position_group = forcats::fct_collapse(
position,
Forward = c("Center Forward", "Right Winger", "Left Winger"),
Midfielder = c("Defensive Midfielder", "Attacking Midfielder",
"Right Midfielder", "Center Midfielder", "Left Midfielder"),
Defender = c("Center Back", "Right Fullback", "Left Fullback"),
Goalkeeper = c("Goalkeeper")
)
)Familiar syntax
Uses dplyr grammar
With mverse
# create position alternatives
position_alternative <- mutate_branch(
as_is = position, # use position as is
# fielder vs goalkeeper
position_fld_vs_gk = if_else(position == "Goalkeeper",
"Goalkeeper", "Fielder"),
# grouping into 4 groups
`Fielder Grouping` = forcats::fct_collapse(
position,
Forward = c("Center Forward", "Right Winger", "Left Winger"),
Midfielder = c("Defensive Midfielder", "Attacking Midfielder",
"Right Midfielder", "Center Midfielder",
"Left Midfielder"),
Defender = c("Center Back", "Right Fullback", "Left Fullback"),
Goalkeeper = c("Goalkeeper")
)
)
# create size alternatives
size <- mutate_branch(height, weight)Without mverse
# create position alternatives
soccer <- mutate(
soccer,
# fielder vs goalkeeper
position_fld_vs_gk = if_else(position == "Goalkeeper",
"Goalkeeper", "Fielder"),
# grouping into 4 groups
position_group = forcats::fct_collapse(
position,
Forward = c("Center Forward", "Right Winger", "Left Winger"),
Midfielder = c("Defensive Midfielder", "Attacking Midfielder",
"Right Midfielder", "Center Midfielder", "Left Midfielder"),
Defender = c("Center Back", "Right Fullback", "Left Fullback"),
Goalkeeper = c("Goalkeeper")
)
)Familiar syntax
Uses dplyr grammar
With mverse
# create position alternatives
position_alternative <- mutate_branch(
as_is = position, # use position as is
# fielder vs goalkeeper
position_fld_vs_gk = if_else(position == "Goalkeeper",
"Goalkeeper", "Fielder"),
# grouping into 4 groups
`Fielder Grouping` = forcats::fct_collapse(
position,
Forward = c("Center Forward", "Right Winger", "Left Winger"),
Midfielder = c("Defensive Midfielder", "Attacking Midfielder",
"Right Midfielder", "Center Midfielder",
"Left Midfielder"),
Defender = c("Center Back", "Right Fullback", "Left Fullback"),
Goalkeeper = c("Goalkeeper")
)
)
# create size alternatives
size <- mutate_branch(height, weight)Less to learn
for those learning R and tidyverse
Interactive exploration tool
extract()
multiverse_tree()
spec_curve()
Interactive exploration tool
Interactive exploration tool
extract()
multiverse_tree()
spec_curve()
# A tibble: 3,144 × 4
# Groups: universe, skintone [432]
universe skintone position_alternative redCards_prop
<dbl> <dbl> <chr> <dbl>
1 1 1 Attacking Midfielder 0.00229
2 1 1 Center Back 0.00642
3 1 1 Center Forward 0.00267
4 1 1 Center Midfielder 0.00307
5 1 1 Defensive Midfielder 0.00350
6 1 1 Goalkeeper 0.00506
7 1 1 Left Fullback 0.00448
8 1 1 Left Midfielder 0.00192
9 1 1 Left Winger 0.00158
10 1 1 Right Fullback 0.00370
11 1 1 Right Midfielder 0.00196
12 1 1 Right Winger 0.00136
13 1 1.5 Attacking Midfielder 0.00258
14 1 1.5 Center Back 0.00360
15 1 1.5 Center Forward 0.00243
16 1 1.5 Center Midfielder 0.00317
17 1 1.5 Defensive Midfielder 0.00500
18 1 1.5 Goalkeeper 0.00487
19 1 1.5 Left Fullback 0.00504
20 1 1.5 Left Midfielder 0.00333
21 1 1.5 Left Winger 0.00164
22 1 1.5 Right Fullback 0.00294
23 1 1.5 Right Midfielder 0.00421
24 1 1.5 Right Winger 0.00360
25 1 2 Attacking Midfielder 0.00248
26 1 2 Center Back 0.00769
27 1 2 Center Forward 0.00453
28 1 2 Center Midfielder 0.00474
29 1 2 Defensive Midfielder 0.00366
30 1 2 Goalkeeper 0.00372
31 1 2 Left Fullback 0.00318
32 1 2 Left Midfielder 0.00404
33 1 2 Left Winger 0.00373
34 1 2 Right Fullback 0.00356
35 1 2 Right Midfielder 0.00160
36 1 2 Right Winger 0.00443
37 1 2.5 Attacking Midfielder 0.00604
38 1 2.5 Center Back 0.00682
39 1 2.5 Center Forward 0.00494
40 1 2.5 Center Midfielder 0
41 1 2.5 Defensive Midfielder 0.00417
42 1 2.5 Goalkeeper 0.00316
43 1 2.5 Left Fullback 0.00804
44 1 2.5 Left Midfielder 0
45 1 2.5 Left Winger 0
46 1 2.5 Right Fullback 0.00438
47 1 2.5 Right Midfielder 0.00450
48 1 2.5 Right Winger 0.00657
49 1 3 Attacking Midfielder 0.00112
50 1 3 Center Back 0.00771
51 1 3 Center Forward 0.00304
52 1 3 Center Midfielder 0.00580
53 1 3 Defensive Midfielder 0.00681
54 1 3 Goalkeeper 0
55 1 3 Left Fullback 0.00320
56 1 3 Left Midfielder 0.00951
57 1 3 Left Winger 0.00691
58 1 3 Right Fullback 0.00667
59 1 3 Right Midfielder 0.00259
60 1 3 Right Winger 0.00511
61 1 3.5 Attacking Midfielder 0.002
62 1 3.5 Center Back 0.00395
63 1 3.5 Center Forward 0
64 1 3.5 Defensive Midfielder 0.00441
65 1 3.5 Goalkeeper 0
66 1 3.5 Left Fullback 0.00402
67 1 3.5 Left Midfielder 0
68 1 3.5 Left Winger 0
69 1 3.5 Right Fullback 0
70 1 3.5 Right Winger 0.00862
71 1 4 Attacking Midfielder 0.00183
72 1 4 Center Back 0.00587
73 1 4 Center Forward 0.00538
74 1 4 Center Midfielder 0.00639
75 1 4 Defensive Midfielder 0.00493
76 1 4 Goalkeeper 0.00463
77 1 4 Left Fullback 0.00375
78 1 4 Left Midfielder 0.00913
79 1 4 Left Winger 0.000892
80 1 4 Right Fullback 0.00519
81 1 4 Right Midfielder 0.00876
82 1 4 Right Winger 0.00458
83 1 4.5 Center Back 0.00549
84 1 4.5 Center Forward 0.00470
85 1 4.5 Defensive Midfielder 0.00822
86 1 4.5 Goalkeeper 0.00196
87 1 4.5 Left Fullback 0.00937
88 1 4.5 Left Midfielder 0
89 1 4.5 Left Winger 0.00588
90 1 4.5 Right Fullback 0.0225
91 1 4.5 Right Midfielder 0
92 1 4.5 Right Winger 0.00103
93 1 5 Attacking Midfielder 0
94 1 5 Center Back 0.00781
95 1 5 Center Forward 0.00382
96 1 5 Center Midfielder 0.00251
97 1 5 Defensive Midfielder 0.00365
98 1 5 Goalkeeper 0.00870
99 1 5 Left Fullback 0.0113
100 1 5 Left Midfielder 0.00680
101 1 5 Left Winger 0.00265
102 1 5 Right Fullback 0.00242
103 1 5 Right Midfielder 0.00926
104 1 5 Right Winger 0.00299
105 2 1 Attacking Midfielder 0.00229
106 2 1 Center Back 0.00642
107 2 1 Center Forward 0.00267
108 2 1 Center Midfielder 0.00307
109 2 1 Defensive Midfielder 0.00350
110 2 1 Goalkeeper 0.00506
111 2 1 Left Fullback 0.00448
112 2 1 Left Midfielder 0.00192
113 2 1 Left Winger 0.00158
114 2 1 Right Fullback 0.00370
115 2 1 Right Midfielder 0.00196
116 2 1 Right Winger 0.00136
117 2 1.5 Attacking Midfielder 0.00258
118 2 1.5 Center Back 0.00360
119 2 1.5 Center Forward 0.00243
120 2 1.5 Center Midfielder 0.00317
121 2 1.5 Defensive Midfielder 0.00500
122 2 1.5 Goalkeeper 0.00487
123 2 1.5 Left Fullback 0.00504
124 2 1.5 Left Midfielder 0.00333
125 2 1.5 Left Winger 0.00164
126 2 1.5 Right Fullback 0.00294
127 2 1.5 Right Midfielder 0.00421
128 2 1.5 Right Winger 0.00360
129 2 2 Attacking Midfielder 0.00248
130 2 2 Center Back 0.00769
131 2 2 Center Forward 0.00453
132 2 2 Center Midfielder 0.00474
133 2 2 Defensive Midfielder 0.00366
134 2 2 Goalkeeper 0.00372
135 2 2 Left Fullback 0.00318
136 2 2 Left Midfielder 0.00404
137 2 2 Left Winger 0.00373
138 2 2 Right Fullback 0.00356
139 2 2 Right Midfielder 0.00160
140 2 2 Right Winger 0.00443
141 2 2.5 Attacking Midfielder 0.00604
142 2 2.5 Center Back 0.00682
143 2 2.5 Center Forward 0.00494
144 2 2.5 Center Midfielder 0
145 2 2.5 Defensive Midfielder 0.00417
146 2 2.5 Goalkeeper 0.00316
147 2 2.5 Left Fullback 0.00804
148 2 2.5 Left Midfielder 0
149 2 2.5 Left Winger 0
150 2 2.5 Right Fullback 0.00438
151 2 2.5 Right Midfielder 0.00450
152 2 2.5 Right Winger 0.00657
153 2 3 Attacking Midfielder 0.00112
154 2 3 Center Back 0.00771
155 2 3 Center Forward 0.00304
156 2 3 Center Midfielder 0.00580
157 2 3 Defensive Midfielder 0.00681
158 2 3 Goalkeeper 0
159 2 3 Left Fullback 0.00320
160 2 3 Left Midfielder 0.00951
161 2 3 Left Winger 0.00691
162 2 3 Right Fullback 0.00667
163 2 3 Right Midfielder 0.00259
164 2 3 Right Winger 0.00511
165 2 3.5 Attacking Midfielder 0.002
166 2 3.5 Center Back 0.00395
167 2 3.5 Center Forward 0
168 2 3.5 Defensive Midfielder 0.00441
169 2 3.5 Goalkeeper 0
170 2 3.5 Left Fullback 0.00402
171 2 3.5 Left Midfielder 0
172 2 3.5 Left Winger 0
173 2 3.5 Right Fullback 0
174 2 3.5 Right Winger 0.00862
175 2 4 Attacking Midfielder 0.00183
176 2 4 Center Back 0.00587
177 2 4 Center Forward 0.00538
178 2 4 Center Midfielder 0.00639
179 2 4 Defensive Midfielder 0.00493
180 2 4 Goalkeeper 0.00463
181 2 4 Left Fullback 0.00375
182 2 4 Left Midfielder 0.00913
183 2 4 Left Winger 0.000892
184 2 4 Right Fullback 0.00519
185 2 4 Right Midfielder 0.00876
186 2 4 Right Winger 0.00458
187 2 4.5 Center Back 0.00549
188 2 4.5 Center Forward 0.00470
189 2 4.5 Defensive Midfielder 0.00822
190 2 4.5 Goalkeeper 0.00196
191 2 4.5 Left Fullback 0.00937
192 2 4.5 Left Midfielder 0
193 2 4.5 Left Winger 0.00588
194 2 4.5 Right Fullback 0.0225
195 2 4.5 Right Midfielder 0
196 2 4.5 Right Winger 0.00103
197 2 5 Attacking Midfielder 0
198 2 5 Center Back 0.00781
199 2 5 Center Forward 0.00382
200 2 5 Center Midfielder 0.00251
201 2 5 Defensive Midfielder 0.00365
202 2 5 Goalkeeper 0.00870
203 2 5 Left Fullback 0.0113
204 2 5 Left Midfielder 0.00680
205 2 5 Left Winger 0.00265
206 2 5 Right Fullback 0.00242
207 2 5 Right Midfielder 0.00926
208 2 5 Right Winger 0.00299
209 3 1 Attacking Midfielder 0.00229
210 3 1 Center Back 0.00642
211 3 1 Center Forward 0.00267
212 3 1 Center Midfielder 0.00307
213 3 1 Defensive Midfielder 0.00350
214 3 1 Goalkeeper 0.00506
215 3 1 Left Fullback 0.00448
216 3 1 Left Midfielder 0.00192
217 3 1 Left Winger 0.00158
218 3 1 Right Fullback 0.00370
219 3 1 Right Midfielder 0.00196
220 3 1 Right Winger 0.00136
221 3 1.5 Attacking Midfielder 0.00258
222 3 1.5 Center Back 0.00360
223 3 1.5 Center Forward 0.00243
224 3 1.5 Center Midfielder 0.00317
225 3 1.5 Defensive Midfielder 0.00500
226 3 1.5 Goalkeeper 0.00487
227 3 1.5 Left Fullback 0.00504
228 3 1.5 Left Midfielder 0.00333
229 3 1.5 Left Winger 0.00164
230 3 1.5 Right Fullback 0.00294
231 3 1.5 Right Midfielder 0.00421
232 3 1.5 Right Winger 0.00360
233 3 2 Attacking Midfielder 0.00248
234 3 2 Center Back 0.00769
235 3 2 Center Forward 0.00453
236 3 2 Center Midfielder 0.00474
237 3 2 Defensive Midfielder 0.00366
238 3 2 Goalkeeper 0.00372
239 3 2 Left Fullback 0.00318
240 3 2 Left Midfielder 0.00404
241 3 2 Left Winger 0.00373
242 3 2 Right Fullback 0.00356
243 3 2 Right Midfielder 0.00160
244 3 2 Right Winger 0.00443
245 3 2.5 Attacking Midfielder 0.00604
246 3 2.5 Center Back 0.00682
247 3 2.5 Center Forward 0.00494
248 3 2.5 Center Midfielder 0
249 3 2.5 Defensive Midfielder 0.00417
250 3 2.5 Goalkeeper 0.00316
251 3 2.5 Left Fullback 0.00804
252 3 2.5 Left Midfielder 0
253 3 2.5 Left Winger 0
254 3 2.5 Right Fullback 0.00438
255 3 2.5 Right Midfielder 0.00450
256 3 2.5 Right Winger 0.00657
257 3 3 Attacking Midfielder 0.00112
258 3 3 Center Back 0.00771
259 3 3 Center Forward 0.00304
260 3 3 Center Midfielder 0.00580
261 3 3 Defensive Midfielder 0.00681
262 3 3 Goalkeeper 0
263 3 3 Left Fullback 0.00320
264 3 3 Left Midfielder 0.00951
265 3 3 Left Winger 0.00691
266 3 3 Right Fullback 0.00667
267 3 3 Right Midfielder 0.00259
268 3 3 Right Winger 0.00511
269 3 3.5 Attacking Midfielder 0.002
270 3 3.5 Center Back 0.00395
271 3 3.5 Center Forward 0
272 3 3.5 Defensive Midfielder 0.00441
273 3 3.5 Goalkeeper 0
274 3 3.5 Left Fullback 0.00402
275 3 3.5 Left Midfielder 0
276 3 3.5 Left Winger 0
277 3 3.5 Right Fullback 0
278 3 3.5 Right Winger 0.00862
279 3 4 Attacking Midfielder 0.00183
280 3 4 Center Back 0.00587
281 3 4 Center Forward 0.00538
282 3 4 Center Midfielder 0.00639
283 3 4 Defensive Midfielder 0.00493
284 3 4 Goalkeeper 0.00463
285 3 4 Left Fullback 0.00375
286 3 4 Left Midfielder 0.00913
287 3 4 Left Winger 0.000892
288 3 4 Right Fullback 0.00519
289 3 4 Right Midfielder 0.00876
290 3 4 Right Winger 0.00458
291 3 4.5 Center Back 0.00549
292 3 4.5 Center Forward 0.00470
293 3 4.5 Defensive Midfielder 0.00822
294 3 4.5 Goalkeeper 0.00196
295 3 4.5 Left Fullback 0.00937
296 3 4.5 Left Midfielder 0
297 3 4.5 Left Winger 0.00588
298 3 4.5 Right Fullback 0.0225
299 3 4.5 Right Midfielder 0
300 3 4.5 Right Winger 0.00103
301 3 5 Attacking Midfielder 0
302 3 5 Center Back 0.00781
303 3 5 Center Forward 0.00382
304 3 5 Center Midfielder 0.00251
305 3 5 Defensive Midfielder 0.00365
306 3 5 Goalkeeper 0.00870
307 3 5 Left Fullback 0.0113
308 3 5 Left Midfielder 0.00680
309 3 5 Left Winger 0.00265
310 3 5 Right Fullback 0.00242
311 3 5 Right Midfielder 0.00926
312 3 5 Right Winger 0.00299
313 4 1 Attacking Midfielder 0.00229
314 4 1 Center Back 0.00642
315 4 1 Center Forward 0.00267
316 4 1 Center Midfielder 0.00307
317 4 1 Defensive Midfielder 0.00350
318 4 1 Goalkeeper 0.00506
319 4 1 Left Fullback 0.00448
320 4 1 Left Midfielder 0.00192
321 4 1 Left Winger 0.00158
322 4 1 Right Fullback 0.00370
323 4 1 Right Midfielder 0.00196
324 4 1 Right Winger 0.00136
325 4 1.5 Attacking Midfielder 0.00258
326 4 1.5 Center Back 0.00360
327 4 1.5 Center Forward 0.00243
328 4 1.5 Center Midfielder 0.00317
329 4 1.5 Defensive Midfielder 0.00500
330 4 1.5 Goalkeeper 0.00487
331 4 1.5 Left Fullback 0.00504
332 4 1.5 Left Midfielder 0.00333
333 4 1.5 Left Winger 0.00164
334 4 1.5 Right Fullback 0.00294
335 4 1.5 Right Midfielder 0.00421
336 4 1.5 Right Winger 0.00360
337 4 2 Attacking Midfielder 0.00248
338 4 2 Center Back 0.00769
339 4 2 Center Forward 0.00453
340 4 2 Center Midfielder 0.00474
341 4 2 Defensive Midfielder 0.00366
342 4 2 Goalkeeper 0.00372
343 4 2 Left Fullback 0.00318
344 4 2 Left Midfielder 0.00404
345 4 2 Left Winger 0.00373
346 4 2 Right Fullback 0.00356
347 4 2 Right Midfielder 0.00160
348 4 2 Right Winger 0.00443
349 4 2.5 Attacking Midfielder 0.00604
350 4 2.5 Center Back 0.00682
351 4 2.5 Center Forward 0.00494
352 4 2.5 Center Midfielder 0
353 4 2.5 Defensive Midfielder 0.00417
354 4 2.5 Goalkeeper 0.00316
355 4 2.5 Left Fullback 0.00804
356 4 2.5 Left Midfielder 0
357 4 2.5 Left Winger 0
358 4 2.5 Right Fullback 0.00438
359 4 2.5 Right Midfielder 0.00450
360 4 2.5 Right Winger 0.00657
361 4 3 Attacking Midfielder 0.00112
362 4 3 Center Back 0.00771
363 4 3 Center Forward 0.00304
364 4 3 Center Midfielder 0.00580
365 4 3 Defensive Midfielder 0.00681
366 4 3 Goalkeeper 0
367 4 3 Left Fullback 0.00320
368 4 3 Left Midfielder 0.00951
369 4 3 Left Winger 0.00691
370 4 3 Right Fullback 0.00667
371 4 3 Right Midfielder 0.00259
372 4 3 Right Winger 0.00511
373 4 3.5 Attacking Midfielder 0.002
374 4 3.5 Center Back 0.00395
375 4 3.5 Center Forward 0
376 4 3.5 Defensive Midfielder 0.00441
377 4 3.5 Goalkeeper 0
378 4 3.5 Left Fullback 0.00402
379 4 3.5 Left Midfielder 0
380 4 3.5 Left Winger 0
381 4 3.5 Right Fullback 0
382 4 3.5 Right Winger 0.00862
383 4 4 Attacking Midfielder 0.00183
384 4 4 Center Back 0.00587
385 4 4 Center Forward 0.00538
386 4 4 Center Midfielder 0.00639
387 4 4 Defensive Midfielder 0.00493
388 4 4 Goalkeeper 0.00463
389 4 4 Left Fullback 0.00375
390 4 4 Left Midfielder 0.00913
391 4 4 Left Winger 0.000892
392 4 4 Right Fullback 0.00519
393 4 4 Right Midfielder 0.00876
394 4 4 Right Winger 0.00458
395 4 4.5 Center Back 0.00549
396 4 4.5 Center Forward 0.00470
397 4 4.5 Defensive Midfielder 0.00822
398 4 4.5 Goalkeeper 0.00196
399 4 4.5 Left Fullback 0.00937
400 4 4.5 Left Midfielder 0
401 4 4.5 Left Winger 0.00588
402 4 4.5 Right Fullback 0.0225
403 4 4.5 Right Midfielder 0
404 4 4.5 Right Winger 0.00103
405 4 5 Attacking Midfielder 0
406 4 5 Center Back 0.00781
407 4 5 Center Forward 0.00382
408 4 5 Center Midfielder 0.00251
409 4 5 Defensive Midfielder 0.00365
410 4 5 Goalkeeper 0.00870
411 4 5 Left Fullback 0.0113
412 4 5 Left Midfielder 0.00680
413 4 5 Left Winger 0.00265
414 4 5 Right Fullback 0.00242
415 4 5 Right Midfielder 0.00926
416 4 5 Right Winger 0.00299
417 5 1 Attacking Midfielder 0.00229
418 5 1 Center Back 0.00642
419 5 1 Center Forward 0.00267
420 5 1 Center Midfielder 0.00307
421 5 1 Defensive Midfielder 0.00350
422 5 1 Goalkeeper 0.00506
423 5 1 Left Fullback 0.00448
424 5 1 Left Midfielder 0.00192
425 5 1 Left Winger 0.00158
426 5 1 Right Fullback 0.00370
427 5 1 Right Midfielder 0.00196
428 5 1 Right Winger 0.00136
429 5 1.5 Attacking Midfielder 0.00258
430 5 1.5 Center Back 0.00360
431 5 1.5 Center Forward 0.00243
432 5 1.5 Center Midfielder 0.00317
433 5 1.5 Defensive Midfielder 0.00500
434 5 1.5 Goalkeeper 0.00487
435 5 1.5 Left Fullback 0.00504
436 5 1.5 Left Midfielder 0.00333
437 5 1.5 Left Winger 0.00164
438 5 1.5 Right Fullback 0.00294
439 5 1.5 Right Midfielder 0.00421
440 5 1.5 Right Winger 0.00360
441 5 2 Attacking Midfielder 0.00248
442 5 2 Center Back 0.00769
443 5 2 Center Forward 0.00453
444 5 2 Center Midfielder 0.00474
445 5 2 Defensive Midfielder 0.00366
446 5 2 Goalkeeper 0.00372
447 5 2 Left Fullback 0.00318
448 5 2 Left Midfielder 0.00404
449 5 2 Left Winger 0.00373
450 5 2 Right Fullback 0.00356
451 5 2 Right Midfielder 0.00160
452 5 2 Right Winger 0.00443
453 5 2.5 Attacking Midfielder 0.00604
454 5 2.5 Center Back 0.00682
455 5 2.5 Center Forward 0.00494
456 5 2.5 Center Midfielder 0
457 5 2.5 Defensive Midfielder 0.00417
458 5 2.5 Goalkeeper 0.00316
459 5 2.5 Left Fullback 0.00804
460 5 2.5 Left Midfielder 0
461 5 2.5 Left Winger 0
462 5 2.5 Right Fullback 0.00438
463 5 2.5 Right Midfielder 0.00450
464 5 2.5 Right Winger 0.00657
465 5 3 Attacking Midfielder 0.00112
466 5 3 Center Back 0.00771
467 5 3 Center Forward 0.00304
468 5 3 Center Midfielder 0.00580
469 5 3 Defensive Midfielder 0.00681
470 5 3 Goalkeeper 0
471 5 3 Left Fullback 0.00320
472 5 3 Left Midfielder 0.00951
473 5 3 Left Winger 0.00691
474 5 3 Right Fullback 0.00667
475 5 3 Right Midfielder 0.00259
476 5 3 Right Winger 0.00511
477 5 3.5 Attacking Midfielder 0.002
478 5 3.5 Center Back 0.00395
479 5 3.5 Center Forward 0
480 5 3.5 Defensive Midfielder 0.00441
481 5 3.5 Goalkeeper 0
482 5 3.5 Left Fullback 0.00402
483 5 3.5 Left Midfielder 0
484 5 3.5 Left Winger 0
485 5 3.5 Right Fullback 0
486 5 3.5 Right Winger 0.00862
487 5 4 Attacking Midfielder 0.00183
488 5 4 Center Back 0.00587
489 5 4 Center Forward 0.00538
490 5 4 Center Midfielder 0.00639
491 5 4 Defensive Midfielder 0.00493
492 5 4 Goalkeeper 0.00463
493 5 4 Left Fullback 0.00375
494 5 4 Left Midfielder 0.00913
495 5 4 Left Winger 0.000892
496 5 4 Right Fullback 0.00519
497 5 4 Right Midfielder 0.00876
498 5 4 Right Winger 0.00458
499 5 4.5 Center Back 0.00549
500 5 4.5 Center Forward 0.00470
501 5 4.5 Defensive Midfielder 0.00822
502 5 4.5 Goalkeeper 0.00196
503 5 4.5 Left Fullback 0.00937
504 5 4.5 Left Midfielder 0
505 5 4.5 Left Winger 0.00588
506 5 4.5 Right Fullback 0.0225
507 5 4.5 Right Midfielder 0
508 5 4.5 Right Winger 0.00103
509 5 5 Attacking Midfielder 0
510 5 5 Center Back 0.00781
511 5 5 Center Forward 0.00382
512 5 5 Center Midfielder 0.00251
513 5 5 Defensive Midfielder 0.00365
514 5 5 Goalkeeper 0.00870
515 5 5 Left Fullback 0.0113
516 5 5 Left Midfielder 0.00680
517 5 5 Left Winger 0.00265
518 5 5 Right Fullback 0.00242
519 5 5 Right Midfielder 0.00926
520 5 5 Right Winger 0.00299
521 6 1 Attacking Midfielder 0.00229
522 6 1 Center Back 0.00642
523 6 1 Center Forward 0.00267
524 6 1 Center Midfielder 0.00307
525 6 1 Defensive Midfielder 0.00350
526 6 1 Goalkeeper 0.00506
527 6 1 Left Fullback 0.00448
528 6 1 Left Midfielder 0.00192
529 6 1 Left Winger 0.00158
530 6 1 Right Fullback 0.00370
531 6 1 Right Midfielder 0.00196
532 6 1 Right Winger 0.00136
533 6 1.5 Attacking Midfielder 0.00258
534 6 1.5 Center Back 0.00360
535 6 1.5 Center Forward 0.00243
536 6 1.5 Center Midfielder 0.00317
537 6 1.5 Defensive Midfielder 0.00500
538 6 1.5 Goalkeeper 0.00487
539 6 1.5 Left Fullback 0.00504
540 6 1.5 Left Midfielder 0.00333
541 6 1.5 Left Winger 0.00164
542 6 1.5 Right Fullback 0.00294
543 6 1.5 Right Midfielder 0.00421
544 6 1.5 Right Winger 0.00360
545 6 2 Attacking Midfielder 0.00248
546 6 2 Center Back 0.00769
547 6 2 Center Forward 0.00453
548 6 2 Center Midfielder 0.00474
549 6 2 Defensive Midfielder 0.00366
550 6 2 Goalkeeper 0.00372
551 6 2 Left Fullback 0.00318
552 6 2 Left Midfielder 0.00404
553 6 2 Left Winger 0.00373
554 6 2 Right Fullback 0.00356
555 6 2 Right Midfielder 0.00160
556 6 2 Right Winger 0.00443
557 6 2.5 Attacking Midfielder 0.00604
558 6 2.5 Center Back 0.00682
559 6 2.5 Center Forward 0.00494
560 6 2.5 Center Midfielder 0
561 6 2.5 Defensive Midfielder 0.00417
562 6 2.5 Goalkeeper 0.00316
563 6 2.5 Left Fullback 0.00804
564 6 2.5 Left Midfielder 0
565 6 2.5 Left Winger 0
566 6 2.5 Right Fullback 0.00438
567 6 2.5 Right Midfielder 0.00450
568 6 2.5 Right Winger 0.00657
569 6 3 Attacking Midfielder 0.00112
570 6 3 Center Back 0.00771
571 6 3 Center Forward 0.00304
572 6 3 Center Midfielder 0.00580
573 6 3 Defensive Midfielder 0.00681
574 6 3 Goalkeeper 0
575 6 3 Left Fullback 0.00320
576 6 3 Left Midfielder 0.00951
577 6 3 Left Winger 0.00691
578 6 3 Right Fullback 0.00667
579 6 3 Right Midfielder 0.00259
580 6 3 Right Winger 0.00511
581 6 3.5 Attacking Midfielder 0.002
582 6 3.5 Center Back 0.00395
583 6 3.5 Center Forward 0
584 6 3.5 Defensive Midfielder 0.00441
585 6 3.5 Goalkeeper 0
586 6 3.5 Left Fullback 0.00402
587 6 3.5 Left Midfielder 0
588 6 3.5 Left Winger 0
589 6 3.5 Right Fullback 0
590 6 3.5 Right Winger 0.00862
591 6 4 Attacking Midfielder 0.00183
592 6 4 Center Back 0.00587
593 6 4 Center Forward 0.00538
594 6 4 Center Midfielder 0.00639
595 6 4 Defensive Midfielder 0.00493
596 6 4 Goalkeeper 0.00463
597 6 4 Left Fullback 0.00375
598 6 4 Left Midfielder 0.00913
599 6 4 Left Winger 0.000892
600 6 4 Right Fullback 0.00519
601 6 4 Right Midfielder 0.00876
602 6 4 Right Winger 0.00458
603 6 4.5 Center Back 0.00549
604 6 4.5 Center Forward 0.00470
605 6 4.5 Defensive Midfielder 0.00822
606 6 4.5 Goalkeeper 0.00196
607 6 4.5 Left Fullback 0.00937
608 6 4.5 Left Midfielder 0
609 6 4.5 Left Winger 0.00588
610 6 4.5 Right Fullback 0.0225
611 6 4.5 Right Midfielder 0
612 6 4.5 Right Winger 0.00103
613 6 5 Attacking Midfielder 0
614 6 5 Center Back 0.00781
615 6 5 Center Forward 0.00382
616 6 5 Center Midfielder 0.00251
617 6 5 Defensive Midfielder 0.00365
618 6 5 Goalkeeper 0.00870
619 6 5 Left Fullback 0.0113
620 6 5 Left Midfielder 0.00680
621 6 5 Left Winger 0.00265
622 6 5 Right Fullback 0.00242
623 6 5 Right Midfielder 0.00926
624 6 5 Right Winger 0.00299
625 7 1 Attacking Midfielder 0.00229
626 7 1 Center Back 0.00642
627 7 1 Center Forward 0.00267
628 7 1 Center Midfielder 0.00307
629 7 1 Defensive Midfielder 0.00350
630 7 1 Goalkeeper 0.00506
631 7 1 Left Fullback 0.00448
632 7 1 Left Midfielder 0.00192
633 7 1 Left Winger 0.00158
634 7 1 Right Fullback 0.00370
635 7 1 Right Midfielder 0.00196
636 7 1 Right Winger 0.00136
637 7 1.5 Attacking Midfielder 0.00258
638 7 1.5 Center Back 0.00360
639 7 1.5 Center Forward 0.00243
640 7 1.5 Center Midfielder 0.00317
641 7 1.5 Defensive Midfielder 0.00500
642 7 1.5 Goalkeeper 0.00487
643 7 1.5 Left Fullback 0.00504
644 7 1.5 Left Midfielder 0.00333
645 7 1.5 Left Winger 0.00164
646 7 1.5 Right Fullback 0.00294
647 7 1.5 Right Midfielder 0.00421
648 7 1.5 Right Winger 0.00360
649 7 2 Attacking Midfielder 0.00248
650 7 2 Center Back 0.00769
651 7 2 Center Forward 0.00453
652 7 2 Center Midfielder 0.00474
653 7 2 Defensive Midfielder 0.00366
654 7 2 Goalkeeper 0.00372
655 7 2 Left Fullback 0.00318
656 7 2 Left Midfielder 0.00404
657 7 2 Left Winger 0.00373
658 7 2 Right Fullback 0.00356
659 7 2 Right Midfielder 0.00160
660 7 2 Right Winger 0.00443
661 7 2.5 Attacking Midfielder 0.00604
662 7 2.5 Center Back 0.00682
663 7 2.5 Center Forward 0.00494
664 7 2.5 Center Midfielder 0
665 7 2.5 Defensive Midfielder 0.00417
666 7 2.5 Goalkeeper 0.00316
667 7 2.5 Left Fullback 0.00804
668 7 2.5 Left Midfielder 0
669 7 2.5 Left Winger 0
670 7 2.5 Right Fullback 0.00438
671 7 2.5 Right Midfielder 0.00450
672 7 2.5 Right Winger 0.00657
673 7 3 Attacking Midfielder 0.00112
674 7 3 Center Back 0.00771
675 7 3 Center Forward 0.00304
676 7 3 Center Midfielder 0.00580
677 7 3 Defensive Midfielder 0.00681
678 7 3 Goalkeeper 0
679 7 3 Left Fullback 0.00320
680 7 3 Left Midfielder 0.00951
681 7 3 Left Winger 0.00691
682 7 3 Right Fullback 0.00667
683 7 3 Right Midfielder 0.00259
684 7 3 Right Winger 0.00511
685 7 3.5 Attacking Midfielder 0.002
686 7 3.5 Center Back 0.00395
687 7 3.5 Center Forward 0
688 7 3.5 Defensive Midfielder 0.00441
689 7 3.5 Goalkeeper 0
690 7 3.5 Left Fullback 0.00402
691 7 3.5 Left Midfielder 0
692 7 3.5 Left Winger 0
693 7 3.5 Right Fullback 0
694 7 3.5 Right Winger 0.00862
695 7 4 Attacking Midfielder 0.00183
696 7 4 Center Back 0.00587
697 7 4 Center Forward 0.00538
698 7 4 Center Midfielder 0.00639
699 7 4 Defensive Midfielder 0.00493
700 7 4 Goalkeeper 0.00463
701 7 4 Left Fullback 0.00375
702 7 4 Left Midfielder 0.00913
703 7 4 Left Winger 0.000892
704 7 4 Right Fullback 0.00519
705 7 4 Right Midfielder 0.00876
706 7 4 Right Winger 0.00458
707 7 4.5 Center Back 0.00549
708 7 4.5 Center Forward 0.00470
709 7 4.5 Defensive Midfielder 0.00822
710 7 4.5 Goalkeeper 0.00196
711 7 4.5 Left Fullback 0.00937
712 7 4.5 Left Midfielder 0
713 7 4.5 Left Winger 0.00588
714 7 4.5 Right Fullback 0.0225
715 7 4.5 Right Midfielder 0
716 7 4.5 Right Winger 0.00103
717 7 5 Attacking Midfielder 0
718 7 5 Center Back 0.00781
719 7 5 Center Forward 0.00382
720 7 5 Center Midfielder 0.00251
721 7 5 Defensive Midfielder 0.00365
722 7 5 Goalkeeper 0.00870
723 7 5 Left Fullback 0.0113
724 7 5 Left Midfielder 0.00680
725 7 5 Left Winger 0.00265
726 7 5 Right Fullback 0.00242
727 7 5 Right Midfielder 0.00926
728 7 5 Right Winger 0.00299
729 8 1 Attacking Midfielder 0.00229
730 8 1 Center Back 0.00642
731 8 1 Center Forward 0.00267
732 8 1 Center Midfielder 0.00307
733 8 1 Defensive Midfielder 0.00350
734 8 1 Goalkeeper 0.00506
735 8 1 Left Fullback 0.00448
736 8 1 Left Midfielder 0.00192
737 8 1 Left Winger 0.00158
738 8 1 Right Fullback 0.00370
739 8 1 Right Midfielder 0.00196
740 8 1 Right Winger 0.00136
741 8 1.5 Attacking Midfielder 0.00258
742 8 1.5 Center Back 0.00360
743 8 1.5 Center Forward 0.00243
744 8 1.5 Center Midfielder 0.00317
745 8 1.5 Defensive Midfielder 0.00500
746 8 1.5 Goalkeeper 0.00487
747 8 1.5 Left Fullback 0.00504
748 8 1.5 Left Midfielder 0.00333
749 8 1.5 Left Winger 0.00164
750 8 1.5 Right Fullback 0.00294
751 8 1.5 Right Midfielder 0.00421
752 8 1.5 Right Winger 0.00360
753 8 2 Attacking Midfielder 0.00248
754 8 2 Center Back 0.00769
755 8 2 Center Forward 0.00453
756 8 2 Center Midfielder 0.00474
757 8 2 Defensive Midfielder 0.00366
758 8 2 Goalkeeper 0.00372
759 8 2 Left Fullback 0.00318
760 8 2 Left Midfielder 0.00404
761 8 2 Left Winger 0.00373
762 8 2 Right Fullback 0.00356
763 8 2 Right Midfielder 0.00160
764 8 2 Right Winger 0.00443
765 8 2.5 Attacking Midfielder 0.00604
766 8 2.5 Center Back 0.00682
767 8 2.5 Center Forward 0.00494
768 8 2.5 Center Midfielder 0
769 8 2.5 Defensive Midfielder 0.00417
770 8 2.5 Goalkeeper 0.00316
771 8 2.5 Left Fullback 0.00804
772 8 2.5 Left Midfielder 0
773 8 2.5 Left Winger 0
774 8 2.5 Right Fullback 0.00438
775 8 2.5 Right Midfielder 0.00450
776 8 2.5 Right Winger 0.00657
777 8 3 Attacking Midfielder 0.00112
778 8 3 Center Back 0.00771
779 8 3 Center Forward 0.00304
780 8 3 Center Midfielder 0.00580
781 8 3 Defensive Midfielder 0.00681
782 8 3 Goalkeeper 0
783 8 3 Left Fullback 0.00320
784 8 3 Left Midfielder 0.00951
785 8 3 Left Winger 0.00691
786 8 3 Right Fullback 0.00667
787 8 3 Right Midfielder 0.00259
788 8 3 Right Winger 0.00511
789 8 3.5 Attacking Midfielder 0.002
790 8 3.5 Center Back 0.00395
791 8 3.5 Center Forward 0
792 8 3.5 Defensive Midfielder 0.00441
793 8 3.5 Goalkeeper 0
794 8 3.5 Left Fullback 0.00402
795 8 3.5 Left Midfielder 0
796 8 3.5 Left Winger 0
797 8 3.5 Right Fullback 0
798 8 3.5 Right Winger 0.00862
799 8 4 Attacking Midfielder 0.00183
800 8 4 Center Back 0.00587
801 8 4 Center Forward 0.00538
802 8 4 Center Midfielder 0.00639
803 8 4 Defensive Midfielder 0.00493
804 8 4 Goalkeeper 0.00463
805 8 4 Left Fullback 0.00375
806 8 4 Left Midfielder 0.00913
807 8 4 Left Winger 0.000892
808 8 4 Right Fullback 0.00519
809 8 4 Right Midfielder 0.00876
810 8 4 Right Winger 0.00458
811 8 4.5 Center Back 0.00549
812 8 4.5 Center Forward 0.00470
813 8 4.5 Defensive Midfielder 0.00822
814 8 4.5 Goalkeeper 0.00196
815 8 4.5 Left Fullback 0.00937
816 8 4.5 Left Midfielder 0
817 8 4.5 Left Winger 0.00588
818 8 4.5 Right Fullback 0.0225
819 8 4.5 Right Midfielder 0
820 8 4.5 Right Winger 0.00103
821 8 5 Attacking Midfielder 0
822 8 5 Center Back 0.00781
823 8 5 Center Forward 0.00382
824 8 5 Center Midfielder 0.00251
825 8 5 Defensive Midfielder 0.00365
826 8 5 Goalkeeper 0.00870
827 8 5 Left Fullback 0.0113
828 8 5 Left Midfielder 0.00680
829 8 5 Left Winger 0.00265
830 8 5 Right Fullback 0.00242
831 8 5 Right Midfielder 0.00926
832 8 5 Right Winger 0.00299
833 9 1 Attacking Midfielder 0.00229
834 9 1 Center Back 0.00642
835 9 1 Center Forward 0.00267
836 9 1 Center Midfielder 0.00307
837 9 1 Defensive Midfielder 0.00350
838 9 1 Goalkeeper 0.00506
839 9 1 Left Fullback 0.00448
840 9 1 Left Midfielder 0.00192
841 9 1 Left Winger 0.00158
842 9 1 Right Fullback 0.00370
843 9 1 Right Midfielder 0.00196
844 9 1 Right Winger 0.00136
845 9 1.5 Attacking Midfielder 0.00258
846 9 1.5 Center Back 0.00360
847 9 1.5 Center Forward 0.00243
848 9 1.5 Center Midfielder 0.00317
849 9 1.5 Defensive Midfielder 0.00500
850 9 1.5 Goalkeeper 0.00487
851 9 1.5 Left Fullback 0.00504
852 9 1.5 Left Midfielder 0.00333
853 9 1.5 Left Winger 0.00164
854 9 1.5 Right Fullback 0.00294
855 9 1.5 Right Midfielder 0.00421
856 9 1.5 Right Winger 0.00360
857 9 2 Attacking Midfielder 0.00248
858 9 2 Center Back 0.00769
859 9 2 Center Forward 0.00453
860 9 2 Center Midfielder 0.00474
861 9 2 Defensive Midfielder 0.00366
862 9 2 Goalkeeper 0.00372
863 9 2 Left Fullback 0.00318
864 9 2 Left Midfielder 0.00404
865 9 2 Left Winger 0.00373
866 9 2 Right Fullback 0.00356
867 9 2 Right Midfielder 0.00160
868 9 2 Right Winger 0.00443
869 9 2.5 Attacking Midfielder 0.00604
870 9 2.5 Center Back 0.00682
871 9 2.5 Center Forward 0.00494
872 9 2.5 Center Midfielder 0
873 9 2.5 Defensive Midfielder 0.00417
874 9 2.5 Goalkeeper 0.00316
875 9 2.5 Left Fullback 0.00804
876 9 2.5 Left Midfielder 0
877 9 2.5 Left Winger 0
878 9 2.5 Right Fullback 0.00438
879 9 2.5 Right Midfielder 0.00450
880 9 2.5 Right Winger 0.00657
881 9 3 Attacking Midfielder 0.00112
882 9 3 Center Back 0.00771
883 9 3 Center Forward 0.00304
884 9 3 Center Midfielder 0.00580
885 9 3 Defensive Midfielder 0.00681
886 9 3 Goalkeeper 0
887 9 3 Left Fullback 0.00320
888 9 3 Left Midfielder 0.00951
889 9 3 Left Winger 0.00691
890 9 3 Right Fullback 0.00667
891 9 3 Right Midfielder 0.00259
892 9 3 Right Winger 0.00511
893 9 3.5 Attacking Midfielder 0.002
894 9 3.5 Center Back 0.00395
895 9 3.5 Center Forward 0
896 9 3.5 Defensive Midfielder 0.00441
897 9 3.5 Goalkeeper 0
898 9 3.5 Left Fullback 0.00402
899 9 3.5 Left Midfielder 0
900 9 3.5 Left Winger 0
901 9 3.5 Right Fullback 0
902 9 3.5 Right Winger 0.00862
903 9 4 Attacking Midfielder 0.00183
904 9 4 Center Back 0.00587
905 9 4 Center Forward 0.00538
906 9 4 Center Midfielder 0.00639
907 9 4 Defensive Midfielder 0.00493
908 9 4 Goalkeeper 0.00463
909 9 4 Left Fullback 0.00375
910 9 4 Left Midfielder 0.00913
911 9 4 Left Winger 0.000892
912 9 4 Right Fullback 0.00519
913 9 4 Right Midfielder 0.00876
914 9 4 Right Winger 0.00458
915 9 4.5 Center Back 0.00549
916 9 4.5 Center Forward 0.00470
917 9 4.5 Defensive Midfielder 0.00822
918 9 4.5 Goalkeeper 0.00196
919 9 4.5 Left Fullback 0.00937
920 9 4.5 Left Midfielder 0
921 9 4.5 Left Winger 0.00588
922 9 4.5 Right Fullback 0.0225
923 9 4.5 Right Midfielder 0
924 9 4.5 Right Winger 0.00103
925 9 5 Attacking Midfielder 0
926 9 5 Center Back 0.00781
927 9 5 Center Forward 0.00382
928 9 5 Center Midfielder 0.00251
929 9 5 Defensive Midfielder 0.00365
930 9 5 Goalkeeper 0.00870
931 9 5 Left Fullback 0.0113
932 9 5 Left Midfielder 0.00680
933 9 5 Left Winger 0.00265
934 9 5 Right Fullback 0.00242
935 9 5 Right Midfielder 0.00926
936 9 5 Right Winger 0.00299
937 10 1 Attacking Midfielder 0.00229
938 10 1 Center Back 0.00642
939 10 1 Center Forward 0.00267
940 10 1 Center Midfielder 0.00307
941 10 1 Defensive Midfielder 0.00350
942 10 1 Goalkeeper 0.00506
943 10 1 Left Fullback 0.00448
944 10 1 Left Midfielder 0.00192
945 10 1 Left Winger 0.00158
946 10 1 Right Fullback 0.00370
947 10 1 Right Midfielder 0.00196
948 10 1 Right Winger 0.00136
949 10 1.5 Attacking Midfielder 0.00258
950 10 1.5 Center Back 0.00360
951 10 1.5 Center Forward 0.00243
952 10 1.5 Center Midfielder 0.00317
953 10 1.5 Defensive Midfielder 0.00500
954 10 1.5 Goalkeeper 0.00487
955 10 1.5 Left Fullback 0.00504
956 10 1.5 Left Midfielder 0.00333
957 10 1.5 Left Winger 0.00164
958 10 1.5 Right Fullback 0.00294
959 10 1.5 Right Midfielder 0.00421
960 10 1.5 Right Winger 0.00360
961 10 2 Attacking Midfielder 0.00248
962 10 2 Center Back 0.00769
963 10 2 Center Forward 0.00453
964 10 2 Center Midfielder 0.00474
965 10 2 Defensive Midfielder 0.00366
966 10 2 Goalkeeper 0.00372
967 10 2 Left Fullback 0.00318
968 10 2 Left Midfielder 0.00404
969 10 2 Left Winger 0.00373
970 10 2 Right Fullback 0.00356
971 10 2 Right Midfielder 0.00160
972 10 2 Right Winger 0.00443
973 10 2.5 Attacking Midfielder 0.00604
974 10 2.5 Center Back 0.00682
975 10 2.5 Center Forward 0.00494
976 10 2.5 Center Midfielder 0
977 10 2.5 Defensive Midfielder 0.00417
978 10 2.5 Goalkeeper 0.00316
979 10 2.5 Left Fullback 0.00804
980 10 2.5 Left Midfielder 0
981 10 2.5 Left Winger 0
982 10 2.5 Right Fullback 0.00438
983 10 2.5 Right Midfielder 0.00450
984 10 2.5 Right Winger 0.00657
985 10 3 Attacking Midfielder 0.00112
986 10 3 Center Back 0.00771
987 10 3 Center Forward 0.00304
988 10 3 Center Midfielder 0.00580
989 10 3 Defensive Midfielder 0.00681
990 10 3 Goalkeeper 0
991 10 3 Left Fullback 0.00320
992 10 3 Left Midfielder 0.00951
993 10 3 Left Winger 0.00691
994 10 3 Right Fullback 0.00667
995 10 3 Right Midfielder 0.00259
996 10 3 Right Winger 0.00511
997 10 3.5 Attacking Midfielder 0.002
998 10 3.5 Center Back 0.00395
999 10 3.5 Center Forward 0
1000 10 3.5 Defensive Midfielder 0.00441
# … with 2,144 more rows
# ℹ Use `print(n = ...)` to see more rowsInteractive exploration tool
Interactive exploration tool
Thank you
- The package is available on CRAN (
install.packages("mverse")) - Experimental features are available on GitHub (
remotes::install_github("mverseanalysis/mverse", ref = "test")) - For those more adventurous, see
multiversepackage by Abhraneel Sarma, Matthew Kay, et al. athttps://mucollective.github.io/multiverse/on whichmverseis built - Demo codes for the slides available at
https://github.com/mjmoon/presentations/tree/main/CANSSI-Ontario-Stat-SW-Conf-22
© 2022. Michael J. Moon. University of Toronto.