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18 Mythbusters: Putting Fantasy Football Beliefs/Anecdotes to the Test
18.1 Getting Started
18.1.1 Load Packages
18.1.2 Specify Package Options
18.1.3 Load Data
We created the player_stats_weekly.RData and player_stats_seasonal.RData objects in Section 4.4.3.
18.2 Do Players Perform Better in their Contract Year?
Considerable speculation exists regarding whether players perform better in their last year of their contract (i.e., their “contract year”). Fantasy football talking heads and commentators frequently discuss the benefit of selecting players who are in their contract year, because it supposedly means that player has more motivation to perform well so they get a new contract and get paid more. To our knowledge, no peer-reviewed studies have examined this question for football players. One study found that National Basketball Association (NBA) players improved in field goal percentage, points, and player efficiency rating (but not other statistics: rebounds, assists, steals, or blocks) from their pre-contract year to their contract year, and that Major League Baseball (MLB) players improved in runs batted in (RBIs; but not other statistics: batting average, slugging percentage, on base percentage, home runs, fielding percentage) from their pre-contract year to their contract year (White & Sheldon, 2014). Other casual analyses have been examined contract-year performance of National Football League (NFL) players, including articles in 2012 (archived here) and 2022 (archived here).
Let’s examine the question empirically. In order to do that, we have to make some assumptions/constraints. In this example, we will make the following constraints:
- We will determine a player’s contract year programmatically based on the year the contract was signed. For instance, if a player signed a 3-year contract in 2015, their contract would expire in 2018, and thus their contract year would be 2017. Note: this is a coarse way of determining a player’s contract year because it could depend on when during the year the player’s contract is signed. If we were submitting this analysis as a paper to a scientific journal, it would be important to verify each player’s contract year.
- We will examine performance in all seasons since 2011, beginning when most data for player contracts are available.
- For maximum statistical power to detect an effect if a contract year effect exists, we will examine all seasons for a player (since 2011), not just their contract year and their pre-contract year.
- To ensure a more fair, apples-to-apples comparison of the games in which players played, we will examine per-game performance (except for yards per carry, which is based on \(\frac{\text{rushing yards}}{\text{carries}}\) from the entire season).
- We will examine regular season games only (no postseason).
- To ensure we do not make generalization about a player’s performance in a season from a small sample, the player has to play at least 5 games in a given season for that player–season combination to be included in analysis.
For analysis, the same player contributes multiple observations of performance (i.e., multiple seasons) due to the longitudinal nature of the data. Inclusion of multiple data points from the same player would violate the assumption of multiple regression that all observations are independent. Thus, we use mixed-effects models that allow nonindependent observations. In our mixed-effects models, we include a random intercept for each player, to allow our model to account for players’ differing level of performance. We examine two mixed-effects models for each outcome variable: one model that accounts for the effects of age and experience, and one model that does not.
The model that does not account for the effects of age and experience includes:
- random intercepts to allow the model to estimate a different starting point for each player
- a fixed effect for whether the player is in a contract year
The model that accounts for the effects of age and experience includes:
- random intercepts to allow the model to estimate a different starting point for each player
- random linear slopes (i.e., random effect of linear age) to allow the model to estimate a different form of change for each player
- a fixed quadratic effect of age to allow for curvilinear effects
- a fixed effect of experience
- a fixed effect for whether the player is in a contract year
Code
# Subset to remove players without a year signed
nfl_playerContracts_subset <- nfl_playerContracts %>%
dplyr::filter(!is.na(year_signed) & year_signed != 0)
# Determine the contract year for a given contract
nfl_playerContracts_subset$contractYear <- nfl_playerContracts_subset$year_signed + nfl_playerContracts_subset$years - 1
# Arrange contracts by player and year_signed
nfl_playerContracts_subset <- nfl_playerContracts_subset %>%
dplyr::group_by(player, position) %>%
dplyr::arrange(player, position, -year_signed) %>%
dplyr::ungroup()
# Determine if the player played in the original contract year
nfl_playerContracts_subset <- nfl_playerContracts_subset %>%
dplyr::group_by(player, position) %>%
dplyr::mutate(
next_contract_start = lag(year_signed)) %>%
dplyr::ungroup() %>%
dplyr::mutate(
played_in_contract_year = ifelse(
is.na(next_contract_start) | contractYear < next_contract_start,
TRUE,
FALSE))
# Check individual players
#nfl_playerContracts_subset %>%
# dplyr::filter(player == "Aaron Rodgers") %>%
# dplyr::select(player:years, contractYear, next_contract_start, played_in_contract_year)
#
#nfl_playerContracts_subset %>%
# dplyr::filter(player %in% c("Jared Allen", "Aaron Rodgers")) %>%
# dplyr::select(player:years, contractYear, next_contract_start, played_in_contract_year)
# Subset data
nfl_playerContractYears <- nfl_playerContracts_subset %>%
dplyr::filter(played_in_contract_year == TRUE) %>%
dplyr::filter(position %in% c("QB","RB","WR","TE")) %>%
dplyr::select(player, position, team, contractYear) %>%
dplyr::mutate(merge_name = nflreadr::clean_player_names(player, lowercase = TRUE)) %>%
dplyr::rename(season = contractYear) %>%
dplyr::mutate(contractYear = 1)
# Merge with weekly and seasonal stats data
player_stats_weekly_offense <- player_stats_weekly_offense %>%
dplyr::mutate(merge_name = nflreadr::clean_player_names(player_display_name, lowercase = TRUE))
#nfl_actualStats_offense_seasonal <- nfl_actualStats_offense_seasonal %>%
# mutate(merge_name = nflreadr::clean_player_names(player_display_name, lowercase = TRUE))
player_statsContracts_offense_weekly <- dplyr::full_join(
player_stats_weekly_offense,
nfl_playerContractYears,
by = c("merge_name", "position_group" = "position", "season")
) %>%
dplyr::filter(position_group %in% c("QB","RB","WR","TE"))
#player_statsContracts_offense_seasonal <- full_join(
# player_stats_seasonal_offense,
# nfl_playerContractYears,
# by = c("merge_name", "position_group" = "position", "season")
#) %>%
# filter(position_group %in% c("QB","RB","WR","TE"))
player_statsContracts_offense_weekly$contractYear[which(is.na(player_statsContracts_offense_weekly$contractYear))] <- 0
#player_statsContracts_offense_seasonal$contractYear[which(is.na(player_statsContracts_offense_seasonal$contractYear))] <- 0
#player_statsContracts_offense_weekly$contractYear <- factor(
# player_statsContracts_offense_weekly$contractYear,
# levels = c(0, 1),
# labels = c("no", "yes"))
#player_statsContracts_offense_seasonal$contractYear <- factor(
# player_statsContracts_offense_seasonal$contractYear,
# levels = c(0, 1),
# labels = c("no", "yes"))
player_statsContracts_offense_weekly <- player_statsContracts_offense_weekly %>%
dplyr::arrange(merge_name, season, season_type, week)
#player_statsContracts_offense_seasonal <- player_statsContracts_offense_seasonal %>%
# arrange(merge_name, season)
player_statsContractsSubset_offense_weekly <- player_statsContracts_offense_weekly %>%
dplyr::filter(season_type == "REG")
#table(nfl_playerContracts$year_signed) # most contract data is available beginning in 2011
# Calculate Per Game Totals
player_statsContracts_seasonal <- player_statsContractsSubset_offense_weekly %>%
dplyr::group_by(player_id, season) %>%
dplyr::summarise(
player_display_name = petersenlab::Mode(player_display_name),
position_group = petersenlab::Mode(position_group),
age = min(age, na.rm = TRUE),
years_of_experience = min(years_of_experience, na.rm = TRUE),
rushing_yards = sum(rushing_yards, na.rm = TRUE), # season total
carries = sum(carries, na.rm = TRUE), # season total
rushing_epa = mean(rushing_epa, na.rm = TRUE),
receiving_yards = mean(receiving_yards, na.rm = TRUE),
receiving_epa = mean(receiving_epa, na.rm = TRUE),
contractYear = mean(contractYear, na.rm = TRUE),
games = n(),
.groups = "drop_last"
) %>%
dplyr::mutate(
player_id = as.factor(player_id),
ypc = rushing_yards / carries,
contractYear = factor(
contractYear,
levels = c(0, 1),
labels = c("no", "yes")
))
player_statsContracts_seasonal[sapply(player_statsContracts_seasonal, is.infinite)] <- NA
player_statsContracts_seasonal$ageCentered20 <- player_statsContracts_seasonal$age - 20
player_statsContracts_seasonal$ageCentered20Quadratic <- player_statsContracts_seasonal$ageCentered20 ^ 2
# Merge with seasonal fantasy points data18.2.1 QB
First, we prepare the data by merging and performing additional processing:
Code
# Merge with QBR data
nfl_espnQBR_weekly$merge_name <- paste(nfl_espnQBR_weekly$name_first, nfl_espnQBR_weekly$name_last, sep = " ") %>%
nflreadr::clean_player_names(., lowercase = TRUE)
nfl_contractYearQBR_weekly <- nfl_playerContractYears %>%
dplyr::filter(position == "QB") %>%
dplyr::full_join(
.,
nfl_espnQBR_weekly,
by = c("merge_name","team","season")
)
nfl_contractYearQBR_weekly$contractYear[which(is.na(nfl_contractYearQBR_weekly$contractYear))] <- 0
#nfl_contractYearQBR_weekly$contractYear <- factor(
# nfl_contractYearQBR_weekly$contractYear,
# levels = c(0, 1),
# labels = c("no", "yes"))
nfl_contractYearQBR_weekly <- nfl_contractYearQBR_weekly %>%
dplyr::arrange(merge_name, season, season_type, game_week)
nfl_contractYearQBRsubset_weekly <- nfl_contractYearQBR_weekly %>%
dplyr::filter(season_type == "Regular") %>%
dplyr::arrange(merge_name, season, season_type, game_week) %>%
mutate(
player = coalesce(player, name_display),
position = "QB") %>%
group_by(merge_name, player_id) %>%
fill(player, .direction = "downup")
# Merge with age and experience
nfl_contractYearQBRsubset_weekly <- player_statsContractsSubset_offense_weekly %>%
dplyr::filter(position == "QB") %>%
dplyr::select(merge_name, season, week, age, years_of_experience) %>%
full_join(
nfl_contractYearQBRsubset_weekly,
by = c("merge_name","season", c("week" = "game_week"))
) %>% select(player_id, season, week, player, everything()) %>%
arrange(player_id, season, week)
#hist(nfl_contractYearQBRsubset_weekly$qb_plays) # players have at least 20 dropbacks per game
# Calculate Per Game Totals
nfl_contractYearQBR_seasonal <- nfl_contractYearQBRsubset_weekly %>%
dplyr::group_by(merge_name, season) %>%
dplyr::summarise(
age = min(age, na.rm = TRUE),
years_of_experience = min(years_of_experience, na.rm = TRUE),
qbr = mean(qbr_total, na.rm = TRUE),
pts_added = mean(pts_added, na.rm = TRUE),
epa_pass = mean(pass, na.rm = TRUE),
qb_plays = sum(qb_plays, na.rm = TRUE), # season total
contractYear = mean(contractYear, na.rm = TRUE),
games = n(),
.groups = "drop_last"
) %>%
dplyr::mutate(
contractYear = factor(
contractYear,
levels = c(0, 1),
labels = c("no", "yes")
))
nfl_contractYearQBR_seasonal[sapply(nfl_contractYearQBR_seasonal, is.infinite)] <- NA
nfl_contractYearQBR_seasonal$ageCentered20 <- nfl_contractYearQBR_seasonal$age - 20
nfl_contractYearQBR_seasonal$ageCentered20Quadratic <- nfl_contractYearQBR_seasonal$ageCentered20 ^ 2
nfl_contractYearQBR_seasonal <- nfl_contractYearQBR_seasonal %>%
group_by(merge_name) %>%
mutate(player_id = as.factor(as.character(cur_group_id())))
nfl_contractYearQBRsubset_seasonal <- nfl_contractYearQBR_seasonal %>%
dplyr::filter(
games >= 5, # keep only player-season combinations in which QBs played at least 5 games
season >= 2011) # keep only seasons since 2011 (when most contract data are available)Then, we analyze the data. Below is a mixed model that examines whether a player has a higher QBR per game when they are in a contract year compared to when they are not in a contract year.
Code
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: qbr ~ contractYear + (1 | player_id)
Data: nfl_contractYearQBR_seasonal
Control: lmerControl(optimizer = "bobyqa")
REML criterion at convergence: 8905.9
Scaled residuals:
Min 1Q Median 3Q Max
-3.2653 -0.5512 0.0912 0.5732 3.2574
Random effects:
Groups Name Variance Std.Dev.
player_id (Intercept) 111.5 10.56
Residual 198.6 14.09
Number of obs: 1063, groups: player_id, 253
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 44.2361 0.8737 231.4158 50.628 <2e-16 ***
contractYearyes 0.2435 1.2011 950.7334 0.203 0.839
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
contrctYrys -0.241 R2m R2c
[1,] 2.923268e-05 0.3595778 contractYear emmean SE df lower.CL upper.CL
no 44.2 0.874 262 42.5 46
yes 44.5 1.300 752 41.9 47
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 Code
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: qbr ~ contractYear + ageCentered20 + ageCentered20Quadratic +
years_of_experience + (1 + ageCentered20 | player_id)
Data: nfl_contractYearQBR_seasonal
Control: lmerControl(optimizer = "bobyqa")
REML criterion at convergence: 8848.2
Scaled residuals:
Min 1Q Median 3Q Max
-3.3856 -0.5210 0.0932 0.5483 3.2851
Random effects:
Groups Name Variance Std.Dev. Corr
player_id (Intercept) 136.2765 11.6738
ageCentered20 0.4514 0.6718 -0.43
Residual 191.2085 13.8278
Number of obs: 1057, groups: player_id, 250
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 39.40393 2.29616 175.97837 17.161 < 2e-16 ***
contractYearyes 0.29562 1.23595 948.22429 0.239 0.81102
ageCentered20 0.86786 0.64643 269.13650 1.343 0.18055
ageCentered20Quadratic -0.07586 0.02358 100.92420 -3.217 0.00174 **
years_of_experience 0.62472 0.54271 290.03262 1.151 0.25064
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) cntrcY agCn20 agC20Q
contrctYrys 0.056
ageCentrd20 -0.735 -0.062
agCntrd20Qd 0.764 0.055 -0.631
yrs_f_xprnc 0.096 -0.040 -0.657 -0.122 R2m R2c
[1,] 0.0132803 0.3959472 contractYear emmean SE df lower.CL upper.CL
no 44.1 0.913 241 42.3 45.9
yes 44.4 1.320 708 41.8 47.0
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 Code
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: pts_added ~ contractYear + (1 | player_id)
Data: nfl_contractYearQBR_seasonal
Control: lmerControl(optimizer = "bobyqa")
REML criterion at convergence: 4855.8
Scaled residuals:
Min 1Q Median 3Q Max
-4.7104 -0.4856 0.0805 0.5366 4.4281
Random effects:
Groups Name Variance Std.Dev.
player_id (Intercept) 2.569 1.603
Residual 4.333 2.082
Number of obs: 1063, groups: player_id, 253
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) -0.85473 0.13128 219.84986 -6.511 5.01e-10 ***
contractYearyes -0.06891 0.17769 939.67476 -0.388 0.698
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
contrctYrys -0.237 R2m R2c
[1,] 0.0001051826 0.3723006 contractYear emmean SE df lower.CL upper.CL
no -0.855 0.131 262 -1.11 -0.596
yes -0.924 0.194 745 -1.31 -0.542
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 Code
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: pts_added ~ contractYear + ageCentered20 + ageCentered20Quadratic +
years_of_experience + (1 + ageCentered20 | player_id)
Data: nfl_contractYearQBR_seasonal
Control: lmerControl(optimizer = "bobyqa")
REML criterion at convergence: 4833.1
Scaled residuals:
Min 1Q Median 3Q Max
-4.8658 -0.4801 0.0835 0.5195 4.4083
Random effects:
Groups Name Variance Std.Dev. Corr
player_id (Intercept) 3.56554 1.8883
ageCentered20 0.01187 0.1089 -0.56
Residual 4.17782 2.0440
Number of obs: 1057, groups: player_id, 250
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) -1.607781 0.347938 169.870515 -4.621 7.53e-06 ***
contractYearyes -0.080246 0.182799 937.931780 -0.439 0.66077
ageCentered20 0.103772 0.096913 273.835497 1.071 0.28522
ageCentered20Quadratic -0.011186 0.003526 102.420446 -3.173 0.00199 **
years_of_experience 0.132677 0.080392 281.954383 1.650 0.09998 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) cntrcY agCn20 agC20Q
contrctYrys 0.056
ageCentrd20 -0.739 -0.063
agCntrd20Qd 0.761 0.059 -0.641
yrs_f_xprnc 0.104 -0.041 -0.658 -0.109 R2m R2c
[1,] 0.01399559 0.4005138 contractYear emmean SE df lower.CL upper.CL
no -0.842 0.135 243 -1.11 -0.576
yes -0.923 0.196 710 -1.31 -0.538
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 Code
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: epa_pass ~ contractYear + (1 | player_id)
Data: nfl_contractYearQBR_seasonal
Control: lmerControl(optimizer = "bobyqa")
REML criterion at convergence: 4533.4
Scaled residuals:
Min 1Q Median 3Q Max
-3.0315 -0.5088 0.0398 0.5664 4.3662
Random effects:
Groups Name Variance Std.Dev.
player_id (Intercept) 2.454 1.566
Residual 3.049 1.746
Number of obs: 1063, groups: player_id, 253
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 1.0733 0.1218 239.6979 8.810 2.58e-16 ***
contractYearyes 0.4241 0.1504 928.0942 2.821 0.0049 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
contrctYrys -0.214 R2m R2c
[1,] 0.00497323 0.4486506 contractYear emmean SE df lower.CL upper.CL
no 1.07 0.122 263 0.833 1.31
yes 1.50 0.172 699 1.159 1.84
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 Code
mixedModelAge_epaPass <- lmerTest::lmer(
epa_pass ~ contractYear + ageCentered20 + ageCentered20Quadratic + years_of_experience + (1 | player_id), # removed random slopes to address convergence issue
data = nfl_contractYearQBR_seasonal,
control = lmerControl(optimizer = "bobyqa")
)
summary(mixedModelAge_epaPass)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: epa_pass ~ contractYear + ageCentered20 + ageCentered20Quadratic +
years_of_experience + (1 | player_id)
Data: nfl_contractYearQBR_seasonal
Control: lmerControl(optimizer = "bobyqa")
REML criterion at convergence: 4504.9
Scaled residuals:
Min 1Q Median 3Q Max
-3.1322 -0.5027 0.0413 0.5370 4.2928
Random effects:
Groups Name Variance Std.Dev.
player_id (Intercept) 2.417 1.555
Residual 2.994 1.730
Number of obs: 1057, groups: player_id, 250
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 3.258e-01 2.815e-01 9.512e+02 1.157 0.24740
contractYearyes 2.381e-01 1.549e-01 9.516e+02 1.537 0.12451
ageCentered20 9.014e-03 8.120e-02 6.851e+02 0.111 0.91165
ageCentered20Quadratic -5.585e-03 2.704e-03 1.012e+03 -2.065 0.03916 *
years_of_experience 1.874e-01 7.157e-02 3.933e+02 2.618 0.00918 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) cntrcY agCn20 agC20Q
contrctYrys 0.063
ageCentrd20 -0.712 -0.058
agCntrd20Qd 0.741 0.057 -0.576
yrs_f_xprnc 0.137 -0.045 -0.705 -0.136 R2m R2c
[1,] 0.02982806 0.46316 contractYear emmean SE df lower.CL upper.CL
no 1.19 0.124 262 0.947 1.43
yes 1.43 0.172 689 1.091 1.77
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 18.2.2 RB
Code
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: ypc ~ contractYear + (1 | player_id)
Data: player_statsContractsRB_seasonal
Control: lmerControl(optimizer = "bobyqa")
REML criterion at convergence: 4820.8
Scaled residuals:
Min 1Q Median 3Q Max
-3.8771 -0.4656 0.0124 0.4849 6.4872
Random effects:
Groups Name Variance Std.Dev.
player_id (Intercept) 0.3922 0.6262
Residual 1.1414 1.0684
Number of obs: 1512, groups: player_id, 482
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 3.910e+00 4.481e-02 4.826e+02 87.271 <2e-16 ***
contractYearyes 5.126e-02 6.978e-02 1.421e+03 0.735 0.463
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
contrctYrys -0.348 R2m R2c
[1,] 0.0003241364 0.2559497 contractYear emmean SE df lower.CL upper.CL
no 3.91 0.0448 556 3.82 4.0
yes 3.96 0.0686 1151 3.83 4.1
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 Code
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: ypc ~ contractYear + ageCentered20 + ageCentered20Quadratic +
years_of_experience + (1 + ageCentered20 | player_id)
Data: player_statsContractsRB_seasonal
Control: lmerControl(optimizer = "bobyqa")
REML criterion at convergence: 4778.2
Scaled residuals:
Min 1Q Median 3Q Max
-4.0565 -0.4514 -0.0042 0.4678 6.2875
Random effects:
Groups Name Variance Std.Dev. Corr
player_id (Intercept) 1.12478 1.0606
ageCentered20 0.01468 0.1212 -0.78
Residual 0.99234 0.9962
Number of obs: 1511, groups: player_id, 481
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 4.274e+00 1.577e-01 5.092e+02 27.108 < 2e-16 ***
contractYearyes 1.877e-01 7.215e-02 1.307e+03 2.602 0.00938 **
ageCentered20 -1.001e-01 5.389e-02 5.980e+02 -1.857 0.06380 .
ageCentered20Quadratic -1.654e-03 3.659e-03 3.355e+02 -0.452 0.65149
years_of_experience 5.229e-02 3.309e-02 3.731e+02 1.580 0.11491
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) cntrcY agCn20 agC20Q
contrctYrys 0.161
ageCentrd20 -0.859 -0.177
agCntrd20Qd 0.797 0.145 -0.812
yrs_f_xprnc 0.025 -0.062 -0.395 -0.139 R2m R2c
[1,] 0.03118983 0.3813675 contractYear emmean SE df lower.CL upper.CL
no 3.85 0.0476 527 3.75 3.94
yes 4.04 0.0706 1129 3.90 4.17
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 Code
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: rushing_epa ~ contractYear + (1 | player_id)
Data: player_statsContractsRB_seasonal
Control: lmerControl(optimizer = "bobyqa")
REML criterion at convergence: 4287.1
Scaled residuals:
Min 1Q Median 3Q Max
-4.6912 -0.5189 0.0883 0.6114 3.4713
Random effects:
Groups Name Variance Std.Dev.
player_id (Intercept) 0.1025 0.3202
Residual 0.9057 0.9517
Number of obs: 1512, groups: player_id, 482
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) -0.65626 0.03296 576.28288 -19.912 <2e-16 ***
contractYearyes 0.04570 0.05926 1508.59478 0.771 0.441
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
contrctYrys -0.428 R2m R2c
[1,] 0.0003919375 0.1020542 contractYear emmean SE df lower.CL upper.CL
no -0.656 0.0330 574 -0.721 -0.591
yes -0.611 0.0542 1059 -0.717 -0.504
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 Code
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: rushing_epa ~ contractYear + ageCentered20 + ageCentered20Quadratic +
years_of_experience + (1 + ageCentered20 | player_id)
Data: player_statsContractsRB_seasonal
Control: lmerControl(optimizer = "bobyqa")
REML criterion at convergence: 4290.5
Scaled residuals:
Min 1Q Median 3Q Max
-4.7511 -0.5077 0.0697 0.6018 3.1622
Random effects:
Groups Name Variance Std.Dev. Corr
player_id (Intercept) 0.316977 0.56301
ageCentered20 0.003557 0.05964 -0.85
Residual 0.873051 0.93437
Number of obs: 1511, groups: player_id, 481
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) -6.595e-01 1.249e-01 3.652e+02 -5.282 2.2e-07 ***
contractYearyes 7.934e-02 6.205e-02 1.328e+03 1.279 0.20123
ageCentered20 5.740e-02 4.140e-02 3.535e+02 1.386 0.16656
ageCentered20Quadratic -1.829e-03 2.853e-03 1.808e+02 -0.641 0.52234
years_of_experience -6.118e-02 2.287e-02 3.833e+02 -2.675 0.00779 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) cntrcY agCn20 agC20Q
contrctYrys 0.150
ageCentrd20 -0.878 -0.197
agCntrd20Qd 0.830 0.156 -0.853
yrs_f_xprnc -0.046 -0.048 -0.301 -0.166 R2m R2c
[1,] 0.01004318 0.139284 contractYear emmean SE df lower.CL upper.CL
no -0.667 0.0337 527 -0.733 -0.601
yes -0.588 0.0559 1051 -0.697 -0.478
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 18.2.3 WR/TE
Code
Code
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: receiving_yards ~ contractYear + (1 | player_id)
Data: player_statsContractsWRTE_seasonal
Control: lmerControl(optimizer = "bobyqa")
REML criterion at convergence: 27103.6
Scaled residuals:
Min 1Q Median 3Q Max
-4.7774 -0.5657 -0.0860 0.5285 4.4960
Random effects:
Groups Name Variance Std.Dev.
player_id (Intercept) 233.9 15.29
Residual 190.1 13.79
Number of obs: 3181, groups: player_id, 938
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 29.2510 0.6018 1149.9717 48.605 < 2e-16 ***
contractYearyes -3.7672 0.6298 2753.7386 -5.982 2.49e-09 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
contrctYrys -0.254 R2m R2c
[1,] 0.006673929 0.554657 contractYear emmean SE df lower.CL upper.CL
no 29.3 0.602 1035 28.1 30.4
yes 25.5 0.752 1930 24.0 27.0
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 Code
mixedModelAge_receivingYards <- lmerTest::lmer(
receiving_yards ~ contractYear + ageCentered20 + ageCentered20Quadratic + years_of_experience + (1 + ageCentered20 | player_id),
data = player_statsContractsWRTE_seasonal,
control = lmerControl(optimizer = "bobyqa")
)
summary(mixedModelAge_receivingYards)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula:
receiving_yards ~ contractYear + ageCentered20 + ageCentered20Quadratic +
years_of_experience + (1 + ageCentered20 | player_id)
Data: player_statsContractsWRTE_seasonal
Control: lmerControl(optimizer = "bobyqa")
REML criterion at convergence: 26762.8
Scaled residuals:
Min 1Q Median 3Q Max
-2.8562 -0.5484 -0.0835 0.4903 3.8045
Random effects:
Groups Name Variance Std.Dev. Corr
player_id (Intercept) 469.026 21.657
ageCentered20 5.791 2.406 -0.69
Residual 143.432 11.976
Number of obs: 3179, groups: player_id, 937
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 17.03925 1.61920 1201.85554 10.523 < 2e-16 ***
contractYearyes -2.89879 0.61202 2537.07095 -4.736 2.30e-06 ***
ageCentered20 2.73922 0.56578 1782.22265 4.841 1.40e-06 ***
ageCentered20Quadratic -0.43513 0.02993 1211.48663 -14.537 < 2e-16 ***
years_of_experience 3.05942 0.43371 1123.96294 7.054 3.03e-12 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) cntrcY agCn20 agC20Q
contrctYrys 0.106
ageCentrd20 -0.794 -0.140
agCntrd20Qd 0.710 0.071 -0.662
yrs_f_xprnc 0.182 0.023 -0.633 -0.086 R2m R2c
[1,] 0.1199563 0.7144681 contractYear emmean SE df lower.CL upper.CL
no 27.9 0.642 1022 26.7 29.2
yes 25.0 0.757 1741 23.5 26.5
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 Code
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: receiving_epa ~ contractYear + (1 | player_id)
Data: player_statsContractsWRTE_seasonal
Control: lmerControl(optimizer = "bobyqa")
REML criterion at convergence: 10536.6
Scaled residuals:
Min 1Q Median 3Q Max
-4.1755 -0.5759 -0.0597 0.5249 3.9512
Random effects:
Groups Name Variance Std.Dev.
player_id (Intercept) 0.5236 0.7236
Residual 1.2726 1.1281
Number of obs: 3179, groups: player_id, 938
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 0.71504 0.03532 1272.25554 20.244 <2e-16 ***
contractYearyes -0.11951 0.04929 3029.75001 -2.425 0.0154 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
contrctYrys -0.356 R2m R2c
[1,] 0.001594279 0.2926485 contractYear emmean SE df lower.CL upper.CL
no 0.715 0.0353 1094 0.646 0.784
yes 0.596 0.0494 2182 0.499 0.692
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 Code
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula:
receiving_epa ~ contractYear + ageCentered20 + ageCentered20Quadratic +
years_of_experience + (1 + ageCentered20 | player_id)
Data: player_statsContractsWRTE_seasonal
Control: lmerControl(optimizer = "bobyqa")
REML criterion at convergence: 10517.2
Scaled residuals:
Min 1Q Median 3Q Max
-4.2197 -0.5696 -0.0529 0.5315 3.9167
Random effects:
Groups Name Variance Std.Dev. Corr
player_id (Intercept) 0.862888 0.9289
ageCentered20 0.006774 0.0823 -0.62
Residual 1.209765 1.0999
Number of obs: 3178, groups: player_id, 937
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 3.283e-01 1.082e-01 9.653e+02 3.034 0.00248 **
contractYearyes -1.184e-01 5.147e-02 2.944e+03 -2.300 0.02155 *
ageCentered20 8.990e-02 3.599e-02 1.087e+03 2.498 0.01265 *
ageCentered20Quadratic -1.139e-02 2.039e-03 4.295e+02 -5.588 4.1e-08 ***
years_of_experience 7.517e-02 2.513e-02 1.015e+03 2.992 0.00284 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) cntrcY agCn20 agC20Q
contrctYrys 0.115
ageCentrd20 -0.821 -0.177
agCntrd20Qd 0.783 0.100 -0.739
yrs_f_xprnc 0.068 0.030 -0.511 -0.136 R2m R2c
[1,] 0.01846712 0.3424349 contractYear emmean SE df lower.CL upper.CL
no 0.704 0.0367 1023 0.632 0.776
yes 0.586 0.0504 2189 0.487 0.685
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 18.2.4 QB/RB/WR/TE
18.3 Conclusion
18.4 Session Info
R version 4.4.2 (2024-10-31)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 22.04.5 LTS
Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.20.so; LAPACK version 3.10.0
locale:
[1] LC_CTYPE=C.UTF-8 LC_NUMERIC=C LC_TIME=C.UTF-8
[4] LC_COLLATE=C.UTF-8 LC_MONETARY=C.UTF-8 LC_MESSAGES=C.UTF-8
[7] LC_PAPER=C.UTF-8 LC_NAME=C LC_ADDRESS=C
[10] LC_TELEPHONE=C LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C
time zone: UTC
tzcode source: system (glibc)
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] lubridate_1.9.3 forcats_1.0.0 stringr_1.5.1 dplyr_1.1.4
[5] purrr_1.0.2 readr_2.1.5 tidyr_1.3.1 tibble_3.2.1
[9] ggplot2_3.5.1 tidyverse_2.0.0 emmeans_1.10.5 MuMIn_1.48.4
[13] lmerTest_3.1-3 lme4_1.1-35.5 Matrix_1.7-1 nflreadr_1.4.1
[17] petersenlab_1.1.0
loaded via a namespace (and not attached):
[1] tidyselect_1.2.1 psych_2.4.6.26 viridisLite_0.4.2
[4] fastmap_1.2.0 digest_0.6.37 rpart_4.1.23
[7] timechange_0.3.0 estimability_1.5.1 lifecycle_1.0.4
[10] cluster_2.1.6 magrittr_2.0.3 compiler_4.4.2
[13] rlang_1.1.4 Hmisc_5.2-0 tools_4.4.2
[16] utf8_1.2.4 yaml_2.3.10 data.table_1.16.2
[19] knitr_1.49 htmlwidgets_1.6.4 mnormt_2.1.1
[22] plyr_1.8.9 RColorBrewer_1.1-3 withr_3.0.2
[25] foreign_0.8-87 numDeriv_2016.8-1.1 nnet_7.3-19
[28] grid_4.4.2 stats4_4.4.2 fansi_1.0.6
[31] lavaan_0.6-19 xtable_1.8-4 colorspace_2.1-1
[34] scales_1.3.0 MASS_7.3-61 cli_3.6.3
[37] mvtnorm_1.3-2 rmarkdown_2.29 generics_0.1.3
[40] rstudioapi_0.17.1 tzdb_0.4.0 reshape2_1.4.4
[43] minqa_1.2.8 DBI_1.2.3 cachem_1.1.0
[46] splines_4.4.2 parallel_4.4.2 base64enc_0.1-3
[49] mitools_2.4 vctrs_0.6.5 boot_1.3-31
[52] jsonlite_1.8.9 hms_1.1.3 pbkrtest_0.5.3
[55] Formula_1.2-5 htmlTable_2.4.3 glue_1.8.0
[58] nloptr_2.1.1 stringi_1.8.4 gtable_0.3.6
[61] quadprog_1.5-8 munsell_0.5.1 pillar_1.9.0
[64] htmltools_0.5.8.1 R6_2.5.1 mix_1.0-12
[67] evaluate_1.0.1 pbivnorm_0.6.0 lattice_0.22-6
[70] backports_1.5.0 broom_1.0.7 memoise_2.0.1
[73] Rcpp_1.0.13-1 coda_0.19-4.1 gridExtra_2.3
[76] nlme_3.1-166 checkmate_2.3.2 xfun_0.49
[79] pkgconfig_2.0.3