mythbusters.qmd

# Mythbusters: Putting Fantasy Football Beliefs/Anecdotes to the Test {#sec-mythbusters}

## Getting Started {#sec-mythbustersGettingStarted}

### Load Packages {#sec-mythbustersLoadPackages}

```{r}
library("petersenlab")
library("nflreadr")
library("lme4")
library("lmerTest")
library("MuMIn")
library("emmeans")
library("tidyverse")
```

### Specify Package Options {#sec-mythbustersPackageOptions}

```{r}
emm_options(lmerTest.limit = 100000)
emm_options(pbkrtest.limit = 100000)
```

### Load Data {#sec-mythbustersLoadData}

```{r}
#| eval: false
#| include: false

load(file = "./data/nfl_playerContracts.RData")
load(file = file.path(path, "/OneDrive - University of Iowa/Teaching/Courses/Fantasy Football/Data/player_stats_weekly.RData", fsep = ""))
load(file = file.path(path, "/OneDrive - University of Iowa/Teaching/Courses/Fantasy Football/Data/player_stats_seasonal.RData", fsep = ""))
load(file = "./data/nfl_espnQBR_seasonal.RData")
load(file = "./data/nfl_espnQBR_weekly.RData")
```

```{r}
load(file = "./data/nfl_playerContracts.RData")
load(file = "./data/player_stats_weekly.RData")
load(file = "./data/player_stats_seasonal.RData")
load(file = "./data/nfl_espnQBR_seasonal.RData")
load(file = "./data/nfl_espnQBR_weekly.RData")
```

We created the `player_stats_weekly.RData` and `player_stats_seasonal.RData` objects in @sec-calculatePlayerAge.

## Do Players Perform Better in their Contract Year? {#sec-contractYear}

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 [@White2014a].
Other casual analyses have been examined contract-year performance of National Football League (NFL) players, including articles in [2012](https://www.4for4.com/2012/preseason/2012-contract-year-players-and-myth-increased-production) (archived [here](https://perma.cc/CT3F-QN5E)) and [2022](https://www.4for4.com/2022/preseason/do-players-perform-better-fantasy-football-contract-year) (archived [here](https://perma.cc/F4F5-7RQZ)).

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](#sec-statisticalPower) 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](#sec-assumptionsRegression) 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:

a) random intercepts to allow the model to estimate a different starting point for each player
a) a fixed effect for whether the player is in a contract year

The model that accounts for the effects of age and experience includes:

a) random intercepts to allow the model to estimate a different starting point for each player
a) 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) a fixed quadratic effect of age to allow for curvilinear effects
a) a fixed effect of experience
a) a fixed effect for whether the player is in a contract year

```{r}
#| code-fold: true

# 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 %>% 
  dplyr::filter(position_group %in% c("QB","RB","WR","TE")) %>% 
  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),
    fantasyPoints = sum(fantasyPoints, na.rm = TRUE), # season total
    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 data
```

### QB {#sec-contractYearQB}

First, we prepare the data by merging and performing additional processing:

```{r}
#| code-fold: true

# 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, fantasyPoints) %>% 
  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
    fantasyPoints = sum(fantasyPoints, 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.

```{r}
mixedModel_qbr <- lmerTest::lmer(
  qbr ~ contractYear + (1 | player_id),
  data = nfl_contractYearQBR_seasonal,
  control = lmerControl(optimizer = "bobyqa")
)

summary(mixedModel_qbr)
MuMIn::r.squaredGLMM(mixedModel_qbr)
emmeans::emmeans(mixedModel_qbr, "contractYear")

mixedModelAge_qbr <- lmerTest::lmer(
  qbr ~ contractYear + ageCentered20 + ageCentered20Quadratic + years_of_experience + (1 + ageCentered20 | player_id),
  data = nfl_contractYearQBR_seasonal,
  control = lmerControl(optimizer = "bobyqa")
)

summary(mixedModelAge_qbr)
MuMIn::r.squaredGLMM(mixedModelAge_qbr)
emmeans::emmeans(mixedModelAge_qbr, "contractYear")
```

```{r}
mixedModel_ptsAdded <- lmerTest::lmer(
  pts_added ~ contractYear + (1 | player_id),
  data = nfl_contractYearQBR_seasonal,
  control = lmerControl(optimizer = "bobyqa")
)

summary(mixedModel_ptsAdded)
MuMIn::r.squaredGLMM(mixedModel_ptsAdded)
emmeans::emmeans(mixedModel_ptsAdded, "contractYear")

mixedModelAge_ptsAdded <- lmerTest::lmer(
  pts_added ~ contractYear + ageCentered20 + ageCentered20Quadratic + years_of_experience + (1 + ageCentered20 | player_id),
  data = nfl_contractYearQBR_seasonal,
  control = lmerControl(optimizer = "bobyqa")
)

summary(mixedModelAge_ptsAdded)
MuMIn::r.squaredGLMM(mixedModelAge_ptsAdded)
emmeans::emmeans(mixedModelAge_ptsAdded, "contractYear")
```

```{r}
mixedModel_epaPass <- lmerTest::lmer(
  epa_pass ~ contractYear + (1 | player_id),
  data = nfl_contractYearQBR_seasonal,
  control = lmerControl(optimizer = "bobyqa")
)

summary(mixedModel_epaPass)
MuMIn::r.squaredGLMM(mixedModel_epaPass)
emmeans::emmeans(mixedModel_epaPass, "contractYear")

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)
MuMIn::r.squaredGLMM(mixedModelAge_epaPass)
emmeans::emmeans(mixedModelAge_epaPass, "contractYear")
```

```{r}
mixedModel_fantasyPtsPass <- lmerTest::lmer(
  fantasyPoints ~ contractYear + (1 | player_id),
  data = nfl_contractYearQBR_seasonal,
  control = lmerControl(optimizer = "bobyqa")
)

summary(mixedModel_fantasyPtsPass)
MuMIn::r.squaredGLMM(mixedModel_fantasyPtsPass)
emmeans::emmeans(mixedModel_fantasyPtsPass, "contractYear")

mixedModelAge_fantasyPtsPass <- lmerTest::lmer(
  fantasyPoints ~ 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_fantasyPtsPass)
MuMIn::r.squaredGLMM(mixedModelAge_fantasyPtsPass)
emmeans::emmeans(mixedModelAge_fantasyPtsPass, "contractYear")
```

### RB {#sec-contractYearRB}

```{r}
#| code-fold: true

player_statsContractsRB_seasonal <- player_statsContracts_seasonal %>% 
  dplyr::filter(
    position_group == "RB",
    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)
```

```{r}
mixedModel_ypc <- lmerTest::lmer(
  ypc ~ contractYear + (1 | player_id),
  data = player_statsContractsRB_seasonal,
  control = lmerControl(optimizer = "bobyqa")
)

summary(mixedModel_ypc)
MuMIn::r.squaredGLMM(mixedModel_ypc)
emmeans::emmeans(mixedModel_ypc, "contractYear")

mixedModelAge_ypc <- lmerTest::lmer(
  ypc ~ contractYear + ageCentered20 + ageCentered20Quadratic + years_of_experience + (1 + ageCentered20 | player_id),
  data = player_statsContractsRB_seasonal,
  control = lmerControl(optimizer = "bobyqa")
)

summary(mixedModelAge_ypc)
MuMIn::r.squaredGLMM(mixedModelAge_ypc)
emmeans::emmeans(mixedModelAge_ypc, "contractYear")
```

```{r}
mixedModel_epaRush <- lmerTest::lmer(
  rushing_epa ~ contractYear + (1 | player_id),
  data = player_statsContractsRB_seasonal,
  control = lmerControl(optimizer = "bobyqa")
)

summary(mixedModel_epaRush)
MuMIn::r.squaredGLMM(mixedModel_epaRush)
emmeans::emmeans(mixedModel_epaRush, "contractYear")

mixedModelAge_epaRush <- lmerTest::lmer(
  rushing_epa ~ contractYear + ageCentered20 + ageCentered20Quadratic + years_of_experience + (1 + ageCentered20 | player_id),
  data = player_statsContractsRB_seasonal,
  control = lmerControl(optimizer = "bobyqa")
)

summary(mixedModelAge_epaRush)
MuMIn::r.squaredGLMM(mixedModelAge_epaRush)
emmeans::emmeans(mixedModelAge_epaRush, "contractYear")
```

```{r}
mixedModel_fantasyPtsRush <- lmerTest::lmer(
  fantasyPoints ~ contractYear + (1 | player_id),
  data = player_statsContractsRB_seasonal,
  control = lmerControl(optimizer = "bobyqa")
)

summary(mixedModel_fantasyPtsRush)
MuMIn::r.squaredGLMM(mixedModel_fantasyPtsRush)
emmeans::emmeans(mixedModel_fantasyPtsRush, "contractYear")

mixedModelAge_fantasyPtsRush <- lmerTest::lmer(
  fantasyPoints ~ contractYear + ageCentered20 + ageCentered20Quadratic + years_of_experience + (1 + ageCentered20 | player_id),
  data = player_statsContractsRB_seasonal,
  control = lmerControl(optimizer = "bobyqa")
)

summary(mixedModelAge_fantasyPtsRush)
MuMIn::r.squaredGLMM(mixedModelAge_fantasyPtsRush)
emmeans::emmeans(mixedModelAge_fantasyPtsRush, "contractYear")
```

### WR/TE {#sec-contractYearWRTE}

```{r}
#| code-fold: true

player_statsContractsWRTE_seasonal <- player_statsContracts_seasonal %>% 
  dplyr::filter(
    position_group %in% c("WR","TE"),
    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)
```

```{r}
mixedModel_receivingYards <- lmerTest::lmer(
  receiving_yards ~ contractYear + (1 | player_id),
  data = player_statsContractsWRTE_seasonal,
  control = lmerControl(optimizer = "bobyqa")
)

summary(mixedModel_receivingYards)
MuMIn::r.squaredGLMM(mixedModel_receivingYards)
emmeans::emmeans(mixedModel_receivingYards, "contractYear")

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)
MuMIn::r.squaredGLMM(mixedModelAge_receivingYards)
emmeans::emmeans(mixedModelAge_receivingYards, "contractYear")
```

```{r}
mixedModel_epaReceiving <- lmerTest::lmer(
  receiving_epa ~ contractYear + (1 | player_id),
  data = player_statsContractsWRTE_seasonal,
  control = lmerControl(optimizer = "bobyqa")
)

summary(mixedModel_epaReceiving)
MuMIn::r.squaredGLMM(mixedModel_epaReceiving)
emmeans::emmeans(mixedModel_epaReceiving, "contractYear")

mixedModelAge_epaReceiving <- lmerTest::lmer(
  receiving_epa ~ contractYear + ageCentered20 + ageCentered20Quadratic + years_of_experience + (1 + ageCentered20 | player_id),
  data = player_statsContractsWRTE_seasonal,
  control = lmerControl(optimizer = "bobyqa")
)

summary(mixedModelAge_epaReceiving)
MuMIn::r.squaredGLMM(mixedModelAge_epaReceiving)
emmeans::emmeans(mixedModelAge_epaReceiving, "contractYear")
```

```{r}
mixedModel_fantasyPtsReceiving <- lmerTest::lmer(
  fantasyPoints ~ contractYear + (1 | player_id),
  data = player_statsContractsWRTE_seasonal,
  control = lmerControl(optimizer = "bobyqa")
)

summary(mixedModel_fantasyPtsReceiving)
MuMIn::r.squaredGLMM(mixedModel_fantasyPtsReceiving)
emmeans::emmeans(mixedModel_fantasyPtsReceiving, "contractYear")

mixedModelAge_fantasyPtsReceiving <- lmerTest::lmer(
  fantasyPoints ~ contractYear + ageCentered20 + ageCentered20Quadratic + years_of_experience + (1 + ageCentered20 | player_id),
  data = player_statsContractsWRTE_seasonal,
  control = lmerControl(optimizer = "bobyqa")
)

summary(mixedModelAge_fantasyPtsReceiving)
MuMIn::r.squaredGLMM(mixedModelAge_fantasyPtsReceiving)
emmeans::emmeans(mixedModelAge_fantasyPtsReceiving, "contractYear")
```

### QB/RB/WR/TE {#sec-contractYearQBRBWRTE}

```{r}
# Placeholder for model predicting fantasy points
# Include player position as a covariate
```

## Conclusion {#sec-mythbustersConclusion}

::: {.content-visible when-format="html"}

## Session Info {#sec-mythbustersSessionInfo}

```{r}
sessionInfo()
```

:::