NFL attendance
Jim Gruman
February 4, 2020
Last updated: 2021-09-09
Checks: 7 0
Knit directory: myTidyTuesday/
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Let’s build a very simple model for NFL attendance
Explore data
Load the attendance and team standings data from Github
attendance <- read_csv("https://raw.githubusercontent.com/rfordatascience/tidytuesday/master/data/2020/2020-02-04/attendance.csv")
standings <- read_csv("https://raw.githubusercontent.com/rfordatascience/tidytuesday/master/data/2020/2020-02-04/standings.csv")
attendance_joined <- attendance %>%
left_join(standings, by = c("year", "team_name", "team"))Explore the files and look for trends. In this boxplot visual, some teams certainly expect higher weekly attendance.
attendance_joined %>%
filter(!is.na(weekly_attendance)) %>%
ggplot(aes(
y = fct_reorder(team_name, weekly_attendance),
x = weekly_attendance,
fill = playoffs
)) +
geom_boxplot(outlier.alpha = 0.5) +
scale_x_continuous(labels = scales::label_comma()) +
labs(
title = "NFL Weekly Attendance",
caption = paste0("Jim Gruman ", Sys.Date()),
x = "",
y = "Weekly Attendance"
) +
theme(legend.position = "bottom")
In this histogram, playoff-bound teams generally have higher point spread margins over the course of many games.
attendance_joined %>%
distinct(team_name, year, margin_of_victory, playoffs) %>%
ggplot(aes(margin_of_victory, fill = playoffs)) +
geom_histogram(position = "identity", alpha = 0.7) +
labs(
title = "NFL Team Margin of Victory",
caption = paste0("Jim Gruman ", Sys.Date()),
x = "Point Spread", y = "Game Count"
) +
theme(legend.position = "bottom")
Across the weeks of the season, this data visualization shows the distribution of attendance by week number.
attendance_joined %>%
mutate(week = factor(week)) %>%
ggplot(aes(week, weekly_attendance, fill = "blue")) +
geom_boxplot(show.legend = FALSE, outlier.alpha = 0.4) +
labs(
title = "NFL Weekly Game Attendance",
caption = paste0("Jim Gruman ", Sys.Date()),
x = "Week of Season", y = "Attendance"
) +
theme(legend.position = "bottom") +
scale_y_continuous(labels = scales::label_comma())
To build models for the prediction of weekly attendance, we will select for features arbitrarily on the team_name, the year, the week of the game, and the margin of victory.
attendance_df <- attendance_joined %>%
filter(!is.na(weekly_attendance)) %>%
dplyr::select(
weekly_attendance, team_name, year, week,
margin_of_victory, strength_of_schedule, playoffs
)Train a Model
First, the data are split into training and testing sets at about 75/25, stratifying for similar playoff outcomes in both.
attendance_split <- attendance_df %>%
initial_split(strata = playoffs)
nfl_train <- training(attendance_split)
nfl_test <- testing(attendance_split)A simple linear model is specified and fit, and the estimates of coefficients are shown here:
lm_spec <- linear_reg(mode = "regression") %>%
set_engine(engine = "lm")
lm_fit <- lm_spec %>%
fit(weekly_attendance ~ ., data = nfl_train)
tidy(lm_fit) %>%
arrange(-p.value) %>%
filter(p.value < 0.05) %>%
knitr::kable()| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| team_namePanthers | 1788.47742 | 766.51134 | 2.333269 | 0.0196599 |
| team_nameEagles | 1867.67406 | 781.27721 | 2.390540 | 0.0168478 |
| (Intercept) | -81456.07886 | 33471.27892 | -2.433611 | 0.0149719 |
| team_nameChiefs | 2123.44169 | 771.24254 | 2.753274 | 0.0059142 |
| team_nameRams | -2619.25130 | 757.80765 | -3.456354 | 0.0005505 |
| team_nameBroncos | 2772.20172 | 764.62900 | 3.625551 | 0.0002902 |
| strength_of_schedule | 222.75149 | 61.34503 | 3.631126 | 0.0002840 |
| team_nameLions | -2864.45966 | 760.61254 | -3.765991 | 0.0001671 |
| team_nameVikings | -2991.38247 | 768.17257 | -3.894154 | 0.0000994 |
| team_nameBears | -3080.42995 | 773.12053 | -3.984411 | 0.0000683 |
| team_nameJaguars | -3120.72506 | 766.39104 | -4.071975 | 0.0000471 |
| team_nameSteelers | -3311.75689 | 766.55313 | -4.320323 | 0.0000158 |
| week | -86.43370 | 19.26394 | -4.486813 | 0.0000073 |
| year | 74.82422 | 16.65373 | 4.492941 | 0.0000071 |
| team_nameColts | -3449.02877 | 764.99840 | -4.508544 | 0.0000066 |
| team_nameBuccaneers | -3516.29291 | 766.37815 | -4.588196 | 0.0000045 |
| team_nameBengals | -4321.88943 | 773.42204 | -5.588009 | 0.0000000 |
| team_nameJets | 4745.24063 | 768.62954 | 6.173638 | 0.0000000 |
| margin_of_victory | 146.78930 | 23.15908 | 6.338305 | 0.0000000 |
| team_nameChargers | -5655.03038 | 758.66937 | -7.453880 | 0.0000000 |
| team_nameRedskins | 5931.63951 | 767.66935 | 7.726816 | 0.0000000 |
| team_nameRaiders | -6343.25992 | 775.39938 | -8.180636 | 0.0000000 |
| team_nameGiants | 6407.18859 | 769.46531 | 8.326806 | 0.0000000 |
| team_nameCardinals | -6470.53879 | 758.95065 | -8.525638 | 0.0000000 |
| team_nameCowboys | 6613.72537 | 763.52992 | 8.662038 | 0.0000000 |
A comparable random forest regression is specified and fit here:
rf_spec <- rand_forest(mode = "regression") %>%
set_engine(engine = "ranger")
rf_fit <- rf_spec %>%
fit(weekly_attendance ~ ., data = nfl_train)
tidy(lm_fit) %>%
arrange(-estimate) %>%
knitr::kable()| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| team_nameCowboys | 6613.72537 | 763.52992 | 8.6620382 | 0.0000000 |
| team_nameGiants | 6407.18859 | 769.46531 | 8.3268063 | 0.0000000 |
| team_nameRedskins | 5931.63951 | 767.66935 | 7.7268156 | 0.0000000 |
| team_nameJets | 4745.24063 | 768.62954 | 6.1736382 | 0.0000000 |
| team_nameBroncos | 2772.20172 | 764.62900 | 3.6255514 | 0.0002902 |
| team_nameChiefs | 2123.44169 | 771.24254 | 2.7532736 | 0.0059142 |
| team_nameEagles | 1867.67406 | 781.27721 | 2.3905395 | 0.0168478 |
| team_namePanthers | 1788.47742 | 766.51134 | 2.3332694 | 0.0196599 |
| team_namePackers | 971.42811 | 760.29413 | 1.2777004 | 0.2013940 |
| team_nameSaints | 637.54436 | 762.73835 | 0.8358625 | 0.4032585 |
| team_nameTexans | 355.51809 | 785.64903 | 0.4525152 | 0.6509108 |
| team_nameDolphins | 332.35203 | 762.20818 | 0.4360384 | 0.6628212 |
| strength_of_schedule | 222.75149 | 61.34503 | 3.6311255 | 0.0002840 |
| team_nameBrowns | 222.40629 | 773.64517 | 0.2874784 | 0.7737538 |
| margin_of_victory | 146.78930 | 23.15908 | 6.3383047 | 0.0000000 |
| year | 74.82422 | 16.65373 | 4.4929414 | 0.0000071 |
| team_nameFalcons | -68.93885 | 773.47578 | -0.0891286 | 0.9289820 |
| week | -86.43370 | 19.26394 | -4.4868125 | 0.0000073 |
| playoffsPlayoffs | -211.03783 | 288.70801 | -0.7309732 | 0.4648180 |
| team_nameRavens | -278.23920 | 772.80223 | -0.3600393 | 0.7188277 |
| team_nameBills | -416.98841 | 763.14401 | -0.5464085 | 0.5848011 |
| team_namePatriots | -545.67186 | 786.66152 | -0.6936552 | 0.4879196 |
| team_nameTitans | -807.91944 | 762.16059 | -1.0600383 | 0.2891608 |
| team_nameSeahawks | -1442.91948 | 779.67975 | -1.8506566 | 0.0642577 |
| team_nameRams | -2619.25130 | 757.80765 | -3.4563537 | 0.0005505 |
| team_nameLions | -2864.45966 | 760.61254 | -3.7659906 | 0.0001671 |
| team_nameVikings | -2991.38247 | 768.17257 | -3.8941542 | 0.0000994 |
| team_nameBears | -3080.42995 | 773.12053 | -3.9844110 | 0.0000683 |
| team_nameJaguars | -3120.72506 | 766.39104 | -4.0719749 | 0.0000471 |
| team_nameSteelers | -3311.75689 | 766.55313 | -4.3203227 | 0.0000158 |
| team_nameColts | -3449.02877 | 764.99840 | -4.5085438 | 0.0000066 |
| team_nameBuccaneers | -3516.29291 | 766.37815 | -4.5881957 | 0.0000045 |
| team_nameBengals | -4321.88943 | 773.42204 | -5.5880091 | 0.0000000 |
| team_nameChargers | -5655.03038 | 758.66937 | -7.4538799 | 0.0000000 |
| team_nameRaiders | -6343.25992 | 775.39938 | -8.1806358 | 0.0000000 |
| team_nameCardinals | -6470.53879 | 758.95065 | -8.5256383 | 0.0000000 |
| (Intercept) | -81456.07886 | 33471.27892 | -2.4336112 | 0.0149719 |
Evaluate Models
results_train <- lm_fit %>%
predict(new_data = nfl_train) %>%
mutate(
truth = nfl_train$weekly_attendance,
model = "lm"
) %>%
bind_rows(rf_fit %>%
predict(new_data = nfl_train) %>%
mutate(
truth = nfl_train$weekly_attendance,
model = "rf"
))
results_test <- lm_fit %>%
predict(new_data = nfl_test) %>%
mutate(
truth = nfl_test$weekly_attendance,
model = "lm"
) %>%
bind_rows(rf_fit %>%
predict(new_data = nfl_test) %>%
mutate(
truth = nfl_test$weekly_attendance,
model = "rf"
))On the training dataset
results_train %>%
group_by(model) %>%
rmse(truth = truth, estimate = .pred) %>%
knitr::kable()| model | .metric | .estimator | .estimate |
|---|---|---|---|
| lm | rmse | standard | 8367.940 |
| rf | rmse | standard | 6079.739 |
On the testing data:
results_test %>%
group_by(model) %>%
rmse(truth = truth, estimate = .pred) %>%
knitr::kable()| model | .metric | .estimator | .estimate |
|---|---|---|---|
| lm | rmse | standard | 8170.598 |
| rf | rmse | standard | 8580.718 |
The random forest model here appears to overfit the training data set, with disappointing results on new data.
results_test %>%
mutate(train = "testing") %>%
bind_rows(results_train %>%
mutate(train = "training")) %>%
ggplot(aes(truth, .pred, color = model)) +
geom_abline(lty = 2, color = "gray80", size = 1.5) +
geom_point(alpha = 0.5) +
facet_wrap(~train)
### Lets try again, with resampling on the training
all_cores <- parallelly::availableCores(omit = 1)
all_coressystem
11 future::plan("multisession", workers = all_cores) # on Windows
nfl_folds <- vfold_cv(nfl_train, strata = playoffs)
rf_res <- fit_resamples(
workflow(weekly_attendance ~ ., rf_spec),
nfl_folds,
control = control_resamples(save_pred = TRUE)
)
rf_res %>%
collect_metrics() %>%
knitr::kable()| .metric | .estimator | mean | n | std_err | .config |
|---|---|---|---|---|---|
| rmse | standard | 8674.5906122 | 10 | 110.4737449 | Preprocessor1_Model1 |
| rsq | standard | 0.1248592 | 10 | 0.0080805 | Preprocessor1_Model1 |
rf_res %>%
unnest(.predictions) %>%
ggplot(aes(weekly_attendance, .pred, color = id)) +
geom_abline(lty = 2, color = "gray80", size = 1.5) +
geom_point(alpha = 0.5) +
labs(
title = "Model Accuracy",
caption = paste0("Jim Gruman ", Sys.Date()),
x = "Attendance Truth", y = "Attendance Prediction"
) +
theme(legend.position = "bottom") +
scale_y_continuous(labels = scales::label_comma()) +
scale_x_continuous(labels = scales::label_comma())
After resampling, the root mean squared error of the random forest model on test data is improved only marginally, compared to the conventional linear model.
Credits: Julia Silge, RStudio Thomas Mock, RStudio
sessionInfo()R version 4.1.1 (2021-08-10)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 19043)
Matrix products: default
locale:
[1] LC_COLLATE=English_United States.1252
[2] LC_CTYPE=English_United States.1252
[3] LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C
[5] LC_TIME=English_United States.1252
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] ranger_0.13.1 vctrs_0.3.8 rlang_0.4.11 yardstick_0.0.8
[5] workflowsets_0.1.0 workflows_0.2.3 tune_0.1.6 rsample_0.1.0
[9] recipes_0.1.16 parsnip_0.1.7.900 modeldata_0.1.1 infer_1.0.0
[13] dials_0.0.9.9000 scales_1.1.1 broom_0.7.9 tidymodels_0.1.3
[17] forcats_0.5.1 stringr_1.4.0 dplyr_1.0.7 purrr_0.3.4
[21] readr_2.0.1 tidyr_1.1.3 tibble_3.1.4 ggplot2_3.3.5
[25] tidyverse_1.3.1 workflowr_1.6.2
loaded via a namespace (and not attached):
[1] readxl_1.3.1 backports_1.2.1 systemfonts_1.0.2
[4] plyr_1.8.6 splines_4.1.1 listenv_0.8.0
[7] digest_0.6.27 foreach_1.5.1 htmltools_0.5.2
[10] viridis_0.6.1 fansi_0.5.0 magrittr_2.0.1
[13] tzdb_0.1.2 globals_0.14.0 modelr_0.1.8
[16] gower_0.2.2 extrafont_0.17 vroom_1.5.4
[19] R.utils_2.10.1 extrafontdb_1.0 hardhat_0.1.6
[22] colorspace_2.0-2 rvest_1.0.1 textshaping_0.3.5
[25] haven_2.4.3 xfun_0.25 crayon_1.4.1
[28] jsonlite_1.7.2 survival_3.2-11 iterators_1.0.13
[31] glue_1.4.2 gtable_0.3.0 ipred_0.9-11
[34] R.cache_0.15.0 Rttf2pt1_1.3.9 future.apply_1.8.1
[37] DBI_1.1.1 Rcpp_1.0.7 viridisLite_0.4.0
[40] bit_4.0.4 GPfit_1.0-8 lava_1.6.10
[43] prodlim_2019.11.13 httr_1.4.2 ellipsis_0.3.2
[46] farver_2.1.0 pkgconfig_2.0.3 R.methodsS3_1.8.1
[49] nnet_7.3-16 sass_0.4.0 dbplyr_2.1.1
[52] utf8_1.2.2 here_1.0.1 labeling_0.4.2
[55] tidyselect_1.1.1 DiceDesign_1.9 later_1.3.0
[58] munsell_0.5.0 cellranger_1.1.0 tools_4.1.1
[61] cachem_1.0.6 cli_3.0.1 generics_0.1.0
[64] evaluate_0.14 fastmap_1.1.0 yaml_2.2.1
[67] ragg_1.1.3 rematch2_2.1.2 bit64_4.0.5
[70] knitr_1.33 fs_1.5.0 future_1.22.1
[73] whisker_0.4 R.oo_1.24.0 xml2_1.3.2
[76] compiler_4.1.1 rstudioapi_0.13 curl_4.3.2
[79] reprex_2.0.1 lhs_1.1.1 bslib_0.3.0
[82] stringi_1.7.4 highr_0.9 gdtools_0.2.3
[85] hrbrthemes_0.8.0 lattice_0.20-44 Matrix_1.3-4
[88] styler_1.5.1 conflicted_1.0.4 pillar_1.6.2
[91] lifecycle_1.0.0 furrr_0.2.3 jquerylib_0.1.4
[94] httpuv_1.6.2 R6_2.5.1 promises_1.2.0.1
[97] gridExtra_2.3 parallelly_1.27.0 codetools_0.2-18
[100] MASS_7.3-54 assertthat_0.2.1 rprojroot_2.0.2
[103] withr_2.4.2 parallel_4.1.1 hms_1.1.0
[106] grid_4.1.1 rpart_4.1-15 timeDate_3043.102
[109] class_7.3-19 rmarkdown_2.10 git2r_0.28.0
[112] pROC_1.18.0 lubridate_1.7.10