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25 Sports and Cognitive Psychology
25.1 Getting Started
25.1.1 Load Packages
25.1.2 Download Football Data
25.2 Overview
There are a number of ways in which analytics have changed sports [Underwood (2019); archived at https://perma.cc/PQ5R-TWFA]. Here is a summary of some of the key ways that analytics has led to changes.
Much of the history of analytics in sports traces back to Bill James. James was a member of the Society for American Baseball Research (SABR). He published a series of Baseball Abstracts, which included players’ statistics. James published the first Baseball Abstract in 1977 (https://www.pbs.org/thinktank/transcript1197.html; archived at https://perma.cc/Y7J7-GB9V). He coined the term Sabermetrics (which was originally named SABRmetrics, based on the name of the society) to refer to advanced metrics and statistical/empirical analysis of baseball. James believed that traditional statistics like batting average, runs batted in (RBIs), and pitchers’ wins did not reflect a player’s true value—i.e., their contribution to the team’s success. Instead, he advocated for the use of more advanced metrics that could provide a deeper understanding of a player’s performance and value such as on-base percentage (OBP), slugging percentage (SLG), wins above replacement (WAR), and fielding independent pitching (FIP). He also developed advanced metrics such as runs created (RC) and defense efficiency rating (DER).
James’ ideas were slow to catch on among those in baseball. Nevertheless, some people eventually caught on to his ideas—and to good success. Billy Beane, a general manager, used Sabermetrics to help the Oakland Athletics, a small market team with a limited budget, better compete with teams with larger budgets. He used statistics such as on-base percentage to identify player value more accurately, especially for identifying undervalued players. The story was described in Michael Lewis’ book, Moneyball, which was turned into a movie. Following publication of Moneyball, Theo Epstein, who was president of the Boston Red Sox and then of the Chicago Cubs, used sabermetrics to help each win the World Series.
In addition to teams using Sabermetrics to evaluate player talent, teams also began to frequently use statistical analysis to inform decision making during games, which led to key changes in the style of play. For instance, defensive shifts—where defensive players moved to locations on the field where particular hitters were most likely to hit the ball—became more common, attempts to steal bases became less common, there were fewer bunts, batters took more pitches (i.e., watched more pitches without swinging), there were more frequent pitching changes (for particular pitcher–batter matchups; such as to have a right-handed pitcher face a left-handed batter or vice versa), and a greater focus on velocity and spin rate among pitchers. Some of these analytics-driven changes in play style eventually led Major League Baseball (MLB) to make rule changes in an attempt to make the game more exciting to watch, including banning defensive shifts, reducing the number of pitching changes allowed, and making the bases larger and easier to steal.
Although baseball was one of the first major sports to embrace analytics, other sports have been transformed by analytics, as well. For instance, in basketball, there has been a greater focus on three points and buckets close to the rim (e.g., dunks and layups), with way fewer midrange shots. Moreover, star players rest more games. Here is an article on how Shane Battier, who was not the quickest, fastest, or most athletic player, used analytics successfully to guard players who were quicker or more athletic than him: https://www.nytimes.com/2009/02/15/magazine/15Battier-t.html [Lewis (2009); archived at https://web.archive.org/web/20250219225627/https://www.nytimes.com/2009/02/15/magazine/15Battier-t.html].
Football has also seen greater use of analytics, although its uptake has been somewhat slower than in many other sports. When asked about how he makes the decision about whether to go for a two-point conversion after a touchdown, Steelers Head Coach Mike Tomlin stated:
We work a menu of plays in that area over the course of the week. We rank them at the latter part of the week, and then we get into the stadium and we play it by ear. A lot of it has to do with the feel or the flow of the game—maybe what personnel group we think they’re going to match our personnel group with. As we start to play and work the ball down the field on the drives that produce the touchdowns before the point after, we have a little inclination of what their personality might be at least in terms of matching our personnel. All of those things weigh into the decision. It legitimately is a feel thing. I think that’s why you play the game. You can take analytics to baseball and things like that, but football is always going to be football. I got a lot of respect for analytics and numbers, but I’m not going to make judgments based on those numbers. The game is the game. It’s an emotional one played by emotional and driven men. That’s an element of the game you can’t measure. Oftentimes, decisions such as that weigh heavily into the equation.
— Steelers Head Coach Mike Tomlin, 2015 (archived at https://perma.cc/7CHJ-BTWX)
That is, Mike Tomlin, suggested that he does not take into account analytics when making decisions. Perhaps that is why the Pittsburgh Steelers were voted one of the least analytically advanced teams in the NFL in 2020 [Walder (2020); archived at https://perma.cc/R7FA-HGGB]. Nevertheless, the Steelers did eventually hire a person focused on analytics [Fowler (2015); archived at https://perma.cc/W7VE-JZQX].
A player talent evaluator for the NFL noted that many people around the league believe that the use of analytics is better suited for baseball than football because baseball involves more games, players, and one-on-one matchups [Reed (2016); archived at https://web.archive.org/web/20200803205803/https://www.cleveland.com/browns/2016/01/in_an_nfl_divided_over_analyti.html]. By contrast, player performance in football may be more dependent on teammates and play calls. The player talent evaluator noted, “In football they don’t know how to use all the numbers yet…They have the data, they have all these different stats but the people I have talked to aren’t completely sure how to use it.” [Reed (2016); archived at https://web.archive.org/web/20200803205803/https://www.cleveland.com/browns/2016/01/in_an_nfl_divided_over_analyti.html]. Some dismiss analytics entirely.
For instance, here is a 2016 video clip of a football commentator, Mike Patrick, making fun of people who compile statistics for informing decision-making in football, calling the people who compile the numbers “guys who wear socks with flip-flops”, suggesting that people who compile analytics to make recommendations in football are out of touch with the realities of football and do not have the same on-the-field understanding as the coaches and players.
Nevertheless, more and more people around the league are using analytics—likely because it works; for examples of articles, see here [Clark (2018); archived at https://perma.cc/7BKP-A4GJ] and here [Awbrey (2020); archived at https://perma.cc/WXE3-53E6]. Head Coach Doug Peterson heavily relied on analytics with the Philadelphia Eagles to help them win the 2017 Super Bowl; for more information, see here [Fox (2021); archived at https://perma.cc/49KQ-R785] and here [Rosenthal (2018); archived at https://perma.cc/2GRF-8Z5K].
Examples of changes in football due to the use of analytics include more often going for it on fourth down, a greater emphasis on the passing game, drafting Running Backs later in the draft (and, more generally, valuing Running Backs less), and trading down in the draft to obtain more low picks (rather than having fewer high picks) because top picks are frequently overvalued (Massey & Thaler, 2013).
25.3 Coaching and Loss/Risk Aversion
25.3.1 Going for It on Fourth Down
It had been known for a long time that going for it on fourth down would frequently increase a team’s chances of winning. Despite that, historically, teams rarely went for it on fourth down and elected to punt or kick a field goal instead. It is curious that there was such a discrepancy between the decisions that would maximize teams’ winning percentage and the decisions coaches actually made. In many fourth down situations, by punting the ball, coaches actively and systematically made decisions that reduced their team’s chances of winning. One potential explanation for the discrepancy is because of coaches’ risk aversion. As noted in Section 14.4.10, when it is possible to experience either a gain or a loss from a decision, loss aversion bias tends to lead people to make risk-averse decisions (Kahneman, 2011). According to this idea, in the case of failing to successfully convert on fourth down, coaches do not want to have to defend their decision to go for it to the media or the owner or general manager. That is, they may often play not to lose, rather than to win, in order to keep their job. However, in many cases, this is the wrong choice (Moskowitz & Wertheim, 2011).
Rates of going for it on fourth down in the NFL were low until 2017. After the 2017 season, rates of going for it on fourth down increased dramatically, as depicted in Figure 25.1.
Code
nfl_pbp4thDown <- nfl_pbp %>%
filter(down == 4) %>%
filter(!(play_type %in% c("no_play","qb_kneel")))
nfl_pbp4thDown$goForIt <- NA
nfl_pbp4thDown$goForIt[which(nfl_pbp4thDown$play_type %in% c("field_goal","punt"))] <- 0
nfl_pbp4thDown$goForIt[which(nfl_pbp4thDown$play_type %in% c("pass","run"))] <- 1
nfl_pbp4thDownPlotData <- nfl_pbp4thDown %>%
filter(!is.na(goForIt)) %>%
group_by(season) %>%
summarise(
goForItPct = mean(goForIt, na.rm = TRUE),
n = n(),
sd = sd(goForIt),
se = sd / n
)
ggplot2::ggplot(
data = nfl_pbp4thDownPlotData,
ggplot2::aes(
x = season,
y = goForItPct)) +
geom_point() +
geom_line() +
geom_ribbon(
aes(
y = goForItPct,
ymin = goForItPct - qnorm(0.975)*se,
ymax = goForItPct + qnorm(0.975)*se),
alpha = 0.2) +
scale_y_continuous(
limits = c(0, NA)
) +
scale_x_continuous(
minor_breaks = seq(0, 3000, 1),
breaks = seq(0, 3000, 5)
) +
labs(
x = "Season",
y = "Proportion of 4th Down Plays that\nare Attempts (to Get the First Down)",
title = "4th Down Attempts (Proportion) by Season",
) +
theme(axis.title.y = element_text(angle = 0, vjust = 0.5)) + # horizontal y-axis title
annotate(
"segment",
x = 2015,
xend = 2017,
y = 0.08,
yend = 0.123,
color = "blue",
linewidth = 1.5,
alpha = 0.6,
arrow = arrow()) +
annotate(
"text",
x = 2015,
y = 0.07,
label = "Rapid increases in 4th down\nattempts after the 2017 season",
hjust = 0.5) # center
As depicted in the Figure 25.2 [which was adapted from a figure by Ben Baldwin; Baldwin (2023); archived at https://perma.cc/S5D8-3NCU], teams went for it on fourth down nearly twice as often in 2021 compared to 2017, when when their win probability was at least 20% (given the current situation at the start of the given play) and they would increase their win probably by going for it. We use the ggtext package (Wilke & Wiernik, 2022) to annotate text:
Code
# labels on the plot
text_df <- tibble(
label = c(
"NFL coaches<br>in <span style='color:#00BFC4'>**2021**</span>",
"NFL coaches<br>in <span style='color:#F8766D'>**2017**</span>"),
x = c(5, 7),
y = c(87.5, 22.5),
angle = c(10, 10),
color = c("black", "black")
)
nfl_4thdown %>%
filter(
vegas_wp > .2,
between(go_boost, -10, 10),
season %in% c(2017, 2021)) %>%
ggplot(
aes(
x = go_boost,
y = go,
color = as.factor(season))) +
geom_vline(xintercept = 0) +
stat_smooth(
method = "gam",
method.args = list(gamma = 1),
formula = y ~ s(x, bs = "cs", k = 10),
show.legend = FALSE,
se = FALSE,
linewidth = 4) +
# this is just to get the plot to draw the full 0 to 100 range
geom_hline(
yintercept = 100,
alpha = 0) +
geom_hline(
yintercept = 0,
alpha = 0) +
ggtext::geom_richtext(
data = text_df,
aes(
x,
y,
label = label,
angle = angle),
color = "black",
fill = NA,
label.color = NA,
size = 5) +
theme_classic() +
labs(
x = "Gain in win probability by going for it",
y = "Go-for-it percentage",
subtitle = "4th down decisions in 2021 versus 2017, win prob. > 20%",
title = glue::glue("How <span style='color:red'>math</span> is changing football")) +
theme(
legend.position = "none",
plot.title = element_markdown(
size = 22,
hjust = 0.5),
plot.subtitle = element_markdown(
size = 13.5,
hjust = 0.5),
axis.title.x = element_text(
size = 14,
face = "bold"),
axis.title.y = element_text(
size = 14,
face = "bold",
angle = 0, # horizontal y-axis title
vjust = 0.5)
) +
scale_y_continuous(
breaks = scales::pretty_breaks(n = 4),
limits = c(0, 100),
expand = c(0, 0)) +
scale_x_continuous(
breaks = scales::pretty_breaks(n = 10),
limits = c(-10, 10),
expand = c(0, 0)) +
annotate(
"text",
x = -1.5,
y = 70,
label = "Should\nkick",
color = "black",
size = 5) +
annotate(
"text",
x = 1.75,
y = 70,
label = "Should\ngo for it",
color = "black",
size = 5) +
annotate(
"segment",
x = -.1,
y = 80,
xend = -2,
yend = 80,
arrow = arrow(length = unit(0.05, "npc")),
color = "black",
linewidth = 2) +
annotate(
"segment",
x = .1,
y = 80,
xend = 2,
yend = 80,
arrow = arrow(length = unit(0.05, "npc")),
color = "black",
linewidth = 2)
NFL teams were later to implement analytics into their decision making than even teams at lower levels of the sport. Some high school teams, such as the Pulaski Academy Bruins (Little Rock, AR), coached by Kevin Kelley, consistently went for it on fourth down well before 2017 (Moskowitz & Wertheim, 2011).
[Bruins Head Football Coach Kevin] Kelley believes that the “quant jocks” don’t go far enough to validate the no-punting worldview and, more generally, the virtues of risk-taking. “The math guys, the astrophysicist guys, they just do the raw numbers and they don’t figure emotion into it—and that’s the biggest thing of all,” he says. “The built-in emotion involved in football is unbelievable, and that’s where the benefits really pay off.” What he means is this: A defense that stops an opponent on third down is usually ecstatic. They’ve done their job. The punting unit comes on, and the offense takes over. When that defense instead gives up a fourth-down conversion, it has a hugely deflating effect. At Pulaski’s games, you can see the shoulders of the opposing defensive players slump and their eyes look down when they fail to stop the Bruins on fourth down.
Based on Romer’s (2006) analysis of third down plays (because few teams went for it on fourth down), focusing on plays in the first quarter (to remove desperation plays), he identified several general conclusions about fourth-down situations:
- Inside the opponent’s 45-yard line, a team is better off going for it than punting with 6 (or less) yards to go (for a first down).
- Inside the opponent’s 33-yard line, a team is better off going for it with 10 (or less) yards to go (unless little time remains and a field goal would decide the game).
- Once reaching the opponent’s 5-yard line, a team is better off going for it.
- Regardless of field position, a team is always better off going for it with 3 (or less) yards to go.
Nevertheless, out of the fourth down plays Romer (2006) identified between 1998–2000 in which it would have been advantageous to go for it, the team made the suboptimal decision (punting or kicking) 90% of the time. “Inasmuch as an academic paper can become a cult hit, Romer’s made the rounds in NFL executive offices, but most NFL coaches seemed to dismiss his findings as the handiwork of an egghead, polluting art with science.” (Moskowitz & Wertheim, 2011, p. 39).
Here is an analysis by the New York Times on when to go for it on fourth down: https://www.nytimes.com/2014/09/05/upshot/4th-down-when-to-go-for-it-and-why.html [NYT 4th Down Bot (2014); archived at https://perma.cc/KA9Y-BRUD]. Here is a fourth down calculator: https://rbsdm.com/stats/fourth_calculator/.
25.4 Other Beliefs in Sports
25.4.1 Icing the Kicker
In a 2008 game between the Jets and Raiders, Jets Kicker Jay Feely missed a game-tying field goal to send the game to overtime. However, moments before the snap, the Raiders called a timeout in an attempt to “ice the kicker.” The idea behind icing the kicker is making the kicker think about the pressure of upcoming kick so he gets “cold feet” (metaphorically speaking) and misses the kick. After the brief timeout, Feely got a second chance and made the field goal to send the game into overtime.
After the game, Feely noted, “I heard the whistle before I started, which is an advantage to the kicker…If you’re going to do that, do that before he kicks. I can kick it down the middle, see what the wind does and adjust. It helps the kicker tremendously.” [Press (2008); archived at https://perma.cc/U7SV-UE2E].
However, does icing the kicker work? There is mixed evidence on icing the kicker. Some studies find some evidence for lower percentage of iced kicks made compared to non-iced kicks (Goldschmied et al., in press), whereas other studies do not (e.g., Berry & Wood, 2004; Gonzalez Sanchez et al., 2024; Moskowitz & Wertheim, 2011). This suggests that, if there is such an effect, the effect size is likely very small, and it may better suit the team to use your timeouts in other situations.
25.4.2 Hot Hand
The belief in the “hot hand” is described in Section 14.5.3.
25.5 Conclusion
25.6 Session Info
R version 4.4.3 (2025-02-28)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.2 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-r0.3.26.so; LAPACK version 3.12.0
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] ggtext_0.1.2 lubridate_1.9.4 forcats_1.0.0 stringr_1.5.1
[5] dplyr_1.1.4 purrr_1.0.4 readr_2.1.5 tidyr_1.3.1
[9] tibble_3.2.1 ggplot2_3.5.1 tidyverse_2.0.0 nflreadr_1.4.1
loaded via a namespace (and not attached):
[1] generics_0.1.3 xml2_1.3.7 stringi_1.8.4 lattice_0.22-6
[5] hms_1.1.3 digest_0.6.37 magrittr_2.0.3 evaluate_1.0.3
[9] grid_4.4.3 timechange_0.3.0 fastmap_1.2.0 Matrix_1.7-2
[13] jsonlite_1.9.1 mgcv_1.9-1 scales_1.3.0 cli_3.6.4
[17] rlang_1.1.5 commonmark_1.9.2 munsell_0.5.1 splines_4.4.3
[21] withr_3.0.2 cachem_1.1.0 yaml_2.3.10 tools_4.4.3
[25] tzdb_0.4.0 memoise_2.0.1 colorspace_2.1-1 vctrs_0.6.5
[29] R6_2.6.1 lifecycle_1.0.4 htmlwidgets_1.6.4 pkgconfig_2.0.3
[33] pillar_1.10.1 gtable_0.3.6 data.table_1.17.0 glue_1.8.0
[37] Rcpp_1.0.14 xfun_0.51 tidyselect_1.2.1 knitr_1.49
[41] farver_2.1.2 htmltools_0.5.8.1 nlme_3.1-167 rmarkdown_2.29
[45] labeling_0.4.3 compiler_4.4.3 markdown_1.13 gridtext_0.1.5