Abstract
This paper examines whether the substitution decisions, under conditions of paper (or realized) losses, stimulate (or moderate) managerial risk taking. Using data on roster changes and field goal attempts (FGAs) in National Basketball Association (NBA) games, I find strong evidence of the significantly causal effects of paper and realized losses (or gains) on the decisions regarding managerial risk taking. While coaches increase their level of risk taking after experiencing the paper losses of lagging behind in the substitution strategy within a game, the effects of realized gains from leading wins, however, offer evidence of higher risk-seeking in the wake of prior wins. Furthermore, the evidence that players lagging behind increase their risk taking in the final stages of the tournament is robust in empirical settings for the shooting decisions. Finally, a coach with longer tenure engages in higher risk taking in substitutions, whereas a team with an older coach of shorter tenure engages in more risk taking in risky 3-point FGAs.
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Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Notes
A growing body of evidence on managers’ decision making suggests that differences in management “style” across individuals at the helm of firms play an important role in sha** corporate policies (Bernile et al., 2017; Bertrand & Schoar, 2003; Dittmar & Duchin, 2016). As pointed out by Schoar and Zuo (2017), “Traditional theories about firm decisions such as capital structure or investment abstract away from the role of CEOs or assume that rational managers will behave identically if faced with the same problem. However, the more recent literature suggests that managers are heterogeneous and matter to the firms that they run” (p. 1425).
Due to this, it comes as no surprise that most existing field studies in the literature on managerial risk taking asymmetrically focus only on the effects of rare, extremely adverse events, such as natural disasters or recessions (e.g., Cameron & Shah, 2015; Cassar et al., 2017; Eckel et al., 2009; Necker & Ziegelmeyer, 2016), rather than of frequent shocks.
Richard Thaler and Eric Johnson first defined the “house money effect,” borrowing the term from casinos. The term makes reference to a gambler who takes winnings from previous bets and uses some or all of them in subsequent bets. The house money effect suggests, for example, that individuals tend to buy higher-risk stocks or other assets after profitable investments (gains). Here, I will examine whether the risk of the substitution strategy increases with a team’s previous wins (gains).
Thaler and Johnson (1990) observe that people take greater risk following gains than following losses, a tendency they refer to as the house-money effect. They argue that having made a gain, the decision maker feels as if he is gambling with other people’s money and thus becomes less risk averse.
Moreover, economic crises and downturns have been shown to increase risk aversion, possibly reducing self employment and investments in stocks, which in turn can amplify macroeconomic downturns.
Normally, a player is substituted only in case of an injury or a foul involving a starting player.
The difference in the numbers of observations between home-team (49.79%) and away-team (50.21%) substitutions shows that away-team coaches switch more times than home-team coaches. The difference between leading (n = 164,876, 47.44%) and lagging (n = 166,851, 48.01%) teams shows the evidence of leading managers substituting fewer times.
Data for this analysis were also collected from kaggle.com and the official score sheets from the NBA available at https://www.nba.com/stats/. I use the data from these two websites as a channel for data verification. The dataset from kaggle.com includes variables of the day of the season, the player, the results of FGAs, home and away scores, seconds left, and the period of the game when the shooting took place. Due to the COVID-19 pandemic, the 2020/21 regular season has been reduced to 72 games for each team. The data period began on December 22, 2020 and ended on January 15, 2021.
Bartling et al. (2015) assign the value 1 to goalkeepers, 2 to defenders, 3 to midfielders, and 4 to strikers. However, Grund and Gürtler (2005) exclude goalkeepers. Defenders, midfielders, and forwards get the value 0, the value 1, and the value 2, respectively.
Each team typically has approximately 88 FGAs per game on average, or has approximately 7.2 thousand FGAs in a regular season. The league has approximately a total of 216 thousand FGAs in a full regular season.
A center is the tallest player in a team, responsible for protecting the rim on defense and scoring close to the basket on offense. A PF is a strong player who typically plays closer to the basket, responsible for rebounding and scoring in the paint. A SF is a versatile player who can both shoot and drive to the basket, often responsible for defending the opposing team's best perimeter player. A PG is typically the team's primary ball-handler and playmaker, responsible for directing the team's offense and setting up scoring opportunities for teammates. The SG is responsible for shooting the ball, and making baskets from beyond the three-point line. SG is often the team’s top scorer.
Important strategic choices like player substitutions might involve collaborative decision-making among not only the head coach but also assistant coaches and staff members. Despite the authors emphasizing the team in Eq. (1) rather than solely focusing on the head coach when studying their personal risk-taking tendencies, there's a possibility that the results obtained might not completely capture the intended conclusions. To address this, the regressions for the team’s risk-taking behavior are adjusted to incorporate the head coach’s individual context within Eq. (1) to tackle this issue. The results support previous findings. I appreciate the valuable suggestions from the anonymous reviewer. The complete results of the regressions for the head coach support previous findings and can be provided by the author if needed.
For example, in a period a coach replaces a center and two shooting guards with a small forward and two point guards, respectively. The outgoing offensive value of a center and two shooting guards is 36.58 (= 10.96 + 2 * 12.81) and the corresponding defensive value is 13.78 (= 7.44 + 2 * 3.17). The incoming offensive value of a small forward and two point guards is 42.45 (= 11.65 + 2 * 15.4) and the corresponding defensive value is 10.52 (= 4.12 + 2 * 3.2). The differential of offensive (/defensive) values between incoming and outgoing players is 5.87(/− 3.26).
It needs to be noted that an omitted variable bias is a potentially concern. That is, the unobservable factors affect coaches’ risk-taking behavior, such as the time-varying atmosphere of teams and games, the time-varying emotional changes in coaches, whether important people (e.g., the general manager or team president) are present, and so on. Since the identification may be suffered from omitted variable bias, unobservable individual effects in panel data and fixed effects regression modeling are employed to partially circumvent this issue. I thank anonymous reviewer for the valuable suggestions.
Overall, the final dataset comprises 7,563 matches (with 45.96 average match-level substitutions), 61,458 periods (with 11.3 average period-level substitutions), and 347,527 substitutions.
Furthermore, the values based on a two-sample t tests for RosterA and ShotA3 are 7.86 (p value = 0. 00) and 7.76 (p value = 0. 00), and reject the null hypothesis with equal means, indicating that lagging coaches do switch fewer players and engage in less risky shootings (and take less risks) than leading coaches.
In addition, Nieken and Sliwka (2010) indicated that “a leading player chooses the risky strategy more often than the trailing players if the outcomes are correlated.”.
The largest number of periods is 8, representing a quadruple-overtime game. In the regular and playoff games in the data period covering the 2015/16 to 2020/21 seasons, there are four games where teams dragged each other into the fourth overtime. One of the four was a playoff game, and it took place at the Moda Center for the Denver Nuggets in Portland against the Blazers on May 3, 2019. The Blazers grinded out a thrilling 140–137 quadruple-overtime (4OT) victory over the Denver Nuggets to protect the home court and seize a 2–1 series lead. It was the first playoff game to reach 4OT in 66 years and only the second in NBA history.
These effects are consistent in the regressions of the random-effects (RE) and fixed-effects (FE) models. At the bottom of Table 4, none of the Hausman (1978) tests rejects the null hypothesis that the difference in coefficients is not systematic (e.g., = 27.96 for Model 7). The random-effects (RE) model is thus supported.
A one-point lead (lag) is very different from a 20-point lead (lag). In the robustness checks for the heterogeneity by magnitude of leads and lags, the negative significance in the coefficients of APD3 for defense from models (5) to (8) of Table A in appendix indicates that a coach tends to decrease the defensive value when the point gap is close (i.e., less than 3-point). That is, compared to a large heterogeneous game, a coach takes more risk and decreases the defensive in team roster. A coach’s risk-taking behavior is differentially affected by the magnitude of leads and lags. I thank anonymous referee for this valuable comment.
After all, players’(/workers’) risk taking on the court(/workplace) inherently differs from that of coaches(/managers) off the court, and this highlights the difference in risk taking between players(/workers) and coaches(/managers).
Higher risk taking may be explained by a higher degree of overconfidence, less herding behavior, or a lower degree of risk aversion. While empirical research has shown that a negative relationship between risk taking and experience is observed (cf. Boyson, 2003), other studies arrive at opposite results (cf. Chevalier and Ellison 1999; Lamont 2002).
In general, 2-point and 3-point FGAs are two possible ways to score in basketball. The former requires that players shoot from a distance of less than 23 feet 9 inches (7.24 m) to get two points when successful. The latter is that they can try to hit the basket from a farther distance in the three-point field goal area, receiving three points when making the shot.
I use the net values of offensive and defensive measurements and different W-L definition as the robustness checks. The results robustly validate previous findings that the role of the realization effect in subsequent risk taking is important. I thank the anonymous reviewers for the helpful comments. The complete results of the regressions for the net value can be provided by the author if needed.
For example, the studies involving Spanish commercial banks and savings banks consider the determinants of risk taking in Spanish financial intermediaries, with a special emphasis on the information regarding ownership structure and the sizes of the different entities (e.g., García-Marco & Robles-Fernandez, 2008). Andries and Haddad’s (2020) model explains how changes in information frequencies affect risk-taking decisions, as observed in the field and the lab. They find that receiving state-dependent alerts following sharp downturns improves welfare, suggesting a role for financial intermediaries as information managers. Evidence from the mutual funds industry shows that managers, whose ability to attract contributions depends on performance relative to other mutual funds, could pick riskier assets and managers opt for riskier investments or production technologies if they are lagging behind (Dijk et al., 2014; Kacperczyk et al., 2015). In consumer product industries, where changes in rank are reported in key publications, managers have been found to scrutinize the trajectories of proximate competitors and take risks (e.g., hold price promotions) to protect their standing.
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This study was funded by Ministry of Science and Technology, Taiwan (NSTC 112–2410-H-128-022).
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Appendix
Appendix
Table A The effects of paper losses and gains on managerial risk taking in substitutions: the robustness checks for the heterogeneity by magnitude of leads and lags
Offence | Defense | |||||||
|---|---|---|---|---|---|---|---|---|
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | |
RE | FE | RE | FE | RE | FE | RE | FE | |
DLag | 0.21** (0.096) | 0.21** (0.096) | 0.21** (0.094) | 0.21** (0.094) | − 0.15* (0.079) | − 0.15* (0.079) | − 0.15* (0.078) | − 0.15* (0.078) |
DLead | 0.12 (0.088) | 0.13 (0.088) | 0.13 (0.086) | 0.13 (0.086) | − 0.087 (0.074) | − 0.089 (0.074) | − 0.089 (0.072) | − 0.091 (0.072) |
DLastquar | 0.085 (0.13) | 0.088 (0.13) | 0.085 (0.13) | 0.085 (0.13) | − 0.10 (0.10) | − 0.10 (0.10) | − 0.10 (0.10) | − 0.10 (0.10) |
Laglastquar | − 0.74*** (0.15) | − 0.74*** (0.15) | − 0.73*** (0.14) | − 0.74*** (0.14) | 0.59*** (0.11) | 0.59*** (0.11) | 0.59*** (0.11) | 0.59*** (0.11) |
Leadlastquar | − 0.50*** (0.14) | − 0.50*** (0.14) | − 0.50*** (0.14) | − 0.50*** (0.14) | 0.40*** (0.11) | 0.40*** (0.11) | 0.40*** (0.11) | 0.40*** (0.11) |
APD3 | 0.075 (0.049) | 0.076 (0.049) | 0.077 (0.048) | 0.077 (0.048) | − 0.075** (0.036) | − 0.076** (0.036) | − 0.076** (0.035) | − 0.077** (0.036) |
APD4_9 | 0.051 (0.048) | 0.051 (0.048) | 0.052 (0.049) | 0.052 (0.048) | − 0.048 (0.038) | − 0.048 (0.038) | − 0.048 (0.038) | − 0.049 (0.038) |
Home_shot | 0.034 (0.024) | 0.033 (0.024) | 0.034* (0.020) | 0.033* (0.018) | − 0.017 (0.018) | − 0.017 (0.017) | − 0.017 (0.015) | − 0.017 (0.013) |
Constant | − 5.98 (5.53) | − 6.02 (5.56) | − 6.04 (5.42) | − 6.04 (5.51) | 8.03* (4.43) | 8.08* (4.46) | 8.03* (4.34) | 8.04* (4.45) |
Coach dummy | Yes | Yes | Yes | Yes | Yes | Yes | Yes | Yes |
Year dummy | Yes | Yes | Yes | Yes | Yes | Yes | Yes | Yes |
Away team dummy | Yes | Yes | Yes | Yes | ||||
Observations | 46,332 | 46,332 | 46,332 | 46,332 | 46,332 | 46,332 | 46,332 | 46,332 |
R-squared | 0.018 | 0.017 | 0.019 | 0.018 | 0.019 | 0.018 | 0.020 | 0.019 |
Number of id | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 |
Hausman test | 17.56 | 19.03 | 24.43 | 26.83 | ||||
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Jane, WJ. Interim information and managerial risk taking in professional basketball. JER (2023). https://doi.org/10.1007/s42973-023-00140-7
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DOI: https://doi.org/10.1007/s42973-023-00140-7