1. Introduction
Due to the anthropogenic greenhouse gas forcing, global warming has continued and has affected the human society and ecosystems. The warming signals are observed in most regions in the world, including Japan (IPCC 2021, see Fig. 2.11b). If the implications of global warming are communicated by familiar examples in daily life, we could raise the awareness of citizens, leading to the strong countermeasures taken by the human society.
Callahan et al. (2023) (hereafter CDDM23) showed that a decrease in air density associated with warmer temperatures reduces aerodynamic drag, resulting in an increase of the number of home runs in the Major League Baseball (MLB) games in the United States. Our motivation is to test the idea of CDDM23 using the data of the Nippon Professional Baseball (NPB), the professional baseball league in Japan.
2. Data
From observational data provided by Japan Meteorological Agency (JMA), we use air temperatures nearest to the ballpark, which is available at https://www.data.jma.go.jp/obd/stats/etrn/index.php. Following CDDM23, we employ the maximum temperature on the game day as a proxy for the environmental temperature of the game. The baseball data are collected from the Professional Baseball Null Data Okiba f3 Phase 1.0 (FY2023) at https://nf3.sakura.ne.jp/index.html. The extracted data are date, time, the name of the stadium, and the number of home runs for games played at a total of 12 stadiums that are home games of the NPB teams. Data for days with maximum temperatures below 10°C are not used due to the small sample size.
Our study differs from CDDM23 as we do not account for individual player skills or external factors like rule or strategy changes. CDDM23 used high-speed camera data to analyze impact angle and speed, which made it possible to eliminate these factors. Such technology only became available in NPB in the 2010s, making a similar analysis currently unfeasible. Thus, our aim is simply to verify if the general relationship between temperature and home runs aligns with CDDM23’s conclusions.
The time span analyzed in this study is from 2005 through 2023. If the name of the stadium was changed during this time span, the most up-to-date name is used. The games at the Es Con Field Hokkaido, which newly became the home of the Hokkaido Nippon-Ham Fighters in 2023, are excluded from the dataset, because the data record is short. Cancelled games are also excluded.
Games that started before 1600 Japanese Standard Time (JST) are referred to as the day games, and those after 1600 JST are as the night games. Out of the 12 stadiums, seven (five) are outdoor ballparks (domes) (Table 1).
Table showing the names of the ballparks in 2023 analyzed in this study and their regression coefficients (i.e., slopes) of the number of home runs per game onto the maximum temperatures on the game day. Note that the Belluna Dome, which does not have walls, is categorized as the outdoor ballpark.
3. Results
Higher maximum temperatures tend to yield more home runs per game. The scatterplot shown in Fig. 1a exhibits a positive regression coefficient (hereafter “slope”) between the maximum temperature of each game day and the number of home runs per game. This relationship is robust throughout the data record used in this study. In Fig. 1b, to overview the magnitude of its sampling variability, we have repeated the aforementioned analysis for the data of 2000s, 2010s, and 2020s. Overall, we have obtained qualitatively similar results for each time span.
(a) The relationship between the maximum temperatures of the game day and the number of home runs per game. The pink symbols show composites of the number of home runs per game for temperature bins by 5°C increments, and the error bars correspond to two standard deviations. Magenta line is the least squares best fit of the composites, whose slope is shown at the bottom right. (b) As in (a), but calculated separately for 2000s, 2010s, and 2020s. (c) Histogram of the slopes, which are calculated as in (a) but by selecting 50% of the data and repeating it 1000 times. Red and blue lines denote the 2.5th and 97.5th percentile of the sample slopes, respectively.
Citation: Bulletin of the American Meteorological Society 105, 12; 10.1175/BAMS-D-24-0139.1
To verify the statistical certainty, we have randomly extracted 50% of the data from all games and have repeated the same analysis 1000 times to obtain the slopes. Figure 1c shows that these slopes fall within the range between 0.009 and 0.025 at the 95% confidence level, confirming that the positive slopes observed in the data are not due to a sampling bias.
In the case of outdoor (dome) games, the number of home runs is sensitive (insensitive) to the maximum temperatures of the game day, which is in accordance with CDDM23. Figure 2a shows the same plots as in Fig. 1a but for outdoor and dome games, which supports a notion that only outdoor games are influenced by outside temperature. In Fig. 2b, we have tested the statistical certainty in the same manner as in Fig. 1c. For outdoor (dome) games, the slopes fall within the range between 0.018 and 0.036 (from −0.003 to 0.016) at the 95% confidence level, suggesting that only the outdoor games are influenced by temperatures with statistical significance.
(a) As in Fig. 1a, but calculated separately for the outdoor ballparks and the indoor domes. (b) As in Fig. 1c, but for the outdoor ballparks and the indoor domes.
Citation: Bulletin of the American Meteorological Society 105, 12; 10.1175/BAMS-D-24-0139.1
From the NPB data, no clear difference in the temperature sensitivity is detected between day games and night games. For day (night) games, the estimated range of slopes at 95% is between 0.012 and 0.037 (0.018 and 0.040). This result is in contrast to CDDM23, which reported that day games are more sensitive to temperatures than night games in outdoor ballparks.
One possible speculation to explain this difference is that all of the ballparks in Japan are close enough to the ocean, whose heat capacity is larger than continents, whereas some ballparks in the United States are located in the middle of the North American continent. Due to the small continental heat capacity, temperature fluctuations between day and night tend to be large at the continental ballparks, which could create difficulty in estimating temperatures at night using maximum temperatures of the same day.
The sensitivity of home runs to temperatures varies among individual outdoor ballparks (Table 1). This sensitivity is particularly strong at the Meiji Jingu Stadium, whereas the ZOZO Marine Stadium and the Hanshin Koshien Stadium are not sensitive to temperatures at all. The two insensitive stadiums may be strongly affected by winds, due to the direction relative to the shore. In fact, Kanda et al. (2008) pointed out that the batter’s box of the ZOZO Marine Stadium is located at the opposite direction to the shore so that a sea breeze during the summer days hinders the travels of batted balls.
At least based on our simple analysis framework, our dataset does not necessarily indicate that global warming signals in the number of home runs in Japan are already detectable. In Fig. 3, we have shown the annual-mean time series of the maximum temperature on all game days and the number of home runs per game. Though an upward trend was observed in the annual-mean maximum temperatures, the number of home runs per game does not exhibit such an upward trend, suggesting that the global warming signal is still too tiny to detect compared to other determinants of home runs. Nevertheless, if we had sufficient high-speed camera data to control for these determinants such as player abilities, equipment changes, or rule changes as in CDDM23, the global warming signal could have been detectable.
Annual-mean time series of the maximum temperatures of the game day (blue; dashed) and the number of home runs per game (red; solid).
Citation: Bulletin of the American Meteorological Society 105, 12; 10.1175/BAMS-D-24-0139.1
4. Conclusions
We have reached three conclusions in this study. First, the number of home runs in NPB exhibits a robust relationship with air temperatures. This relationship is observed only in outdoor stadiums, which is consistent with the case of MLB games in the United States as shown by CDDM23. As to dome games, even if the outside temperature varies, the temperatures remain relatively constant so that air density variations are reduced, resulting in the insensitivity of the number of home runs to outside temperatures.
Second, even when the analysis is limited to outdoor stadiums, the influence of temperature on home runs varies for each stadium. This diversity of the warming response may be caused by multiple factors, such as the altitudes and the building structure of the stadium and the climatological wind speeds and directions relative to the orientation of the ball park. Further data analysis is needed to understand what determines the sensitivity of home runs to temperatures.
Third, the temperature rise in Japan since 2005 was insufficient to yield a detectable increase of the number of home runs in NPB. This insufficiency does not contradict with CDDM23, however. In this study, we have used the maximum temperature data on the day of the game provided by JMA as a proxy of the temperatures at the time and location of the game, which could serve as a possible factor that blurs the warming signal in the data. In addition, the number of home runs in NPB in early 2010s is known to have been influenced by variations of the restitution coefficient secretly installed in the official NPB balls. This artifact appears to be large enough to prevent us from detecting a significant warming response from the short record.
Nevertheless, based on our analyses of seasonal and interannual variations and the comparison between the outdoor and dome games, we could draw a reasonable conclusion that more home runs in NPB will be generated by global warming in coming years. Unless the NPB balls are changed again, this projection will be further ensured by the observational evidence that warming signals in the northwest Pacific are stronger than the most regions on Earth (Wu et al. 2012).
Aside from air resistance considered in this study, other factors also affect the flying distance of a batted ball, such as the impact angle and speed, in addition to individual player ability and physical condition. In CDDM23, data on the impact angle and speed were obtained from a high-speed camera and were analyzed after removing these factors. As mentioned in the data section, similar technology in NPB has been introduced only in the 2010s, so the same analysis is virtually impossible at this stage. Nevertheless, it is notable that, even without removing these factors, simple regression analyses are enough to detect the influences of temperatures reported by CDDM23.
Acknowledgments.
The second author is supported by Japan Society for the Promotion of Science (JSPS) Kakenhi (20K14554, 22H04487, 23H01241, and 23K13169) and the MEXT program for the advanced studies of climate change projection (SENTAN) Grant JPMXD0722680395. We are grateful to Eruten-san (https://x.com/Lovely_T_1978) for archiving the baseball data, to JMA for the temperature data, to the authors of CDDM23, and to the anonymous reviewers for taking time to review our manuscript.
Data availability statement.
From observational data provided by Japan Meteorological Agency (JMA), we use air temperatures nearest to the ballpark, which is available at https://www.data.jma.go.jp/obd/stats/etrn/index.php. The baseball data are collected from the Professional Baseball Null Data Okiba f3 Phase 1.0 (FY2023) at https://nf3.sakura.ne.jp/index.html.
References
Callahan, C. W., N. J. Dominy, J. M. DeSilva, and J. S. Mankin, 2023: Global warming, home runs, and the future of America’s pastime. Bull. Amer. Meteor. Soc., 104, E1006–E1016, https://doi.org/10.1175/BAMS-D-22-0235.1.
IPCC, 2021: Climate Change 2021: The Physical Science Basis. V. Masson-Delmotte et al., Eds., Cambridge University Press, 2391 pp.
Kanda, T., T. Sugimoto, K. Ueno, S. Haginoya, A. Hori, and Y. Kawashima, 2008: Wind structure in the Chiba Marine Stadium and synoptic factor causing strong winds. Tenki, 55, 241–250.
Wu, L., and Coauthors, 2012: Enhanced warming over the global subtropical western boundary currents. Nat. Climate Change, 2, 161–166, https://doi.org/10.1038/nclimate1353.
