Park effects

Because baseball allows for unique field dimensions, each stadium is prone to favoring certain outcomes, and thus can favor pitchers or hitters. This has become the most prominent park effect, known as park factors (PF), which indicate the difference between a team's offense and defense in home and road games. These calculations generally exclude Coors Field, due to its higher altitude, and interleague games, due to the variation of the designated hitter (DH) until the 2020 season, when the DH position was added by the National League.{{Cite web|title=Park Factors – 5 Year Regressed {{!}} Sabermetrics Library|url=https://library.fangraphs.com/park-factors-5-year-regressed/|access-date=2020-10-01}}

Used as a part of many statistical prediction models, park factors can explain varying offensive outputs of specific players, teams and eras of baseball. These factors can be produced based on many offensive statistics, but are generally and most easily calculated based on team runs and home runs.

A general description of park factors includes comparing the number of runs scored and allowed by each individual team at home and subsequently compared to league average. League average can be adjusted for each team to account for which stadiums each team actually played in, but statistically, the difference is marginal and is thus ignored. Runs scored are compared to games (or outs, as there are 27 outs in a game) rather than plate appearances, because the outs per game stay constant while the number of plate appearances changes. The following formulas calculate park factors:{{Cite web|title=Park Factors {{!}} Sabermetrics Library|url=https://library.fangraphs.com/principles/park-factors/|access-date=2020-10-01}}

$$\backslash mathrm\{PF\}\; =\; \backslash frac\{HT\}\{(T-1)(R+H)\}$$

where $H$ is the number of home runs per game, $R$ is the number of road runs per game, and $T$ is the number of teams in the league.

The intermediate park factor (iPF) makes PF applicable to composite stats rather than just home stats. iPF is calculated as follows:

$\backslash mathrm\{iPF\}\; =\; \backslash frac\{\backslash mathrm\{PF\}\; +1\}\{2\}$

The final PF (fPF) uses weights to regress the data based on which year it came from. Although weights can be calculated in various ways, the general consensus is any differences are marginal. fPF is calculated as follows:

$\backslash mathrm\{fPF\}\; =\; 1-(1-\backslash mathrm\{iPF\})X\_i$

where $X\_i$ is the weight for the $i$th year.

These calculations give fPF on a scale of 1, meaning that 1 is the league average and every hundredth (0.01) above or below 1 corresponds to one percent above or below the league average. For example, an fPF of 1.20 means that offense, based on runs, is expected to be 20% increased; and, vice versa, a fPF of 0.80 means that offense is expected to be decreased by 20%.

Park factors have recently been applied to leagues outside the MLB. In Minor League Baseball, there are 160 affiliate teams above the rookie complex level, across 14 leagues, of which all have their own park factors, determined by various offensive stats, the most common being runs and home runs.{{Cite web|last=Eddy|first=Matt|title=Minor League Baseball Park Factors 2019|url=https://www.baseballamerica.com/stories/minor-league-park-factors-2019/|access-date=2020-10-01|website=www.baseballamerica.com|date=15 November 2019 }} Further examples include the calculation of park factors in Nippon Professional Baseball{{Cite web|title=Park Factors|url=http://npbstats.com/glossary-eng/park-factors/|access-date=2020-10-01|website=NPB STATS|language=en-US}} and prospective future calculations by FanGraphs in the Korea Baseball Organization.{{Cite web|title=Introducing KBO Stats on FanGraphs!|url=https://blogs.fangraphs.com/introducing-kbo-stats-on-fangraphs/|access-date=2020-10-01|website=FanGraphs Baseball|date=8 May 2020 }} Park factors have even been calculated for non-professional leagues, such as the Cape Cod League, a top summer collegiate baseball league in the United States.{{Cite web|last=sabr|title=cWAR: Modifying Wins Above Replacement with the Cape Cod Baseball League – Society for American Baseball Research|url=https://sabr.org/journal/article/cwar-modifying-wins-above-replacement-with-the-cape-cod-baseball-league/|access-date=2020-10-01|language=en-US}}

Altitude affects all sports in various ways. At higher altitudes, all physical activity becomes more difficult{{Cite web|title=Altitude Physiology in Basketball|url=https://www.basketballvmi.com/altitude-physiology|access-date=2020-10-21|website=www.basketballvmi.com}} for many reasons, including the lower oxygen levels. But beyond the impact on the athletes, who experience physiological effects in all sports, higher altitudes also result in less air resistance on moving objects. In baseball, this lower air resistance produces more runs. While much of the research regarding the effects of altitude on the flight of baseballs is relative to more home runs, altitude has been shown to increase offense in all aspects which contact is made.{{Cite web|last=admin|title=High Altitude Offense: An Empirical Examination of the Relationship Between Runs Scored and Stadium Elevation – Society for American Baseball Research|url=https://sabr.org/journal/article/high-altitude-offense-an-empirical-examination-of-the-relationship-between-runs-scored-and-stadium-elevation/|access-date=2020-10-21|language=en-US}} The only MLB stadium of significantly high altitude is Coors Field; however, there are several other professional stadiums throughout the country also at high altitudes. MLB stadium altitudes range from the {{convert|5211|ft}} above sea level of Coors Field to the {{convert|20|ft}} of Philadelphia's Citizen Bank Park.{{Cite web|title=Citizens Bank Park, Pennsylvania Latitude/Longitude|url=https://www.lat-long.com/Latitude-Longitude-2044562-Pennsylvania-Citizens_Bank_Park.html|access-date=2020-10-21|website=www.lat-long.com}} Yet, one must consider that much of the influence of altitudes is de facto calculated in a stadium's park factor as a result of total offensive output by stadium.

File:Curva_Norte_Estadio_Hernando_Siles.jpg

In basketball, just as in baseball, altitudes impact shot basketballs. Shooters tend to expand their shooting range as the basketballs experience less air resistance when shot. This is why it is generally expected that teams who play their home games at higher altitudes have a stronger home court advantage;{{Cite web|last=Rush|first=Joel|title=Study Affirms Altitude Boosts Denver Nuggets' Home Advantage, But Do Other Factors Blunt The Impact?|url=https://www.forbes.com/sites/joelrush/2018/09/12/study-affirms-altitude-boosts-denver-nuggets-home-advantage-but-do-other-factors-blunt-the-impact/|access-date=2020-10-21|website=Forbes|language=en}} however, this has also been seen to produce a weaker away game production for these same high-altitude teams.

In football, these same effects on moving objects is in play, allowing the football to travel further with the same energy put into it. Thus kickers tend to kick from further distances with ease, and quarterbacks throw further with the same ease. However, players have disagreed on how strong an influence the altitude of the venue plays in the outcome of the game and performance of the players.{{Cite web|title=Elevation 5280'|url=https://www.empowerfieldatmilehigh.com/stadium-information/about-us/elevation-5280%27#:~:text=For%20visiting%20teams,%20coming%20to,of%20an%20opponents%20game%20plan|access-date=2020-10-21|website=www.empowerfieldatmilehigh.com}}

Soccer, being a worldwide sport, has more variance among its stadiums as well as the geography of these stadiums. This results in stadiums over double the maximum American stadium altitude, and consequently, stronger effects. This has driven much controversy over the validity of certain stadiums, such as the Estadio Hernando Siles in Bolivia, which sits close to {{convert|12000|ft}} above sea level. Due to the stadium's extremely high altitude, the Estadio Hernando Siles was, at one point, facing a ban by FIFA attributed to an unfair advantage, but the ban was revoked after about a year. Latin American countries and leaders argued that this was not intentional but rather a lay of the land and discriminated against many South American countries.{{Cite web|title=Estadio Hernando Siles - La Paz - The Stadium Guide|url=https://www.stadiumguide.com/estadio-hernando-siles/|access-date=2020-10-22|language=nl}}

One of the more noticeable park effects in basketball occurs in NCAA basketball. There is noticeably lower shooting numbers in domed stadiums, usually football stadiums temporarily converted to a basketball arena, compared to typical basketball arenas. This has become so well accepted that even sport betting bookmakers have been known to lower point-based bets in domed stadiums.{{Cite news|last=Tracy|first=Marc|date=2016-03-31|title=In College Basketball, Cavernous Stadiums Tend to Dampen Shooting (Published 2016)|language=en-US|work=The New York Times|url=https://www.nytimes.com/2016/04/01/sports/ncaabasketball/nrg-stadium-houston-dome-final-four.html|access-date=2020-10-21|issn=0362-4331}} The most notable stadium which has wreaked havoc on shooting numbers is NRG Stadium, usual home of the Houston Texans, but at times the home of some college basketball games. However, there are studies which debunk this effect, labeling it as a myth. Using various measures of offense (points, free throws, multiple shooting percentages), it has been argued that domed stadiums do not average lower offensive numbers to any significance, and in some instances are better.{{Cite web|title=Analysis: College Basketball's Dome Effect Is A Myth|url=https://www.eldo.co/domed-football-stadiums-effect-on-shooting-final-four-ncaa-tournament-college-basketball.html|access-date=2020-10-21|website=ELDORADO|language=en}}

File:Rink_-_IIHF_vs_NHL.jpg

While the NHL has a constant rink size throughout the league, Olympic hockey uses a larger rink, and there are various rink sizes in NCAA hockey.{{Cite web|last=Dec 30th 2017 - 8pm|first=Brad Elliott Schlossman {{!}}|title=Once a trend in college hockey, Olympic-sized rinks are going away {{!}}|url=https://www.fccnn.com/sports/4381283-once-trend-college-hockey-olympic-sized-rinks-are-going-away|access-date=2020-10-21|website=www.fccnn.com|date=31 December 2017 |language=en}} Although not measured quite to the extent of baseball, varying rink sizes do strongly impact the outcome of the game and how specific players perform. Those who have played on various sized rinks tend to agree that the smaller the rink, the quicker the pace of the game. Conversely, for larger rinks, in which there is more space to play, players have more time to react and skate.{{Cite web|title=Not every 200 foot by 85 foot NHL rink is the same|url=https://www.nhl.com/news/not-every-200-foot-by-85-foot-nhl-rink-is-the-same/c-501626|access-date=2020-10-21|website=NHL.com|language=en-US}}

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Category:Sports science