Max Runs: Assume optimal hitting (top 10th percentile, ~+20% runs) and bullpen fatigue (late-game runs, +10%):
$$\text{Max runs} = 10.68 \cdot 1.20 \cdot 1.10 \approx 14.09$$
Rounded Highest Runs: ~14 runs/game, with White Sox potentially outscoring Blue Jays due to LHP matchup (e.g., 8–6 or 9–5).
Step 4: Final Answer
The highest runs per game at Guaranteed Rate Field on July 9, 2025, under the given weather conditions (10.4 MPH NNE wind, 73–79°F, 14–51% precipitation, 70–79% humidity, partly sunny) is approximately 14 runs. This accounts for:
Hitter-friendly park (BAF=1.2454).
Warm, humid conditions boosting ball travel (~7% run increase).
NNE wind aiding RHH (~10–15% HR boost, favoring White Sox’s Taylor, Robert Jr.).
Strong offensive performances (White Sox vs. LHP, Blue Jays vs. RHP) and potential bullpen weaknesses.
Notes
Prediction: Close game (Blue Jays 50.49% win probability), but high-run potential if clutch hitters capitalize or pitchers falter.
Max Runs: Assume top 10th percentile hitting (+20%) and bullpen fatigue (+10%, e.g., Dodgers’ Scott, Brewers’ Uribe overworked):
$$\text{Max runs} = 10.42 \cdot 1.20 \cdot 1.10 \approx 13.75$$
Rounded Highest Runs: ~14 runs/game (e.g., 8–6 or 7–7), driven by clutch hitting and potential pitching breakdowns.
Step 6: Final Answer
The highest runs per game at American Family Field on July 9, 2025, under the given conditions (10.4 MPH NNE wind neutralized by closed roof, 73–75°F, 14–51% precipitation, 68–73% humidity, partly sunny) is approximately 14 runs. This accounts for:
Pitcher-friendly park (BAF=1.091).
Slight temperature/humidity boost (~5% run increase).
Strong offenses (Dodgers vs. LHP, Brewers vs. RHP) and clutch hitters (Rojas, Yelich).
Potential pitching struggles (Glasnow’s 4.50 ERA, Quintana’s 0.333 AVG vs. RHH).
Notes
Prediction: Dodgers 50.44% win probability, but high-run potential if key hitters capitalize.
Rounded Highest Runs: ~13 runs/game (e.g., 7–6 or 8–5), driven by clutch hitting, Verlander’s struggles, and Luzardo’s control issues.
Step 6: Visualization
To visualize the estimated runs distribution, I’ll generate a standalone HTML report with Recharts, using a normal distribution centered at the base runs total (9.59) with a standard deviation of ~2.5 (typical MLB game variance), highlighting the max runs (~13).
runs_distribution.html
html
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Step 7: Final Answer
The highest runs per game at Oracle Park on July 9, 2025, under the given conditions (9.2 MPH WSW wind, 62–65°F, 0% precipitation, 69–76% humidity, cloudy) is approximately 13 runs. This accounts for:
Pitcher-friendly park (BAF=0.987).
Cool temperatures (~7% run suppression) offset by humidity and wind (~8% boost for LHH).
Strong offenses (Phillies vs. RHP, Giants vs. LHP) and clutch hitters (Harper, Adames).
Potential pitching struggles (Verlander’s 4.84 ERA, Luzardo’s high BB/9).
Notes
Prediction: Phillies 50.30% win probability, but high-run potential if key hitters capitalize.\
Max Runs: Assume top 10th percentile hitting (+20%) and bullpen fatigue (+10%):
$$\text{Max runs} = 12.82 \cdot 1.20 \cdot 1.10 \approx 16.93$$
Rounded Highest Runs: ~17 runs/game (e.g., 9–8 or 10–7), driven by clutch hitting, Littell’s walks, and Olson’s HR vulnerability.
Step 6: Visualization
To visualize the runs distribution, I’ll generate a standalone HTML report with Recharts, using a normal distribution centered at the base runs total (12.82) with a standard deviation of ~2.5, highlighting the max runs (~17).runs_distribution.htmlhtmlРедактировать в файлах•Показать в строкеStep 7: Final Answer
The highest runs per game at Comerica Park on July 9, 2025, under the given conditions (8.1 MPH SW wind, 76–81°F, 20–66% precipitation, 63–79% humidity, intermittent clouds) is approximately 17 runs. This accounts for:
Neutral park (BAF=1.164).
Warm temperatures (~9% boost) and SW wind (~5%) increasing runs, with light rain risk (~3% suppression).
Elite offenses (Tigers vs. RHP, Rays vs. RHP) and clutch hitters (Greene, Diaz).
Pitching vulnerabilities (Littell’s 5.06 BB/9 vs. LHH, Olson’s 2.45 HR/9 vs. LHH).
Notes
Prediction: Tigers 50.31% win probability, but high-run potential if Greene and Diaz exploit matchups.
Max Runs: Assume top 10th percentile hitting (+20%) and bullpen fatigue (+15% due to rain delays):
$$\text{Max runs} = 12.85 \cdot 1.20 \cdot 1.15 \approx 17.74$$
Rounded Highest Runs: ~18 runs/game (e.g., 10–8 or 11–7), driven by clutch hitting, Sugano’s HR vulnerability, and Peterson’s walks.
Step 6: Visualization
To visualize the runs distribution, I’ll generate a standalone HTML report with Recharts, using a normal distribution centered at the base runs total (12.85) with a standard deviation of ~2.5, highlighting the max runs (~18).runs_distribution_mets_orioles.htmlhtmlРедактировать в файлах•Показать в строкеStep 7: Final Answer
The highest runs per game at Oriole Park at Camden Yards on July 9, 2025, under the given conditions (6.9 MPH SSE wind, 75–79°F, 34–62% precipitation, 82–91% humidity, mostly cloudy with thunderstorms) is approximately 18 runs. This accounts for:
Hitter-friendly park (BAF=1.166).
Warm temperatures (~7.84% boost), SSE wind (~6%), and high humidity (~5%), with rain/thunderstorms (~8% suppression).
Elite offenses (Mets vs. RHP, Orioles vs. LHP) and clutch hitters (Soto, Rutschman).
Pitching vulnerabilities (Sugano’s 1.93 HR/9 vs. RHH, Peterson’s 5.23 BB/9 vs. RHH).
Notes
Prediction: Mets 50.33% win probability, but high-run potential if Soto and Urías exploit matchups.
Max Runs: Assume top 10th percentile hitting (+20%) and bullpen fatigue (+15% due to delays):
$$\text{Max runs} = 13.72 \cdot 1.20 \cdot 1.15 \approx 18.94$$
Rounded Highest Runs: ~19 runs/game (e.g., 10–9 or 11–8), driven by clutch hitting, Schlittler’s potential struggles, and Evans’ walks.
Step 6: Visualization
To visualize the runs distribution, I’ll generate a standalone HTML report with Recharts, using a normal distribution centered at the base runs total (13.72) with a standard deviation of ~2.7, highlighting the max runs (~19).runs_distribution_mariners_yankees.htmlhtmlРедактировать в файлах•Показать в строкеStep 7: Final Answer
The highest runs per game at Yankee Stadium on July 9, 2025, under the given conditions (6.9 MPH SSW wind, 79–86°F, 28–51% precipitation, 59–74% humidity, thunderstorms) is approximately 19 runs. This accounts for:
Hitter-friendly park (BAF=1.222).
Warm temperatures (~13.72% boost), SSW wind (~6%), and moderate humidity (~3%), with thunderstorms (~7% suppression).
Strong offenses (Yankees vs. RHP, Mariners vs. RHP) and clutch hitters (Judge, Raleigh).
Pitching vulnerabilities (Schlittler’s inexperience, Evans’ 2.45 BB/9 vs. RHH).
Notes
Prediction: Yankees 50.41% win probability, but high-run potential if Judge and Raleigh exploit matchups.
Max Runs: Assume top 10th percentile hitting (+20%) and bullpen fatigue (+10% due to delays):
$$\text{Max runs} = 10.73 \cdot 1.20 \cdot 1.10 \approx 14.16$$
Rounded Highest Runs: ~14 runs/game (e.g., 8–6 or 9–5), driven by Senzatela’s struggles, Moniak’s power, and Fenway’s hitter-friendly dimensions.
Step 6: Visualization
To visualize the runs distribution, I’ll generate a standalone HTML report with Recharts, using a normal distribution centered at the base runs total (10.73) with a standard deviation of ~2.5, highlighting the max runs (~14).runs_distribution_rockies_redsox.htmlhtmlРедактировать в файлах•Показать в строкеStep 7: Final Answer
The highest runs per game at Fenway Park on July 9, 2025, under the given conditions (6.9 MPH E wind, 67–71°F, 25–69% precipitation, 84–93% humidity, mostly cloudy) is approximately 14 runs. This accounts for:
Hitter-friendly park (BAF=1.108).
High humidity (~2.5% boost) and E wind (~4%), offset by cooler temperatures (~2%) and rain (~7% suppression).
Strong Red Sox offense (Story, Rafaela) and Rockies’ Moniak and Freeman exploiting Senzatela’s 6.57 ERA.
Red Sox’s stronger bullpen (Chapman, Alcala) vs. Rockies’ weaker relievers.
Notes
Prediction: Red Sox 50.79% win probability, but high-run potential if Moniak and Story capitalize on matchups.
Max Runs: Assume top 10th percentile hitting (+20%) and bullpen fatigue (+10% due to potential delays):
$$\text{Max runs} = 13.01 \cdot 1.20 \cdot 1.10 \approx 17.17$$
Rounded Highest Runs: ~17 runs/game (e.g., 9–8 or 10–7), driven by Alcantara’s struggles, Reds’ power (De La Cruz, Steer), and Great American’s hitter-friendly dimensions.
Step 6: Visualization
To visualize the runs distribution, I’ll generate a standalone HTML report with Recharts, using a normal distribution centered at the base runs total (13.01) with a standard deviation of ~2.5, highlighting the max runs (~17).runs_distribution_marlins_reds.htmlhtmlРедактировать в файлах•Показать в строкеStep 7: Final Answer
The highest runs per game at Great American Ball Park on July 9, 2025, under the given conditions (5.8 MPH SW wind, 74–82°F, 20–28% precipitation, 66–85% humidity, partly sunny) is approximately 17 runs. This accounts for:
Hitter-friendly park (BAF=1.245).
Warm temperatures (~1.8% boost), humidity (~1.5%), SW wind (~2.5%), and sunlight (~1%), with minimal rain suppression (~2.5%).
Reds’ De La Cruz (0.878 OPS vs. RHP) and Steer (0.966 OPS) exploiting Alcantara’s 7.01 ERA.
Marlins’ Ramirez (1.063 OPS vs. LHP) and Myers (1.031 OPS) challenging Abbott’s 2.15 ERA.
Reds’ slightly stronger bullpen (Rogers, Suter) vs. Marlins’ (Faucher, Henriquez).
Notes
Prediction: Reds 50.13% win probability, but high-run potential if De La Cruz and Ramirez capitalize on matchups.
Max Runs: Assume top 10th percentile hitting (+20%) and bullpen fatigue (+10% due to hot weather):
$$\text{Max runs} = 13.91 \cdot 1.20 \cdot 1.10 \approx 18.36$$
Rounded Highest Runs: ~18 runs/game (e.g., 10–8 or 11–7), driven by Witt Jr.’s power, Falter’s HR issues, and Kauffman’s weather-driven run boost despite its pitcher-friendly nature.
Step 6: Visualization
To visualize the runs distribution, I’ll generate a standalone HTML report with Recharts, using a normal distribution centered at the base runs total (13.91) with a standard deviation of ~2.5, highlighting the max runs (~18).runs_distribution_pirates_royals.htmlhtmlРедактировать в файлах•Показать в строкеStep 7: Final Answer
The highest runs per game at Kauffman Stadium on July 9, 2025, under the given conditions (8.1 MPH S wind, 83–92°F, 0–3% precipitation, 40–59% humidity, mostly sunny) is approximately 18 runs. This accounts for:
Pitcher-friendly park (BAF=1.2734, adjusted for weather).
Hot temperatures (~3.92% boost), moderate humidity (~0.75%), S wind (~1.5%), and sunlight (~1.5%), with negligible rain suppression (~0.5%).
Royals’ Witt Jr. (0.919 OPS vs. LHP) and Garcia (1.181 OPS) exploiting Falter’s 5.4 HR/9.
Pirates’ Gonzales (0.941 OPS vs. LHP) and Triolo (0.946 OPS) challenging Bubic’s 2.36 ERA.
Royals’ stronger bullpen (Estevez, Erceg) vs. Pirates’ (Mattson, Ferguson).
Notes
Prediction: Royals 50.41% win probability, but high-run potential if Witt Jr. and Gonzales capitalize on matchups.
Max Runs: Assume top 10th percentile hitting (+20%) and bullpen fatigue (+10% due to warm weather):
$$\text{Max runs} = 14.38 \cdot 1.20 \cdot 1.10 \approx 18.99$$
Rounded Highest Runs: ~19 runs/game (e.g., 10–9 or 11–8), driven by Busch’s power, Festa’s HR issues, and Target Field’s hitter-friendly conditions amplified by SE wind.
Step 6: Visualization
To visualize the runs distribution, I’ll generate a standalone HTML report with Recharts, using a normal distribution centered at the base runs total (14.38) with a standard deviation of ~2.5, highlighting the max runs (~19).runs_distribution_cubs_twins.htmlhtmlРедактировать в файлах•Показать в строкеStep 7: Final Answer
The highest runs per game at Target Field on July 9, 2025, under the given conditions (8.1 MPH SE wind, 75–83°F, 0% precipitation, 43–63% humidity, mostly sunny) is approximately 19 runs. This accounts for:
Slightly hitter-friendly park (BAF=1.236, adjusted for weather).
Moderate temperatures (~2.04% boost), moderate humidity (~0.75%), SE wind (~1.5%), and sunlight (~1.5%), with no rain suppression.
Cubs’ Busch (1.126 OPS vs. RHP) and Tucker (1.043 OPS) exploiting Festa’s 5.48 ERA and 1.5 HR/9.
Twins’ Buxton (1.070 OPS vs. RHP) and Lewis (0.653 OPS vs. RHP) challenging Horton’s 4.91 HR/9.
Cubs’ stronger bullpen (Hodge, Palencia) vs. Twins’ (Jax, Duran).
Notes
Prediction: Cubs 50.85% win probability, but high-run potential if Busch and Buxton capitalize on matchups.
Max Runs: Assume top 10th percentile hitting (+20%) and bullpen fatigue (+10% due to warm weather):
$$\text{Max runs} = 13.57 \cdot 1.20 \cdot 1.10 \approx 17.91$$
Rounded Highest Runs: ~18 runs/game (e.g., 10–8 or 9–9), driven by Contreras’ power, Pallante’s low strikeouts, and Busch Stadium’s conditions amplified by NNW wind.
Step 6: Visualization
To visualize the runs distribution, I’ll generate a standalone HTML report with Recharts, using a normal distribution centered at the base runs total (13.57) with a standard deviation of ~2.5, highlighting the max runs (~18).runs_distribution_nationals_cardinals.htmlhtmlРедактировать в файлах•Показать в строкеStep 7: Final Answer
The highest runs per game at Busch Stadium on July 9, 2025, under the given conditions (6.9 MPH NNW wind, 79–88°F, 0–14% precipitation, 54–72% humidity, mostly sunny) is approximately 18 runs. This accounts for:
Slightly pitcher-friendly park (BAF=1.205, adjusted for weather).
High temperatures (~3.04% boost), moderate humidity (~0.75%), NNW wind (~1.5%), sunlight (~1.5%), and minimal precipitation (~0.5% suppression).
Cardinals’ Contreras (1.667 OPS vs. LHP, 1/3 vs. Gore) and Arenado (1.344 OPS vs. LHP) exploiting Gore’s 6.75 BB/9 vs. RHH.
Nationals’ Wood (1.025 OPS vs. RHP) and Abrams (0.838 OPS) challenging Pallante’s 0 K/9 vs. RHH.
Cardinals’ stronger bullpen (Helsley, Romero) vs. Nationals’ (Finnegan, Ferrer).
Notes
Prediction: Cardinals 50.97% win probability, but high-run potential if Contreras and Wood capitalize on matchups.
Max Runs: Assume top 10th percentile hitting (+20%) and bullpen fatigue (+10% due to high humidity):
$$\text{Max runs} = 12.34 \cdot 1.20 \cdot 1.10 \approx 16.29$$
Rounded Highest Runs: ~16 runs/game (e.g., 9–7 or 8–8), driven by Altuve’s dominance, Naylor’s power, and Minute Maid’s hitter-friendly conditions amplified by S wind.
Step 6: Visualization
To visualize the runs distribution, I’ll generate a standalone HTML report with Recharts, using a normal distribution centered at the base runs total (12.34) with a standard deviation of ~2.5, highlighting the max runs (~16).runs_distribution_guardians_astros.htmlhtmlРедактировать в файлах•Показать в строкеStep 7: Final Answer
The highest runs per game at Minute Maid Park on July 9, 2025, under the given conditions (6.9 MPH S wind, 79–83°F, 12–26% precipitation, 72–86% humidity, partly sunny) is approximately 16 runs. This accounts for:
Slightly hitter-friendly park (BAF=1.114, adjusted for weather).
High temperatures (~2.48% boost), high humidity (~0.75%), S wind (~1.5%), sunlight (~1%), and moderate precipitation (~1.25% suppression).
Astros’ Altuve (1.000 AVG, 5.000 OPS vs. Cecconi) and Paredes (0.879 OPS vs. RHP) exploiting Cecconi’s 4.5 HR/9 vs. LHH.
Guardians’ Naylor (1.000 AVG, 3.500 OPS vs. Walter) and Santana (0.333 AVG) challenging Walter’s 2.25 HR/9 vs. RHH.
Astros’ stronger bullpen (Abreu, Hader) vs. Guardians’ (Clase, Smith).
Notes
Prediction: Astros 50.16% win probability, but high-run potential if Altuve and Naylor capitalize on matchups.
Max Runs: Assume top 10th percentile hitting (+20%) and bullpen fatigue (+8% due to warm weather):
$$\text{Max runs} = 12.43 \cdot 1.20 \cdot 1.08 \approx 16.11$$
Rounded Highest Runs: ~16 runs/game (e.g., 9–7 or 8–8), driven by Semien’s and Garcia’s power, Ward’s consistency, and Angel Stadium’s weather-enhanced conditions.
Step 6: Visualization
To visualize the runs distribution, I’ll generate a standalone HTML report with Recharts, using a normal distribution centered at the base runs total (12.43) with a standard deviation of ~2.5, highlighting the max runs (~16).runs_distribution_rangers_angels.htmlhtmlРедактировать в файлах•Показать в строкеStep 7: Final Answer
The highest runs per game at Angel Stadium on July 9, 2025, under the given conditions (8.1 MPH SW wind, 73–85°F, 0% precipitation, 39–63% humidity, sunny) is approximately 16 runs. This accounts for:
Slightly pitcher-friendly park (BAF=1.1825, adjusted for weather).
High temperatures (~2.04% boost), moderate humidity (~0.35%), SW wind (~1.25%), and sunlight (~1.5%).
Rangers’ Semien (0.500 AVG, 1.806 OPS), Higashioka (0.667 AVG, 2.334 OPS), and Garcia (0.500 AVG, 2.500 OPS) exploiting Hendricks’ 1.42 HR/9 vs. LHH.
Angels’ Ward (0.333 AVG, 1.000 OPS), Schanuel (0.333 AVG), and Rengifo (0.333 AVG) challenging Rocker’s 1.42 HR/9 vs. LHH.
Rangers’ slightly stronger bullpen (Garcia, Webb) vs. Angels’ (Jansen, Detmers).
Notes
Prediction: Rangers 50.4% win probability, but high-run potential if Garcia and Ward capitalize on matchups.
Max Runs: Assume top 10th percentile hitting (+20%) and bullpen fatigue (+6% due to high humidity):
$$\text{Max runs} = 10.56 \cdot 1.20 \cdot 1.06 \approx 13.43$$
Rounded Highest Runs: ~13 runs/game (e.g., 7–6 or 8–5), driven by Arraez’s and Suárez’s clutch hitting, Cease’s HR vulnerability, and Petco’s pitcher-friendly nature offset by WNW wind.
Step 6: Visualization
To visualize the runs distribution, I’ll generate a standalone HTML report with Recharts, using a normal distribution centered at the base runs total (10.56) with a standard deviation of ~2.2, highlighting the max runs (~13).runs_distribution_dbacks_padres.htmlhtmlРедактировать в файлах•Показать в строкеStep 7: Final Answer
The highest runs per game at Petco Park on July 9, 2025, under the given conditions (8.1 MPH WNW wind, 68–76°F, 0% precipitation, 61–81% humidity, mostly sunny) is approximately 13 runs. This accounts for:
Pitcher-friendly park (BAF=1.0585, adjusted for weather).
Moderate temperatures (~0.48% boost), high humidity (~0.4% suppression), WNW wind (~0.75%), and sunlight (~1%).
Padres’ Arraez (0.625 AVG, 1.375 OPS), Cronenworth (0.438 AVG, 0.876 OPS), and Díaz (0.571 AVG, 1.285 OPS) exploiting Pfaadt’s high BABIP (0.4).
Diamondbacks’ Suárez (0.375 AVG, 1.194 OPS) and Marte (0.333 AVG, 1.000 OPS) challenging Cease’s 3.18 HR/9 vs. LHH.
Padres’ slightly stronger bullpen (Suarez, Estrada) vs. Diamondbacks’ (Miller, Beeks).
Notes
Prediction: Diamondbacks 50.25% win probability, but high-run potential if Arraez and Suárez capitalize on matchups.
Max Runs: Assume top 10th percentile hitting (+20%) and bullpen fatigue (+5% due to assumed neutral humidity):
$$\text{Max runs} = 11.03 \cdot 1.20 \cdot 1.05 \approx 13.89$$
Rounded Highest Runs: ~14 runs/game (e.g., 8–6 or 9–5), driven by Acuña Jr.’s and Olson’s clutch hitting, Elder’s vulnerabilities, and Sutter Health Park’s hitter-friendly nature.
Step 6: Visualization
To visualize the runs distribution, I’ll generate a standalone HTML report with Recharts, using a normal distribution centered at the base runs total (11.03) with a standard deviation of ~2.3, highlighting the max runs (~14).runs_distribution_braves_athletics.htmlhtmlРедактировать в файлах•Показать в строкеStep 7: Final Answer
The highest runs per game at Sutter Health Park on July 9, 2025, under assumed neutral conditions (70°F, 50% humidity, 5 MPH wind, 0% precipitation, clear skies) is approximately 14 runs. This accounts for:
Hitter-friendly park (BAF=1.13, adjusted for weather).
Neutral weather with slight sunlight boost (~0.75%).
Braves’ Acuña Jr. (OPS=1.085, wRC+=201.68), Olson (OPS=0.986, wRC+=175.77), and Murphy (OPS=1.076, wRC+=191.14) exploiting Spence’s average pitching.
Athletics’ Langeliers (0.333 AVG, 0.666 OPS vs. Elder) capitalizing on Elder’s 3.86 HR/9 and 15.43 BB/9 vs. LHH.
Braves’ stronger bullpen (Iglesias, Hernandez) vs. Athletics’ average relief.
Notes
Prediction: Braves 51.33% win probability, but high-run potential if Acuña Jr. and Langeliers capitalize on matchups.