London Calling to the Faraway Towns

The historic rivalry between the New York Mets and the Philadelphia Phillies has been filled with memorable moments and dramatic showdowns, none perhaps more iconic than the culmination of the 2007 regular season.

The stage was set for a thrilling finale as the Mets and Phillies battled for the division crown in the National League East. With the Mets holding a comfortable seven-game lead over the Phillies with just 17 games remaining, it seemed like the division title was within their grasp. However, the script took an unexpected turn as the Mets stumbled in the final stretch, losing five of their last 12 games, while the Phillies surged ahead, winning 13 of their last 17.

The tension reached its peak on the final day of the regular season, with both teams vying for a shot at the postseason and ultimate bragging rights. The Mets pinned their hopes on veteran pitcher Tom Glavine, facing off against the Florida Marlins, while the Phillies relied on Jamie Moyer against the Washington Nationals.

In a twist of fate, the Mets faltered, while the Phillies triumphed, clinching their first postseason appearance since 1993. The rivalry was further fueled by Phillies shortstop Jimmy Rollins' bold prediction earlier in the season, proclaiming the Phillies as the team to beat in the NL East. Despite early scepticism and a slow start to the season, the Phillies rallied behind Rollins' confidence, ultimately proving their mettle on the field.

The London Series stands as a key highlight within the MLB World Tour, a venture designed to expand the reach of Major League Baseball to fans across the globe. This weekend, spectators will be immersed in the intensity of one of baseball's most legendary rivalries. Following the successful editions featuring the Yankees–Red Sox rivalry in 2019 and the Cubs vs. Cardinals showdown in 2023, this event continues to elevate baseball's international appeal, promising excitement and unforgettable moments for fans worldwide.

The dimensions of the baseball field at London Stadium diverge from those of a traditional ballpark in several notable ways, potentially favoring offensive play styles. Unlike standard MLB stadiums, which often feature varying outfield dimensions tailored to the specific characteristics of each venue, London Stadium offers a uniform and relatively expansive outfield space.

In contrast to many MLB stadiums where outfield dimensions can vary significantly, the dimensions at London Stadium are consistent throughout. For example, the distance to the foul poles measures 330 feet (100.6 m), while the center field extends to 385 feet (117.4 m). These dimensions are notably spacious compared to some MLB parks, where shorter distances to the outfield walls can result in more frequent home runs.

Moreover, the power alleys, areas of the outfield where many extra-base hits occur, are extended to 387 feet (118 m) in the 2023 series, further amplifying the offensive potential of the ballpark. This increased outfield distance provides hitters with a greater opportunity to drive the ball into the gaps and capitalize on scoring opportunities.

Additionally, the relatively low height of the outfield fence, standing at 16 feet (4.9 m), could contribute to a higher likelihood of home runs being hit. This feature contrasts with MLB stadiums where outfield walls are often taller, making it more challenging for hitters to clear the fence and score home runs.

Overall, the dimensions of London Stadium's baseball field, characterized by expansive outfield space and favorable distances to the outfield walls, are likely to promote offensive strategies and increase the frequency of scoring opportunities for both teams. This unique aspect adds an element of excitement and unpredictability to the games, enhancing the overall fan experience during the London Series. What happens on Saturday 8th June, when we pit the two teams against each other in London?

Analyzing Phillies and Mets Offense and Defense

In baseball, accurately gauging a team's offensive and defensive abilities is essential for predicting their performance and game outcomes. To achieve this, we employ statistical methods that analyze historical batting and pitching data. Let's dive into how we calculate offense and defense scores for the Philadelphia Phillies and the New York Mets, explaining the reasoning behind our approach.

Offense Score Calculation

The offense score represents a team's ability to score runs, which primarily depends on their batting performance. To calculate this score, we employ a linear regression model using various batting statistics as features. These features include:

• AB (At Bats): The total number of times a player bats.
• H (Hits): The number of times a batter successfully reaches base without an error by the defense.
• HR (Home Runs): The number of hits that allow the batter to circle all the bases and score a run.
• BB (Walks): The number of times a batter receives four balls and is awarded first base.
• RBI (Runs Batted In): The number of runs scored due to a batter's actions.
• SB (Stolen Bases): The number of times a baserunner successfully advances to the next base without the ball being hit.
• AVG (Batting Average): The ratio of hits to at-bats, indicating a batter's success in hitting the ball.

By fitting these features to a linear regression model with the target variable being the total runs scored (R), we obtain coefficients for each feature. These coefficients represent the impact of each batting statistic on the team's offensive performance.

Batting Model:

The batting model aims to predict the total runs scored by a team based on various batting statistics. It utilizes a linear regression approach.

The equation for the batting model can be represented as:

Where:

• R represents the total runs scored.
• AB,H,HR,BB,RBI,SB and AVG are the batting statistics.
• β0,β1,β2,...,β7 are the coefficients estimated by the regression model.
• ? represents the error term.

Defense Score Calculation

The defense score reflects a team's ability to prevent runs, primarily influenced by their pitching performance. Similar to the offense score, we utilize a linear regression model, but this time with pitching statistics as features. These features include:

• IP (Innings Pitched): The total number of innings a pitcher has thrown.
• ER (Earned Runs): The number of runs that scored without the aid of an error or passed ball.
• SO (Strikeouts): The number of batters a pitcher has struck out.
• BB (Walks): The number of times a pitcher issues a base on balls.
• HR (Home Runs Allowed): The number of home runs a pitcher has given up.
• ERA (Earned Run Average): The average number of earned runs a pitcher allows per nine innings pitched.

By fitting these pitching statistics to a linear regression model with the target variable being the earned run average (ERA), we obtain coefficients representing the impact of each pitching metric on the team's defensive performance.

Pitching Model:

The pitching model aims to predict the team's earned run average (ERA) based on various pitching statistics. It also uses a linear regression approach.

The equation for the pitching model can be represented as:

Where:

• ERA represents the earned run average.
• IP,ER,SO,BB, and HR are the pitching statistics.
• β0,β1,β2,...,β5 are the coefficients estimated by the regression model.
• ? represents the error term.

These equations describe how each model calculates the predicted outcome (runs scored or earned run average) based on the input features (batting or pitching statistics) and the coefficients learned during the training process.

Rationale and Interpretation

Our approach utilizes linear regression models to quantify the relationships between various batting and pitching metrics and their impact on offensive and defensive performance. By examining the coefficients derived from these models, we gain insights into which factors contribute most significantly to a team's ability to score runs (offense) or prevent their opponents from scoring (defense).

Mean Squared Error (MSE) and R-squared Score

Mean Squared Error (MSE) is a metric that quantifies the average squared difference between the actual and predicted values by the regression model. In simpler terms, it measures the average squared deviation of the predictions from the actual values.

For the Phillies Batting Model, the MSE value of 12.70 indicates that, on average, the squared difference between the actual and predicted runs scored by the Phillies' offense is approximately 12.70. This value gives us an understanding of the magnitude of errors in our predictions.

The R-squared score, on the other hand, measures the proportion of the variance in the dependent variable (runs scored) that is predictable from the independent variables (batting statistics). An R-squared score of 0.91 for both the Phillies and Mets Batting Models suggests that approximately 91% of the variance in runs scored by these teams can be explained by their respective batting statistics. In other words, the batting models have a high degree of explanatory power and provide a good fit to the data.

Moving on to the Pitching Models, we encounter extremely low MSE values (3.59e-29), which essentially means that the squared difference between the actual and predicted values is virtually zero. This indicates an exceptionally low level of error in the predictions made by the pitching models. Furthermore, both the Phillies and Mets Pitching Models achieve a perfect R-squared score of 1.0, indicating that 100% of the variance in earned run average (ERA) can be explained by the pitching statistics considered in the models. This suggests an excellent fit of the pitching models to the data, with all variability in ERA being accounted for by the pitching metrics used.

In summary, the MSE and R-squared scores provide valuable insights into the performance and accuracy of the regression models. They indicate the level of error in predictions and the extent to which the models explain the variability in the dependent variable, thus aiding in the assessment of model reliability and effectiveness.

Results and Interpretation

Let's analyze the results obtained for the Phillies and Mets:

Offense Score for Phillies: 48.32

Defense Score for Phillies: 26.46

Offense Score for Mets: 38.56

Defense Score for Mets: 33.59

For both teams, the mean squared error (MSE) and R-squared scores provide insights into the performance and goodness of fit of the regression models for both batting and pitching statistics. The low MSE and high R-squared values indicate that the models accurately capture the relationships between the input features and the target variables, yielding reliable estimates of offensive and defensive capabilities.

Simulation:

The simulate_match function is a key component in predicting the outcome of a baseball game between the Philadelphia Phillies and the New York Mets, particularly in the context of the London Stadium. The adjustment of offense ratings within this function reflects an understanding of how the unique dynamics of London Stadium may influence offensive performance. By applying a london_stadium_factor of 1.05, the function effectively boosts the offensive potential of both teams, considering the smaller dimensions of the stadium which tend to favor hitters. This adjustment acknowledges the likelihood of increased scoring opportunities in a venue with a more compact playing field, aligning with the observed tendency for smaller stadiums to yield higher offensive output.

London Stadium's smaller pitch size compared to traditional baseball fields is influenced by various factors, including spatial constraints and the venue's original design for different sporting events. Unlike many Major League Baseball (MLB) stadiums, which are tailored to specific outfield dimensions based on architectural considerations and historical context, London Stadium offers a relatively uniform and compressed playing space. This deviation from the standard dimensions seen in MLB parks contributes to a more condensed outfield area, potentially increasing the frequency of hits and home runs. The decision to adjust offense ratings in the simulate_match function recognizes this deviation and seeks to account for the likelihood of enhanced offensive production resulting from the unique dimensions of London Stadium.

In the simulation process, offensive ratings for both teams are boosted to reflect the anticipated impact of London Stadium's smaller pitch size on batting outcomes. This adjustment acknowledges the historical tendency for hitters to benefit from playing in venues with shorter distances to the outfield walls, facilitating higher scoring rates and increased offensive output. By incorporating this adjustment into the simulation model, the simulate_match function provides a more accurate representation of the offensive capabilities of the Phillies and Mets when competing in the distinct setting of London Stadium.

Monte Carlo Simulation:

A Monte Carlo simulation is a computational technique used to model the probability of different outcomes in a process that involves randomness or uncertainty. It's particularly useful when it's impractical or impossible to derive a closed-form solution mathematically. Here's how it works and how it applies to our scenario of predicting the winner between the Mets and Phillies:

1. Basic Concept: In a Monte Carlo simulation, you repeatedly sample from probability distributions to simulate the uncertain elements of a system. Each iteration of the simulation represents one possible outcome.
2. Sampling Process: In our case, we're simulating a baseball game between the Mets and Phillies. We're uncertain about the outcome due to various factors like player performance, stadium dynamics, etc. We use probability distributions to represent these uncertainties. For example, we might model a team's offensive and defensive performance using normal distributions based on their respective scores.
3. Simulation Iterations: We run a large number of simulations (in this case, 1000) to explore a wide range of potential outcomes. For each simulation, we sample from the probability distributions for offensive and defensive performance to determine the scores for both teams.
4. Outcome Analysis: After all simulations are complete, we analyze the results to determine the likelihood of each team winning. We count the number of simulations in which each team comes out victorious.
5. Probability Calculation: The probability of each team winning is calculated by dividing the number of simulations in which that team wins by the total number of simulations.
6. Mathematics and Equations:

• Let's say N is the total number of simulations (1000 in our case).
• P(Phillies?win) is the probability of the Phillies winning, and P(Mets?win) is the probability of the Mets winning.
• If nPhillies is the number of simulations in which the Phillies win, and nMets is the number of simulations in which the Mets win, then:

In our code, the simulate_match function encapsulates the simulation process. It takes as input the offensive and defensive scores of both teams, simulates a match outcome based on these scores, and returns the scores for each team. We then run this simulation 1000 times, tallying the number of wins for each team and calculating their respective probabilities of winning based on the outcomes. This allows us to make probabilistic predictions about the likely winner of a game between the Mets and Phillies.

What Goes Down?

Based on our Monte Carlo simulation with 1000 iterations, we've determined that the probability of the Philadelphia Phillies winning against the New York Mets stands at approximately 0.613 (or 61.3%). Conversely, the probability of the Mets emerging victorious is approximately 0.387 (or 38.7%).

These results suggest that, based on our model and the simulated match outcomes, the Phillies have a higher likelihood of beating the Mets in their hypothetical encounter. Out of the 1000 simulations conducted, the Phillies emerged victorious in 613 instances. This indicates that, under similar conditions and with the factors considered in our simulation, the Phillies demonstrated a competitive edge over the Mets, winning the majority of the simulated matchups.

While these probabilities provide valuable insights into the potential outcomes of a game between the Phillies and Mets, it's essential to recognize the inherent uncertainties and assumptions in our model. Factors such as player performance variability, real-time game dynamics, and unforeseen events during a match could influence the actual result differently from our simulated predictions.

Nevertheless, by conducting a large number of simulations and analyzing the probabilities, we gain a probabilistic perspective on the likely outcome of the matchup.

Let's go Mets!