1. The Math of Baseball
Will Cranford
11/1/2018

2. Abstract/GOAL
In this presentation I will introduce the game of baseball, discuss the limitations of simple statistics, and examine the ways that teams evaluate batters and pitchers.

3. What is baseball?

4. Video Summary
There are 9 players on defense at one time, and the offense cycles through a 9 hitter lineup.
Each team gets 3 outs per time at bat. An out is made when a batter strikes out, Flies out, or grounds out, or when a baserunner is forced out.
A team scores a run when a baserunner crosses home plate with fewer than 3 outs.
Each team gets 9 chances to score per game. The team with the most runs at the end of the game wins.

5. ANY QUESTIONS?
It’s important that you’ve got the basics understood before we move on.

6. Why Baseball?
Long history, mountains of data. MLB was founded in 1869, play by play data recorded since ,000 games played, more than 14 million at bats recorded.
Easier to isolate individual player contributions than in most other team sports.
More publicly available statistics and analysis than any other sport.

7. Example Stat Line for a batter
KEY:
PA: Number of times a player comes to the plate to bat.
R: Number of times a player crosses home plate.
RBI: Number of baserunners a player causes to score when he’s at bat.
SB: Number of times a player steals a base.
AVG: Ratio of hits to at bats.

8. Problems Which stats are valuable?
Which stats are independent of teammate production?
Which stats are effected by the environment in which the game is played?

9. Goodhart’s Law
“when a measure becomes a target, it ceases to be a good measure”
Examples: SAT/ scientific publication
If players recognize certain statistics are value, they will aim to achieve those statistics at the expense of winning.
Ex: Bobby Abreu/ Round numbers
-- RBI’s from 2002 to 2009: 85,101,105,102,107,101,100,103

10. How do you Value a Player?
The ultimate goal of player evaluation in baseball is to figure out how many wins a player would add to your team, and how much that player would be worth as a free agent.
Two types of players: Hitters and pitchers.

11. Player Evaluation: Hitters
Hitters are evaluated on:
Batting ability
Baserunning Ability
Fielding ability
Intangibles?

12. Hitters: batting The Run Expectancy Matrix:
Each of the 24 base out states is represented in the matrix by the expected number of runs a team will score for the rest of the inning from that state.

13. Run Expectancy added
You can see how many runs a player added to the team’s expected total by using this stat:

14. EXAMPLES With 0 outs and no one on base, a batter hits a double.
The next batter singles, advancing the runner to third.
The next batter grounds into a double play, scoring the runner from third.
The next 3 batters walk.
The next batter hits a home run, scoring 4 runs.

15. EXAMPLES With 0 outs and no one on base, a batter hits a double.
The next batter singles, advancing the runner to third.
The next batter grounds into a double play, scoring the runner from third.
The next 3 batters walk.
The next batter hits a home run, scoring 4 runs.

16. EXAMPLES
With 0 outs and no one on base, a batter hits a double.
The next batter singles, advancing the runner to third.
The next batter grounds into a double play, scoring the runner from third.
The next 3 batters walk.
The next batter hits a home run, scoring 4 runs.
Runs

17. EXAMPLES
With 0 outs and no one on base, a batter hits a double.
The next batter singles, advancing the runner to third.
The next batter grounds into a double play, scoring the runner from third.
The next 3 batters walk.
The next batter hits a home run, scoring 4 runs.
+.684 Runs

18. EXAMPLES
With 0 outs and no one on base, a batter hits a double.
The next batter singles, advancing the runner to third.
The next batter grounds into a double play, scoring the runner from third.
The next 3 batters walk.
The next batter hits a home run, scoring 4 runs.
-.686 Runs

19. +.654 Runs Combined EXAMPLES
With 0 outs and no one on base, a batter hits a double.
The next batter singles, advancing the runner to third.
The next batter grounds into a double play, scoring the runner from third.
The next 3 batters walk.
The next batter hits a home run, scoring 4 runs.
+.654 Runs Combined

20. EXAMPLES
With 0 outs and no one on base, a batter hits a double.
The next batter singles, advancing the runner to third.
The next batter grounds into a double play, scoring the runner from third.
The next 3 batters walk.
The next batter hits a home run, scoring 4 runs.
Runs

21. Hitters: Batting
To calculate a player’s total runs added over the course of the season, sum up the player’s runs added from each plate appearance.
The major league leader in 2018 added 71 expected runs to his team’s total during the season, .44 runs per game.

22. Problems with run expectancy added
Does not account for teammates’ performance.
Does not account for stadium conditions.

23. Fixing said problems
To eliminate the influence of Teammates’ performance, the average value for each batting event is used instead of the run expectancy matrix.

24. Accounting for Conditions
Baseball stadiums aren’t uniform.
Park size, altitude play a role.
Denver, Mexico City add distance to fly balls
Park factors

25. Hitters: Baserunning
Baserunning value can be added by advancing while the ball is hit in play or by stealing a base.
When should baserunners steal?
Runner on first, 1 out:
72.5% of the time
To find runs added, use run expectancy matrix, sum baserunning impact over season.

26. Hitters: Fielding Measuring fielding is a little more difficult.
Fewer statistics for defense.
The problem with errors.
A new era: statcast

27. Hitters: Total Value
Value= Batting runs + Baserunning Runs + Fielding Runs
Certain positions are more difficult to play, they get a positional bonus/penalty.

28. The idea of “the replacement”
The player’s run value is measured against how well a hypothetical replacement would do. The replacement is generally seen as a minor league player.
“The Replacement” exists in many forms in industry. What happens if an experienced worker is replaced with a college graduate?

29. Converting to wins
It has been found that there are 9 runs per win added. To find Wins above replacement, find the total runs above replacement and divide by 9.
Best MLB players produce around 8 wins above replacement per year.

30. Assessing Pitcher value
Evaluating pitchers is a little less clear.
How much credit goes to the pitcher, how much goes to the defense?
It’s been found that pitchers have little control over balls in play. They only can control the number of strikeouts they produce, the number of walks they give up, and the number of home runs they give up.

31. Outliers Shohei Ohtani, from japan, pitches and hits.
How do you account for this versatility using wins above replacement?

32. ANY QUESTIONS? Recap Went over the rules of baseball
Discussed problems with simple statistics
Evaluated hitters on batting, baserunning and fielding.
Evaluated pitchers.
ANY QUESTIONS?