# What if the Mound Was Moved Back?

Moving the mound back is a proposed solution to the ever-increasing rate of strikeouts in the modern game of baseball. The effect of moving the mound back one foot will be tested in the Atlantic League from August this year. Without the results of this test, we don’t know much about how this rule change could affect the delicate balance between pitchers and hitters. There are many unknowns such as:

- How much will the perceived velocity decrease benefit hitters?
- Will the added break on pitches benefit pitchers?
- Will throwing a further distance add injury risk or cause a loss of pitcher control?
- Will batters change their approach if it is easier to make contact?

In this article I aim to use my model of predicted pitch outcomes to investigate how moving the mound back may change the game. I’ve written previously about modeling the deadened baseball and I shall take a similar approach here.

### Modeling Mound Movement

The toughest part of this project is to generate reasonable assumptions from which to create models and predictions. Ideally, I would use data from other times the mound has moved and this would inform my strategy. Moving the mound back hasn’t happened since 1893, and unfortunately we didn’t have pitch tracking data back then.

I shall be using Statcast data from the 2020 season to model the effect of mound movement. Pitch velocities and movement will be modified based on how I expect pitch quality to change when the mound is moved back.

### Assumptions

For clarity, I shall list my set of assumptions here. Firstly the physical assumptions, which have been chosen such that my models of ball flight and effective pitch speed do not become prohibitively complicated:

- The ball does not decelerate during the pitch.
- The latest decision point for a batter is 175 milliseconds before contact.
- The effective velocity of a pitch is determined by the time taken to reach the latest decision point.
- The break on a ball (relative to a ball thrown with no spin) is produced by a constant acceleration in a fixed direction.
- The quality of a pitch thrown from a variable distance can be explained by only modifying the speed and break in my pitch prediction model.

Secondly, the assumptions about player behaviour which are necessary to produce a quantitative prediction of the effect of moving the mound back:

- Pitchers will have the same level of control from a more distant mound. This allows me to use the 2020 season as a representative sample of pitches
- Batters have the same approach when facing pitchers from a modified mound. My model is trained on data from the 2015-2020 seasons and predicts outcomes based on batter behaviour in this time period
- The effects of pitch tunnelling and deception are unchanged. These are not accounted for in my model and therefore I am unable to model their change.

These assumptions will clearly not all hold true. The ball does decelerate during the pitch and player behaviour will undoubtedly change in unforeseen ways. Treat this exercise as a zeroth-order approximation for the effect of moving the mound, and take its conclusions with a grain of salt. Data from the Atlantic League will help to answer many of the questions which I cannot, but until that arrives, we are limited to theoretical exploration.

### Modeling Effective Velocity

The most important effect of moving the mound back will be an increase in reaction time for hitters. This increase in reaction time should counteract the effect of increasing pitch velocity. To model this increase in reaction time I will be using the concept of effective velocity.

Effective velocity is often used in relation to pitcher extension. A pitcher who has a larger stride and throws from closer to the plate will give a hitter less reaction time and so his pitches have a higher effective velocity than the radar gun would suggest. The same principle can be applied to moving the mound back. Throwing from further away will increase the reaction time for the hitter, and therefore reduce the effective velocity of the pitch.

Statcast measures effective velocity, and while I don’t know the exact calculation that goes into it (I believe it involves using the velocity of the pitch at home plate), I can make a linear model combining pitch speed and extension to approximate the calculation.

With this I can now rescale pitch velocities, assuming that effective velocity due to mound position works the same way as effective velocity due to extension.

Having modeled Statcast’s effective velocity, I wondered whether I could create my own version based on the decision point for a batter, and whether this would provide significantly different results. The decision point is the point in the ball’s flight at which the batter has to decide whether to swing or not. This is based on the limits of human reaction time and bat speed. The time for a hitter to react to a pitch is the time between it being released and it reaching the decision point (around 24 feet from home plate depending on pitch speed).

As I stated in the assumptions section, I took the decision point for a batter to be 175 ms before contact and that the ball does not decelerate during the pitch. The effective velocity produced here is the velocity of a pitch released from the unchanged mound which would require the same reaction time as the pitch from the mound which has moved. Some manipulation of speed = distance / time produces the formula below.

Where pitch velocity, v, is in ft/s, x is the distance the mound is moved back in feet, and extension is the pitcher’s release point extension on the pitch, measured in feet. From here on this model of the effective pitch speed will be referred to by “Decision Distance”.

Comparing these two methods for calculating expected velocity produces stark differences. For 1 foot of mound movement, the different models give either just over 1 mph of effective velocity difference or 3 mph.

According to unnamed MLB officials, they expect an extra foot of distance to reduce the effective velocity of a 93.3 mph fastball to 91.6 mph. This is somewhere between my two models, which is a positive sign for the validity of my method. I will use both models when making predictions of the effect of moving the mound back to indicate the range of uncertainty present in this analysis.

### Modeling Break

In addition to the effect of increasing hitters’ reaction times, another important change is that breaking balls will have further to travel, increasing the amount of movement before the ball reaches home plate. To model this effect, I shall make use of my assumption that the break on the ball is produced by a constant acceleration in a fixed direction. A quick application of the SUVAT equations gives the effective break on the ball as:

Where b is the break on the ball in either the vertical or horizontal direction (defined as movement relative to a ball with zero spin induced movement), and x is the mound movement distance in feet.

I’m in two minds on whether the extra movement on the ball will produce better quality breaking balls. The ball may move further from a more distant mound, but that movement isn’t being caused by a greater amount of spin based acceleration and so there may be no greater amount of deception than before. Therefore I will make predictions both including and excluding the effect of the extra movement to see if it makes a large difference.

In total, I now have four different models for how moving the mound back will affect the quality of pitches thrown: two models for how effective velocity will change, and for each of these I will either include or exclude the effect of greater movement on breaking pitches.

With all this there is just one final step, and that is converting these pitches with altered velocity and movement into strikeout rates, run values, and more.

### From Pitch Quality to Outcomes

In the past I’ve created a model to predict outcomes of pitches by using pitch quality. This was used to create xxxFIP, an ERA estimator which doesn’t use the outcomes of pitches. Creating this model has been an iterative process, and my current method is to predict events using a set of nested models as shown in green in the diagram below:

Each model returns a probability of the possible outcomes. These probabilities can be chained together to produce the overall probability of any of the events shown for a given pitch. The models use gradient boosted decision trees with the following inputs:

- Pitch Type
- Pitch location as it crosses the plate
- Vertical and horizontal movement
- Velocity
- Spin rate
- Pitcher arm slot (release point x and z) and extension
- Pitcher handedness
- Batter handedness
- Count (balls and strikes)

For this project I shall mainly be considering the swing decision, contact, and fair/foul models.

These models will be run with the 2020 season pitch data to produce a baseline for the expected results with an unchanged mound. Then I will adjust the pitch velocities and movements according to the effective velocity models and the break model which I described above. Rerunning the predictions with the new modified pitch data will provide an estimate for the effect of moving the mound back.

As I stated before, this is a quick and dirty analysis with many assumptions, some of which are more reasonable than others. There is a large range of possible outcomes that could result from moving the mound back, much larger than the range shown here. Testing on real players in real games is the only way to know what will happen for sure. This is simply my best attempt to predict what would happen using the tools available to me.

### Effects of Moving the Mound

The justification for moving the mound back is to reduce the rate of strikeouts. League-wide whiff rates have been rising yearly and therefore the predicted whiff rate is the ideal place to start looking at my predictions.

In the above graph we can see that moving the mound back is likely to reduce the number of swings and misses. The whiff rate reduction is around 1% per foot of mound movement but with a large variation depending on the model used. At one foot of mound movement the predicted whiff rate could vary from 0.7% lower than normal to 1.6% lower.

The choice of effective velocity model has a larger effect than whether the increase in break is included or not. This implies that the change in reaction time will be a more important factor than the increased movement on pitches.

In addition to whiff rate, I can look at the expected rate of balls in play when contact is made. Increasing the number of balls in play is seen by some as an aesthetic improvement to baseball and it helps to speed up the pace of play if more balls are put into play rather than being fouled off.

The predicted ball in play % on contact increases by between 1-2% per foot of mound movement. Lower effective velocities make it easier for hitters to time their swings, which should lead to a greater number of fair balls on contact.

Another interesting effect to examine is how batter swing rates will change if the mound is moved back. This is the most likely of my predictions to be incorrect because it depends very strongly on one of my assumptions which is unlikely to be true: that batters will maintain the same approach with a different mound distance.

Using my models and assumptions, swing rates would be down by a small amount with the mound moved back. I believe this is because batters will be more likely to lay off pitches outside the zone when pitchers have less effective stuff due to the increased reaction time.

Interestingly, when I extended the mound movement distance beyond three feet, the predicted swing rate began to rise dramatically. For extreme changes in mound distance the effective velocity will become so low that previously competitive pitches become meatballs. These meatballs would encourage a much larger swing percentage from hitters which causes the increase seen from my model predictions.

A final prediction is to look at how the run environment might change with a different mound distance. I do this calculation by collecting the predicted outcomes for all pitches and using linear weights to convert these to predicted run values.

Moving the mound back is likely to make the run scoring environment more friendly to hitters by around 1-2.5 runs per 1,000 pitches when moving the mound by 1 foot. There are about 150 pitches per game by each team, so runs per game would rise by between 0.15 and 0.4 with these assumptions.

This is a large but not unprecedented difference. For comparison, runs per game rose by 0.4 between the 2018 and 2019 seasons. Adding between 0.15 and 0.4 runs per game to the current 2021 rate of 4.37 would keep the run scoring environment within the normal range between 4-5 from the past 20 years.

With league-wide changes examined, I can also look at specific pitchers who would be most and least affected by moving the mound back.

### The Biggest Winners and Losers

A moved mount would not affect all players equally. Some hitters will be more adept when facing balls from a greater distance than others, and some pitchers may have control issues when adjusting to a new distance. I cannot model these effects, however I can look at which pitchers throw pitches that would be most affected by moving the mound back.

I shall focus on two main changes for individual pitchers: whiff rate and run value.

Assuming that the mound is moved by one foot, the predicted new whiff rate is found by averaging the results from all four of the different models which I described earlier. The graph below shows how the whiff rate on pitches is expected to change for pitchers who drew at least 200 swings in the 2020 season. An interactive version is hosted on my original blog post here.

Some types of pitcher are affected more than others. Those who rely on high velocity fastballs such as Nick Anderson, Walker Buehler, Gerrit Cole, Josh Staumont, and Liam Hendriks show the largest decreases in their whiff rate, around 3-4% when averaging the different models together.

Meanwhile, pitchers who throw more slowly are not as affected, and in fact the extra movement may even help them to generate more swings and misses on their breaking balls. These pitchers include Zach Davies, Zack Greinke, Rich Hill, and Ryan Thompson.

Moving the mound back will not be a great equalizer. Those who have previously dominated the strikeout leaderboards will continue to do so as the variation in whiff rate due to moving the mound back one foot is much smaller than the intrinsic variation that already exists between pitchers.

I can do a similar comparison looking at predicted run value per pitch. In the graph below, higher run value implies a worse pitch. Only pitchers who threw at least 200 pitches were included.

Similar trends can be seen here as with predicted whiff rate. Pitchers who rely on high velocity see the largest decrease in effectiveness of their pitches, meanwhile those who have slow sliders and curveballs with a ton of movement are less affected. As seen with whiff rate, the changes in run values are relatively small. A change in mound distance of one foot will not turn a star into a scrub or vice versa.

### Conclusions

In this article I have attempted to predict how moving the mound back would affect MLB pitching. My models make use of many assumptions, some of which are unlikely to hold true, but they provide a very rough estimate for how the effective velocity and the movement of pitches will change with mound distance.

Assuming no changes in batter and pitcher behavior, and using pitch tracking data from the 2020 season, the changes expected when moving the mound back are that there will be:

- Lower effective pitch velocity (1-3 mph per foot of mound movement)
- More contact (0.7-1.6% per foot of mound movement)
- More balls in play on contact (1-2% per foot of mound movement)
- A higher run-scoring environment (0.15-0.4 runs per game per foot of mound movement)
- Less swings (0.5% lower swing rate per foot of mound movement)

Moving the mound back 1 foot will have noticeable league-wide changes, however, it is unlikely for there to be a large change on an individual level in the relative value between different pitchers. Those who throw mainly fastballs at high velocities will be most affected by the change, but not so much that they become significantly less valuable.

The mound distance has not changed since the 19th century. If such a significant change is to be considered within the game, then its effects should be well understood to avoid unforeseen consequences. It will be interesting to see whether data from tests in the Atlantic League agree or disagree with these predictions. If they are in agreement, then prediction methods such as this could provide a useful way for MLB to tune the mound distance to produce the level of changes in the game which they want to see.

*This post is adapted from my blog, which can be found here.*

That is an impressive amount of work you have done. But if I had to make one statement, it would be this…..”If anything is done to help the hitters, I shudder at the totals that will be put up by Vladdy Guerrero, Fernando Tatis, Ronald Acuna and Juan Soto.

This is very well done Cameron, I am impressed by the detail that your model covers. I am curious to see if pitchers with wider approach angles to the plate, like Chris Sale’s slider will benefit, as it can start even further off the plate and still be a strike. Also other impacts that the model couldn’t cover such as slight changes in spin and seam shifted wakes. Great article!

This is really great and detailed work! One factor where a moved back mound might not decrease Ks as much as anticipated is the Vertical Approach Angle of the pitch which would seem to flatten (?). On the hitting side, the increased Attack Angles and higher swing speeds are a much larger contributor to Ks than is commonly believed. As the AA/VAA differential increases, Ks increase as the time of intersection between the ball/bat paths shortens; however, the increased offensive value from the higher AAs outweigh the K cost so the trend has continued (also, EV independent contact quality goes… Read more »