Olin College

Out of Left Field Evidence For and Against ’s Conventional Wisdom

Christopher Joyce 10/4/2012

This project aims to map baseball conventional wisdom to facts, and see if the things that ‘everybody knows’ about baseball are supported or contradicted by statistical evidence. I found that most baseball conventional wisdom does not line up with statistics, and in some cases is outright contradicted. Contents Background & Dataset ...... 2 Exploration #1: Walks per Country ...... 4 Exploration #2: Good-Fielding Shortstops ...... 6 Exploration #3: Knuckleballers and Control ...... 8 Conclusions ...... 10 Bibliography ...... 11

Background & Dataset Baseball is a sport with a 140 year old history, but it’s only in the past 30 years or so that there’s been much focus on analyzing baseball with statistics (an approach called ), rather than what the old hands think they know about the game. One of the first books about sabermetrics was written by an engineering professor at Johns Hopkins, Earnshaw Cook, in 1964 [1]. Teams had used statistics before this point, but it was somewhat controversial and back-alley – the idea of wasn’t in the public eye.

For a few decades, there was a back and forth between those who believed in baseball by statistics, and those who believed in baseball by feel. This debate was silenced in the early 2000’s, when Moneyball was published [2]. Theo Epstein, the GM of the Boston Red Sox said, “That book hit The New York Times best-seller list. People who own baseball teams read The New York Times best-seller list. So they started asking questions about the processes their front offices were using, and it changed things really quickly.”

Despite this advance, statistics haven’t fully converted all of baseball’s old guard. While all 30 MLB clubs incorporate statistics into their player evaluations, only 15 to 20 of them rely on it “heavily” [2]. This means a full half to a third of baseball teams still do things, in large part, by ‘feel’. Statistics have certainly informed what scouts look for, by redefining what a useful player is. For example, on- base percentage wasn’t even a metric people looked at heavily as recently as 2002 [2]; but both a walk and a single will get a player on base, and in a position to score a .

It seems pretty clear, given all this, that much of baseball’s conventional wisdom may be downright wrong; however, fans and announcers will still insist about what they ‘know’ of baseball – even without any facts [3]. In example, there’s an old baseball adage that ‘You can’t walk your way off the island’, referring to players from Latin America who will swing wildly at pitches, with the thought that it’s harder to get noticed by pro scouts by exercising restraint at the plate, and fighting through grueling at-bats; than it is by hitting balls way outside the strike zone for home runs [4]. This is something that ‘everybody knows’, but I have never seen any data to support.

Some of baseball’s conventional wisdom is so pervasive that it’s actually not possible to do statistical analysis of why it might be true – an example being lefty catchers. The perception exists – mostly unsubstantiated – that it’s a crippling disadvantage for a catcher to be left-handed because they’d have a hard time making a pickoff move to first around a right-handed batter. This feeling is so pervasive that there have only been five left-handed catchers to play in at least 100 games [5]. The last catcher to play as a lefty in the MLB did so in 1989; and as of 2009, there was not a single left-handed catcher in the MLB or the minor leagues [6].

Teams eventually started making their decisions based on data rather than what ‘everyone knows’, in no small part because of the general manager of the Oakland A’s, Billy Beane. Beane was one of the first to make a real effort to go against the grain of what ‘everyone knew’. Rather than just incorporating statistics, where statistics disagreed with his math, he’d trust the math [7]. I used Sean Lahman’s compendium of data, which came in a .csv format. It includes notable individual statistics dating all the way back to 1870, as well as team records. This dataset is free, easily importable into Python for analysis, and quite complete. There were a few mismatched tags I had to modify, but none of them affected numbers within the dataset. I only use a part of the dataset – player tables, batting tables, fielding tables, and pitching tables. This dataset is ripe for more analysis, however, most baseball stereotypes exist about individual players, not teams.

Seeing as this dataset came from the internet, I validated it by spot-checking certain player statistics. I checked certain statistics that jumped out at me when reading through summaries I generated of the data set, and found that they were true, just not expected. For example, I found that an individual (Ed Porray) whose birth country was listed as “A Boat on the Atlantic Ocean” was, in fact, born while at sea. I feel confident that my dataset accurately represents what occurred in baseball, with some possible human error, given these tests.

Exploration #1: Walks per Country One common piece of conventional wisdom was discussed above – “You can’t walk your way off the island”. The stereotype is that players from Latin America – the Dominican Republic specifically – swing at a lot of balls that aren’t hittable, with the thought that pro scouts don’t notice those who take long at-bats. To test this, I summed all plate appearances and walks by players born in each country, and took the walks-per-plate-appearance number for each nation that has sent a man to the majors.

First, I made a histogram of walks by country since 1970. I chose to throw out all pre-1970 data to be sure that I was only getting data in the modern era for this analysis – it seems like a fairer comparison to only look at dates after Hispanic players had been playing in the MLB at a high level for a decade or so. I chose the 1970 season as my cutoff point for this reason.

Figure 1: Walks per at-bat, by country.

This chart seems to show that Germans are walking machines; while Afghans actively try not to walk. This comes across as funny right from the get-go; because this spread is so huge. Clearly, something is not quite right within the dataset. My next strategy was to create a cutoff for a total number of plate appearances a country needs to have to be considered. I chose this to be 5000; because the average starting player will come to bat about 500 times in a season, and ten player- seasons seems like an appropriate sample size to define as the lower bound for comparison.

Figure 2: Walks per at-bat, by country, 5,000 plate appearances per country cutoff.

This graph shows the difference much more clearly. The maximum difference is 4 walks per 100 plate appearances. Interestingly, the Dominican Republic does not have the lowest walks-per-plate- appearance figure – they’re about one walk in a hundred above Mexico, which has the lowest walks per 100 of any country. The league average is about one walk in a hundred above the DR.

Absolute numbers do indicate a difference in walks by Dominicans versus the league average. It’s hard to create a real test statistic for this data, because my dataset comprises all players who have ever taken a swing in the major leagues; and so extrapolating from this dataset means very little. However, I can reasonably make the claim that, while an absolute difference does exist, it shouldn’t be one that can be reasonably picked out without statistical analysis of the type done here.

Monte Carlo simulations indicate that the specific difference being analyzed – that of Dominicans versus the league average – has a probability of happening by chance of less than 1 in ten thousand for ten thousand iterations. Given that, I am willing to call the bias statistically significant; however, that is separable from whether the stereotype is reasonably noticeable without statistical analysis.

The thing to note here with respect to debunking or confirming the stereotype is not the likelihood of the effect, but rather the size of the effect. If this behavior was being picked out fairly by announcers, they would be more likely to refer to Canadians as walking machines, or Mexicans as those who never walk, not Dominicans. Those effects are significantly larger; to the tune of 2 walks in a hundred off of the league average; as compared to about 1 in 100 for Dominicans. If an effect twice as strong goes unnoticed, I think it’s reasonable to chalk this effect up to confirmation bias: when someone sees a Dominican strike out, they add it as a data point supporting a stereotype they want to believe.

Exploration #2: Good-Fielding Shortstops Another common baseball stereotype is that the better a fielder your shortstop, the worse a hitter he is. To analyze this, I ran two correlations: between games per error and batting average, and between assists per game and batting average. Both of these are good, simple measures of defensive quality. There are more complicated metrics in existence, but I chose to use errors and assists because, if a shortstop has few errors but few assists as well, he may not actually be a good defensive shortstop – he might just be slow. It’s not an error if you never get to the ball. On the other hand, a player who makes a lot of assists but also has many errors may not actually be much good to his team – his mistakes could be more costly than his good plays. By using both, I can get more information about correlations.

Batting average is a good measure of hitting efficiency. Some players hit for extra bases, some single, some single, steal, and score on someone else’s hit; some never actually score runs or bat in runs because they play on bad teams. However, batting average is a solid indicator of hitting that doesn’t depend on teammates.

The correlation coefficient between batting average and games between errors is -0.088 – a minimal correlation. There are a few players who hit very well – upwards of a .350 career batting average – who commit more errors than the average player – but, a few outliers do not make a trend; and to say that certain fantastic hitting shortstops can get away with being worse fielders is not an

indictment of all shortstops. Shortstops fall into an extremely narrow range.

Games between Errors (log transform) (log Errors between Games

Batting Average (linear)

Figure 3: Correlation between batting average and games between errors. The correlation coefficient here indicates not much correlation, as does a cursory look at the graph.

An alternate metric to look at for defensive efficacy is assists per game. The fact that shortstops seem to mess up at similar rates gives good data on mistakes, but doesn’t tell us anything about defensive excellence. The correlation coefficient here is 0.1645 – twice as good as for errors, but still a narrow range. It’s important to note that, if the stereotype were true, the correlation we’d expect would be negative. There is more likely to be a correlation between assists and batting average than

between errors and batting average – but the effect is in the wrong direction to confirm this stereotype.

Assists Per Game (Linear) Game Per Assists

Batting Average (linear)

Figure 4: Correlation between assists per game and batting average. It’s hard to pick out a clear relationship here, except that there are certain shortstops who have many assists, yet mediocre batting averages.

A rule of thumb value for statistical significance at the 95% certainty level is that if the absolute value of the correlation coefficient is greater than 2 divided by the square root of the sample size; the results are statistically significant [8]. These correlations meet this standard. The data conflicts as to whether it supports the stereotype, however – games between errors does line up with the stereotype, assists per game does not. Therefore, this stereotype, while partially true, is not strongly supported.

Exploration #3: Knuckleballers and Control Everybody knows that knuckleballers can’t control the ball. The reason that knuckleballers are such effective pitchers is that nobody knows where the ball is going – not the hitter, not the catcher, and not even the pitcher. Assuming this is true, knuckleballers should walk a lot of batters – they can throw it in the direction of the plate, but don’t have the precise control that other pitchers do.

Figure 5: CDF of knuckleballers and conventional pitchers, walks per 100 batters. The worst knuckleballer does walk batters much more frequently than conventional pitchers; and the best knuckleballer walks batters more frequently than the best conventional pitchers, but all in all, knuckleballers actually walk fewer batters per 100 batters faced.

To investigate this, I created a CDF of batters walked per 100 batters faced for knuckleballers, superimposed over a CDF of the same metric for other pitchers. Knuckleballers have a much lower variance distribution than conventional pitchers, with the middle 50 percent of knuckleballers walking between 8 and 10 batters per 100 batters faced. This same range for conventional pitchers is closer to 10-15 batters per 100.

The pitchers with the best control of their pitches, in this case, are those with the lowest probability of walking a batter. The 10th percentile of knuckleballers and the 10th percentile of conventional pitchers walk batters with almost identical frequency: 6.4 per 100 for knuckleballers, 6.6 per 100 for conventional pitchers. The 50th percentile is where a difference starts to open up; at 8.5 vs. 10.6 for knuckleballers as compared to conventional pitchers. The 90th percentile has an even greater difference; with 15 walks in 100 for knuckleballers and 25 per 100 for conventional pitchers. Charlie Hough, a former major league knuckleballer, has told people that it takes one day to learn to throw a knuckleball, but a lifetime to learn to throw a knuckleball for strikes [9].

One reason this might be true is because knuckleballers can afford to just throw the ball to the catcher. Unlike a power pitcher, the knuckleballer doesn’t have to aim for the corners of the strike zone, and try and aim the pitch very precisely where it’s hard to hit but still in the strike zone. Given that knuckleballs deviate randomly, a pitcher really doesn’t gain anything by trying to throw to the outside. Knuckleball deviations have been shown to be truly random, and as such, there’s really no reason to believe that a knuckleballer would even attempt to exercise fine control over where his pitch is going [10].

R.A. Dickey, the only currently active knuckleballer in the major leagues, notes in intervies that he only tries to aim vertically, not horizontally: “I aim for about two above the catcher's helmet, and if I can get the ball going on that trajectory, I know, more or less, if it's going to fall within the strike zone.” [9]. Part of the reason Dickey would aim above the catcher’s helmet is gravity – pitches fall as they move in air. Assuming a standard (non-knuckleball) trajectory, a pitch aimed two baseballs above the catcher’s head would go straight down the middle of the strike zone.

Conclusions The pervasive stereotypes that I’ve investigated seem to be mostly without merit. Those that are supported are weaker versions of themselves; and some are just not substantiated. While Dominicans do seem to walk more than the league average; the data suggests that this effect shouldn’t be able to be noticed.

Dominicans do seem to walk more than average; but evidence indicates that this bias isn’t noticeable without statistical analysis – which is not the origin of the stereotype. A similar observation can be made about the offensive versus defensive prowess of shortstops – it’s partially true, but not strongly so. Knuckleballers, however, seem to have just as good or better control as any other pitcher in the major leagues.

The biggest takeaway from these investigations is that, while sabermetrics has vastly changed the way baseball is measured and analyzed, there’s a lot of work left to do. A lot of common knowledge seems to be downright wrong; and some of it is so pervasive that statistical analysis can’t even be done to even investigate whether conventional wisdom merits a reinvestigation.

Bibliography

[1] T. Verducci, "Great Moments in Sabermetric History," Sports Illustrated, 26 September 2011.

[2] T. Verducci, "The Art of Winning An (even More) Unfair Game," Sports Illustrated, 26 September 2011.

[3] L. Cappetta, "Sabermetrics: Are New Age Numbers in Baseball Replacing Common Sense?," Bleacher Report, 31 March 2012.

[4] J. Crasnick, "Plate Discipline So Important Nowadays," ESPN, 5 May 2009.

[5] "Left Handed Catchers," [Online]. [Accessed 4 Novermber 2012].

[6] A. Schwarz, "Left-Handed and Left Out," New York TImes, 15 August 2009.

[7] M. Lewis, Moneyball: The Art of Winning an Unfair Game, W.W. Norton & Company Inc., 2003.

[8] D. Walsh, "A Simple Rule of Thumb for Statistically Significant Correlation," [Online]. Available: http://frank.mtsu.edu/~dwalsh/436/CORRSIG.pdf. [Accessed 2 12 2012].

[9] R. Dickey, Interviewee, R.A. Dickey On "Winding Up" As A Knuckleballer. [Interview]. 10 April 2012.

[10] A. M. Nathan, "Analysis of Knuckleball Trajectories," in 9th Conference of the International Sports Engineering Association, 2012.

[11] H. Cruz, "Remembering Roberto Clemente," ESPN, 2 October 2012.

[12] S. Lahman, "Lahman's Baseball Database," 2012.