Can Statcast Project a Female Position Player?

In March of 2018, FanGraphs’ legal expert, Sheryl Ring, posed the question as to whether professional baseball could legally exclude women, exploring it in her customary comprehensive style. Ever since then, I’ve been asking myself what I consider a related question: What would a LeBron James-class female athlete be like? At what level of baseball could she compete? Could she be an average player? Better? What positions could she play?

A “LeBron James-class athlete,” according to this author, is an athlete who is simultaneously the fastest, strongest and most athletic without any trade-offs. In other words, Mike Trout with Aaron Judge/Giancarlo Stanton exit velos and Byron Buxton speed. Thanks to Statcast, we now can quantify what such an athlete would look like in terms of Sprint Speed and Exit Velocities. We’ll essentially take the assumption that from a skills (pitch recognition, route running, optimizing launch angle…) standpoint, there should be no difference between men and women. The only measurable difference would be with respect to physical tools such as size, strength and speed.

This discussion should be solely an analytical one. However, whenever any subject related to gender is broached, it tends to morph into a political debate. If you’re curious as to my political leanings, find me on Twitter, where I talk mostly about Canadian politics. I am not here attempting to right a social injustice; rather, I am here to deliver to you a dispassionate analytical viewpoint on the subject in a world inundated with hyperbolic rhetoric. My aim here is to provide you with salient data and allow you, the reader, to arrive at your own conclusions, should you disagree with mine.

There is no question the average man is faster and stronger than the average woman. However, I doubt the average man could return a serve against Bianca Andreescu, nor would the average man survive a minute in the UFC octagon with Cris “Cyborg” Justino, nor Amanda Nunes. We are not dealing with average people at this level. We are looking at the outliers of all outliers, the truly exceptional individuals who possess abilities the average human (male or female) can not come close to replicating.

We’ll take a look at some real-world numbers and leverage Statcast data to see if we can find a realistic ceiling for our athlete, ideally with a specific baseball player we can point to.

The Effect of Population Size on Extreme Outliers

The average Chinese man is shorter than the average American man by about three inches. Despite this, Yao Ming was the tallest NBA player during his time playing for the Houston Rockets. While this is purely anecdotal, it underscores the notion that the larger the sample size, the more extreme your most extreme individuals will be.

The real question is, how to quantify the effect of population size? How do we estimate how much faster the fastest athlete would be if the population was 10 times as large? For that matter, how do we even measure the population size, or its standard deviation? There are so many assumptions, it would render almost any model open for extreme interpretation and/or manipulation. Generally speaking, I am leery of models that are not easily understood by the average fan, or at the very least the average Hardball Times reader. I’m especially wary of using models in which small changes in assumptions can lead to large changes in results.

In lieu of a statistical model that could be tweaked to produce pretty much any answer, let’s look at a real-world example, specifically comparing the U.S. to Canada. We’re going to compare the measurable athletic performance of American athletes as compared to Canadian athletes. In many ways, Canada is a nice (pun intended) proxy for American demographics. Both countries are wealthy, former British colonies and magnets for international migration. More importantly, generally speaking, the countries share similar interests in athletics.

We will rely on two assumptions. Our first is the population size of female athletes competing at a level that could lead to a professional athletic career is less than 10% of the equivalent male population size for the major team sports. This is based on the theory that economics drive participation — that devoting your life to an athletic goal is a significant risk. Said risk becomes more palatable when the corresponding reward grows.

Hockey is the biggest sport in Canada (for now). There are numerous high-level teams here, easily over 100 teams between the CHL, AHL and NHL. This doesn’t even include American teams, which would push this number closer to 200. The Canadian Women’s Hockey League had precisely six teams before closing its doors earlier this year. Despite Canada being one of the more progressive countries in the world, the population of professional female hockey players in Canada was significantly less than 10% of the equivalent male population prior to 2019. Currently, it stands at 0%.

Basketball is arguably the closest to baseball in terms of number of teams, with 56 professional basketball teams between the NBA and the NBA G League, compared to 12 WNBA teams. However, in terms of revenue, it’s not even close. The total amount of money paid out to WNBA athletes was roughly $12 million. That’s about the salary of one average NBA player. More specifically, the NBA spends roughly $3 billion on its athletes, without accounting for the other billions in potential endorsements the top athletes also get.

Soccer is very popular across the Americas. Currently, CONCACAF (FIFA’s branch in the Americas) lists 210 ranked men’s teams. That compares to nine teams in the National Women’s Soccer League.

Based on this, I am comfortable asserting that for all major team sports, there is significantly less than 10% of the economic opportunity for women than there is for men. This may play out differently in individual sports such as tennis, golf, and martial arts; however, it stands to reason the economic opportunity is also indicative of the level of participation and the intensity of said participation.

Our second key assumption is that Canada is demographically and environmentally similar to the U.S. Canada has roughly 10% of the population of the U.S. and generally competes in the same sports and athletics.

We’ll look at elite sprinters to set a baseline for the population-size effect on speed, based on the spread between the top American sprinters and the top Canadian sprinters of all time. We’ve chosen the 100-meter sprint, since it is an event Canada has historically done well in on the world stage, including setting a long-since-broken world record. We’ll also take a look at more esoteric events such as shot put, javelin throw and discus throw to get a measure of the effect on exit velocities.

Quantifying the Boost in Speed Due to Population Size

Canada has a rich history in the 100-meter sprint, including at one point being the home country of the world’s fastest man, Donavan Bailey. Twenty-two years ago, Bailey, Bruny Surin, Glenroy Gilbert, and Robert Esmie won gold for Canada at the 4×100-meter relay. Andre De Grasse became a national sensation when he held his own against Usain Bolt at the most recent Olympics. However, despite this rich history, the top American athletes still outshine the top Canadian athletes by a significant margin. The aforementioned Bailey, who is still the fastest Canadian ever, has been eclipsed by four Americans (Tyson Gay, Justin Gatlin, Maurice Greene, and Christian Coleman). If we compare the fastest American to the fastest Canadian, we get about a 1.5% boost in speed. If we compare the average of the top eight in each country, we get a boost of about 1.4%. Let’s conclude that in terms of raw speed, the population size effect would be at least 1.4%.

Quantifying the Boost in Raw Power Due to Population Size

We’ll turn to IAAF competitions to estimate this as well. Generally speaking, IAAF-governed events are strictly regulated, are adjusted for weather effects, and offer a platform for all countries to compete, even if those countries don’t have any athletes with a realistic chance at winning a medal. We’ll be selecting the IAAF events shot put, discus throw and javelin throw as our allegories for “how far can a human launch an arbitrary object?” We get the following differential between the top Americans and top Canadians:

Shot put: 5.7%
Javelin throw: 7.5%
Discus throw: 6.8%

One could argue these athletic events have so few people competing in them as to render the above results largely meaningless. It is this author’s opinion that this underscores the premise of how population sizes can have drastic impacts on the top athletes produced by said population. If we start with a small population, the new outliers gained by expanding the population size will be that much more extreme in comparison.

One could also argue these are poor allegories for baseball power in that they are completely different motions and mechanics. It is this author’s opinion that the physical tools required to launch an object as far as possible are generally the same, differing mechanics notwithstanding. I have little doubt, had Stanton or Judge trained their whole lives to hit golf balls instead of baseballs, they likely would outhit all of the major hitters in the PGA.

Let’s conclude and assess the population size impact on pure power to be roughly 6.5%.

How fast would our first female athlete be?

Speed should be straightforward to quantify thanks to the Statcast Sprint Speed metric and IAAF sprint speed comparisons for both genders.

Before we begin, let’s take a short aside and compare the legendary Bolt’s sprint speed to major league sprint speeds. We’ll ignore for the moment equipment, surface, and training differences. In 2009, Usain Bolt posted a mind-boggling time of 9.58 seconds in the 100-meter dash. Here’s how that broke down in 20-meter (65.6 foot) increments.

For comparison, under major league conditions, Tim Locastro topped the major leagues in 2019 with a sprint speed of 30.8 feet per second. Bolt’s top speed was 10 feet per second faster than that. Based on the chart above, Bolt’s time to first base would have been an insane 3.5 seconds. Though we’re comparing apples to avocados, it does give you a glimpse of just how fast the fastest sprinters are going.

The quickest time ever recorded by a woman in the 100-meter sprint was an amazing 10.49 seconds by Florence Griffith-Joyner. As per the IAAF, there are at least 1,700 men who have posted a 100-meter sprint time of 10.30 or faster. We can conclude that our athlete would likely not be Byron Buxton, nor would she be Billy Hamilton.

Per IAAF numbers, the 10 fastest men in 100-meter history posted an average time of 9.74 seconds, or 33.68 feet/second average speed on their sprints. The 10 fastest women of all time posted an average time of 10.72 seconds, or 30.69 feet/second average speed. Thus, before we take into consideration the effect population size has on our outliers, we can say the fastest woman would top out about 91.1% of the fastest man.

In our analysis of the population-size effect, we estimated we would see an increase of at least 1.4% speed if our population of female sprinters was equivalent to that of men. Using Locastro as the benchmark, our athlete could be as fast as 30.8*.911*1.014 = 28.45 ft/sec. If we change the benchmark to the average of the 10 fastest in the majors (30.1 feet/sec), we would get a 27.81 ft/sec sprint speed. If we throw out the 1.4% population size adjustment, we would get 27.4 feet/second.

A sprint speed of 28.4 feet/second would be equivalent to Albert Almora, Bo Bichette and Wil Myers.

A sprint speed of 27.8 feet/second would be equivalent to Jose Ramirez, Yoan Moncada and Lorenzo Cain.

A sprint speed of 27.4 feet/second would be equivalent to Marcell Ozuna, Jason Heyward and Juan Soto.

It is this author’s opinion that the 1.4% adjustment is actually low. Whatever the actual adjustment should be for population size, it definitively should be non-zero. Here are the average sprint speeds by major league positions.

We can safely conclude that our athlete would have, at the very least, enough speed to play second base, based on our conservative estimate, and more than enough speed to play any outfield position. While the fastest center fielders clearly would be faster, at 28.4 ft/sec, she would be as fast as George Springer, A.J. Pollock, Cain and Jackie Bradley Jr.

How Strong Would Our First Female Major League Player Be?

Finding an objective measure for strength is not as simple as finding one for speed. However, we do have a number of sports we can use to compare the top men to the top women.

Tennis serve speed: 83% as fast.
Golf driving distance: 82% as far.
Weightlifting: roughly 80% as heavy.

It’s intriguing that the tennis and golf driving metrics are consistent with each other. These were two sports I feel translate well to baseball. Shot put and discus throws have different weights for men and women, making them useless for comparisons. Weightlifting was tough to do as a direct comparison since the weight classes often are slightly mismatched. Interestingly, we see the population-size effect here. It probably safe to assume the ratio of women to men playing tennis is higher than the ratio of women to men as competitive weightlifters, though I don’t have any hard numbers to back that assertion.

We estimated if we expanded our pool of competitive female athletes by a factor of 10, we would see the hardest serves and the farthest drives by women be at least 6.5% greater. Again, you may disagree with this adjustment; however, some adjustment is required. Let’s take the 83% from tennis, as that’s probably the sport with the largest economic incentives for women. The prize money at Grand Slam events pay out equally to men and women.

If we use Judge’s 95.9 mph average exit velocity as our benchmark and include our 6.5% population-size adjustment, we arrive at 84.8 mph. If we take the average of the top 10 and include the adjustment, we get 82.6 mph. If we assume only a 3% adjustment, we get 79.9 mph.

If we use Aroldis Chapman’s or Jordan Hicks’ throwing velocities as a benchmark, we easily could see a woman hit 87 (with a 3% adjustment) to 90 mph (6.5% adjustment), which clearly would be enough arm to pitch, let alone play a major league position.

A few exit velocity reference points:

84.7 mph average exit velo would be equivalent to David Fletcher, Jose Iglesias and Mallex Smith.

82.6 mph would be equivalent to Yangervis Solarte, Delino DeShields Jr. and Locastro.

79.9 mph would be equivalent to Hamilton, Roman Quinn and Bubba Starling.

Conclusion

In 2019, Kevin Newman had an average sprint speed of 28.5 mph and an average exit velocity of 84.7 mph, making him our ideal analog. We could delve into another 2,000 words about launch angles and making efficient use of exit velo. However, it is far simpler just to point to Newman. If every girl today believed she had the potential to be at least an above-average player in baseball, there is no doubt in this author’s mind that one day we’d see one of them grow into a major league position player. She would be at least as good as 2019 Kevin Newman, in terms of physical tools, and much, much better if she plays like Jose Altuve.

References & Resources

• https://www.fangraphs.com/blogs/can-major-league-baseball-legally-exclude-a-woman/
• https://www.iaaf.org/records/all-time-toplists/
• https://baseballsavant.mlb.com/
• https://footballdatabase.com/ranking/north-america/5
• https://en.wikipedia.org/wiki/List_of_average_human_height_worldwide
• https://www.worldlongdrive.com/volvik-world-long-drive-championship-live-scoring/
• https://www.forbes.com/sites/davidberri/2018/09/04/what-wnba-players-want/#76f019f933eb
• https://www.iwf.net/results/olympic-records/