How Does Eye Color Affect Day/Night Splits?

Kris Bryant hasn’t disappointed in his first taste of the big leagues. Entering Tuesday, he had posted nearly 50 plate appearances and posted a 170 wRC+ to continue his domination of professional pitching. With the Cubs boasting a playoff probability greater than 50% and Bryant batting cleanup, the team is seemingly primed to break a streak of five straight losing seasons. Despite this, I have been skeptical of whether Bryant is all that good of a fit for the Cubs, given all the day games they play.

The Cubs led the majors in day games from 2006–2013, and were No. 2 in 2014. Certain obstacles come with the terrain of day games, such as the difficulty of playing one following a night game that ended about 15 hours earlier. Another less obvious challenge is that light-eyed players are said to struggle with sensitivity to bright sunlight. As sports optometrist Dr. Donald Teig explained to the New York Times in 2011, light-eyed people lack pigment in their macula, a pinhead-sized spot on the retina. The relationship of macular pigment (MP) density with one’s ability to withstand glare is strong and positive, so people with a less-dense MP are more overwhelmed by bright light and glare.

In turn, their contrast sensitivity (the ability to appreciate subtle differences in the foreground and background) is reduced. Sensitivity to contrast is vital in processing the spin of a pitched baseball’s red seams as it hurtles forth. Exacerbating the matter, light-eyed people are slower than dark-eyed people to recover from this “dazzled” state. For a batter, these two issues would compound the difficulty of taking 0.2 seconds to decide whether to swing, and then 0.2 seconds to actually swing.

You can see this creating a disadvantage for light-eyed hitters in matinees, and well, Kris Bryant has very bright blue eyes. Cubs fans may find Bryant’s blues to be dreamy, but maybe they’ll leave him adversely affected, to a particularly large degree, as he plays more day games in Chicago. That gives rise to my question here—are players’ daytime numbers really impacted by whether they have light or dark eyes?

Bryant’s dominant four dozen spring training plate appearances, mostly taking place in the early afternoon in often-cloudless Arizona, don’t disprove that he and others are affected by bright conditions, nor does his initial stint in Wrigleyville. To see how eye color actually affects hitters’ performance in the daytime, we need to look at way more players and way more plate appearances.

In 2011, when eye color emerged as a reason for Josh Hamilton’s poor daytime numbers, Dave Cameron looked at a crowd-sourced group of 25 blue-eyed players and didn’t find any prevailing day/night split. I want to take the topic a step further: by looking at hitters’ stats in a specified period (2006-2014) and classifying almost every player’s eye color with more granular distinctions. That means including all players possible, green- and brown-eyed ones included, and identifying variations among standard colors. With this process, not only can we compare players to themselves (with their personal day/night splits), we can compare players to each other (across eye colors).

Classification Procedure

To assign players into buckets, I’m going to use the nine-category grouping system designed by four ophthalmologists in a paper that appeared in Clinical and Experimental Ophthalmology in 2011. There are two broad categories—blues, and then a continuum from green to hazel to brown—with subcategories that follow in the table below:

Eye Color Categories

Blues	Green to Hazel to Brown
1) Light Blue	4) Fully Green
2) Darker Blue	5) Green with a brown iris ring
3) Blue with a brown pupil ring	6) Peripheral green/central brown
	7) Brown with some peripheral green
	8) Fully brown
	9) Very dark brown (appearing “black” in many cases)

The categories were designed so that, while you and I may differ in classifying eye colors into one of the nine buckets, it will generally only be by one subcategory above or below (i.e., from a “6” to either a “5” or a “7”). Obviously there’s subjectivity to this exercise, but I was as objective as possible, going over each player twice to compare my identifications. You can look at the approximately 800 grades in the Google doc below.

I deliberately avoided a pixel-based classification method because player pictures weren’t taken with the idea that they’d be used for scientific study. The color examples in that 2011 Ophthalmology paper depict eyes open wide with just a tiny speck of glare. When it comes to player photos, variations in the openness of eyelids, the dilation of pupils, the amount of glare, and the position of glare could all cause issues with applying a pixel-based method. Even sampling a speck of color using something like Photoshop’s eyedropper tool will yield different results, depending on where exactly in the iris one obtains the information. With the nine categories, I’m optimistic that any overarching effects will shine through, if they do exist.

I principally looked at players’ head shots on their ESPN player profiles, using the height and width components of the image URLs to enhance each photo’s resolution.  Not only is this good if you would like to closely admire A-Rod across a glass pane, but it also makes it pretty easy to put a “grade” on a player’s eye color.  Alex Rodriguez has a green iris with a brown ring, which I think is a pretty clear “5.”

In addition to flexible sizing, the other nice thing about ESPN’s head shots is that they have as close to standardized lighting as we’ll find.  Players will consistently be wearing their home white jerseys in lighting-controlled environments. Eye colors will otherwise look different as ambient lighting changes, heightening the likelihood that grades taken from action shots are inconsistent. Visual context matters! One’s surroundings, shirt color, and emotions can all influence the appearance of eye color.  Due to glare and/or blurriness, I did at times consider separate high-quality photo-day images for clarity (usually captured by USA Today), but an ESPN photo was always the “baseline,” and thus was needed for a player to be included. ESPN has these freely scalable images for players who were in the majors from 2011 onward.

Sample and Set-up

Players’ eye color classifications were applied to all of their career statistics from 2006 onward. (Eye color can change with age, but it’s infrequent, and we’ll assume that this hasn’t happened for any player.) I cut player-seasons off at 2006 for several reasons: 1) from 2005 onward, there are steep drop-offs in the percentage of day games covered by my grades, 2) there has been a recent spike in the number of day games after night games around this time, as documented by Russell Carleton in a Baseball Prospectus article last October, and 3) amphetamine and stimulant testing was instituted in time for the 2006 season. While Carleton didn’t find any changes in day game-after-night game performance in the pre- and post-testing eras, I’ll go along with the conventional wisdom on this point that the “environment” of day games has changed.

To have plate appearances included in the sample, players needed to have totals of 10 daytime starts and 10 nighttime starts across the nine-year period. Any game beginning before 2:15 p.m. was considered a day game, and any game starting from 6 p.m. onward a night game. All other games were termed as late-afternoon games and left out so as not to create especially inconsistent differences in lighting and shadows in the day/night bins.  I looked at only plate appearances taken by players who were in the starting lineup, and no pitchers were included. Plate appearances at domed stadiums and exhibition sites were tossed out, as were daytime plate appearances taken in retractable-roof stadiums in which the roof was closed.

And again, the players needed to have that scalable ESPN profile picture for me to derive the eye color. Here’s the percentage of daytime plate appearances, based on the above criteria, that I can account for with an eye color and incorporate into this study:

Percent of Applicable Daytime PA Matched with Eye Colors

Year	Percent
2006	61.2%
2007	70.0%
2008	78.9%
2009	89.0%
2010	95.4%
2011	98.9%
2012	99.6%
2013	99.1%
2014	98.0%

Each player’s stats across the sample were bucketed by park (as Tom Tango did in this 2011 article), and then the delta method was applied. Here, the delta method dictates that we take the smaller total of either day or night games (almost always the former) so that player-park samples are equally represented in the daytime and night.

At first, I’m going to remove catcher seasons, as catchers are subject to much different usage patterns. We can see this in the charts below, which plot the percentage of daytime starts in a season as a function of that year’s PA with a LOESS smoother put through the points.  Infielders/outfielders are on the left, and catchers are on the right.

In spending time at baseball’s most grueling position, full-time catchers generally play far fewer day games than their backups. Chances are, your favorite team’s backup sees a healthy amount of playing time in matinees so the full-time backstop can avoid the day game-after-night game. Catchers can also bias the data when the full-timer is given the preceding night off to be rested for the upcoming day game. The general point is that the rest allotted to catchers could obscure day game effects. Meanwhile, other position players play right around 30 percent day games, a total that decreases at a far gentler rate with rising plate appearance totals.

Included in all wOBA figures presented are adjustments for the quality of opposing pitchers and the left/right platoon advantage.

Results

If we consider all included players (without taking eye color into account), there’s no prevailing day/night split. Infielders and outfielders registered a .3341 wOBA at night, and a .3345 wOBA during the day.

Now let’s split infielders and outfielders by eye color classification. The Difference column is key; this is where Day wOBA is subtracted from Night wOBA, meaning that negative differences will indicate that players do worse in day games. Also, pay close attention to the Standard Deviation column, which indicates the uncertainty level for each eye color subset. All differences, standard deviations, and confidence intervals are expressed as wOBA points.

Infielder & Outfielder Day/Night wOBA Splits by Eye Category

Eye Color	PA	Day wOBA	Night wOBA	Difference (D-N)	Std. Dev.	95% Confidence Interval
1	16,229	.3333	.3305	+2.8	5.6	(-8.2, +13.7)
2	23,560	.3335	.3329	+0.5	4.7	(-8.6, +9.7)
3	13,011	.3245	.3258	-1.2	6.2	(-13.4, +11.0)
4	14,488	.3420	.3445	-2.5	6.0	(-14.3, +9.2)
5	24,909	.3478	.3416	+6.3	4.6	(-2.7, +15.2)
6	14,453	.3232	.3200	+3.2	5.9	(-8.4, +14.7)
7	31,009	.3412	.3374	+3.8	4.1	(-4.2, +11.8)
8	56,881	.3339	.3320	+1.9	3.0	(-4.0, +7.8)
9	81,979	.3309	.3351	-4.2	2.5	(-9.0, +0.7)

We’re given results that run completely against our Bayesian prior. The lightest blue-eyed players hit better in the daytime, while grade 2s and 3s were basically equals in the day and night. The results are even more unexpected if we consider the green-to-brown continuum from buckets 5–9, as hitters’ daytime stats worsen as their eye color darkens. Hitters in bucket 5 hit +6.3 points better in the day, an effect that keeps shrinking until getting to the darkest brown-eyed players, who post the worst day split out of all groups at -4.2 points.

It’s important to point out that we’re dealing with pretty small samples throughout the bins. That may be surprising, given that the buckets are comprised of tens of thousands of plate appearances, but split effects such as these require greater amounts of PA. Here we’re taking a standard split (day/night) and breaking it up in nine ways. The corresponding uncertainties are reflected in standard deviations that are often larger than the effect sizes, culminating in confidence intervals that include 0 well within their range. Saying that the light green types hit 2.5 points worse in the day—leaving us 95 percent confident that the true estimate is between -14.3 points worse in the day and +9.2 points better—just doesn’t tell us much.

Only those with the grades 5 and 9 look the most “promising,” in that their confidence intervals are farthest from 0. But given that the signs are the opposite of the expectation, I’m more inclined to dismiss this near “significance” as noise. That could be random variation and/or other variables lurking in the background. For instance, there could be issues with varying temperature and differing concentrations of players entering games with a sleep deficit.

There are a couple of additional ways we can look at the data, so let’s not give up on this just yet. To expand our sample with the same players, let’s combine the eye color numbers across larger categories, binning the blues (buckets 1-3), light green to hazel (4-6), and hazel to dark brown (7-9).

Infielder & Outfielder Day/Night wOBA Splits by Eye Category Range

Eye Color Range	PA	Day wOBA	Night wOBA	Difference (D-N)	Std. Dev.	95% Confidence Interval
1 – 3	52,800	.3312	.3304	+0.8	3.1	(-5.3, +6.9)
4 – 6	53,850	.3397	.3366	+3.1	3.1	(-3.0, +9.1)
7 – 9	169,869	.3338	.3345	-0.7	1.7	(-4.1, +2.7)

The standard deviations and corresponding confidence intervals shrink, but the effect sizes do as well. Again, we’re given results that run against the prior scientific reasoning: not only are the differences the opposite of what we’d expect, but the point estimates and sample sizes are so small that we’re left with the strong possibility that eye color doesn’t have a hand in day/night performance variation.

Now let’s consider differences in walk rate (BB/PA) and strikeout rate (SO/PA) across the nine eye categories. It seems obvious that, if a batter is struggling to see the ball, he’ll strike out more and walk less. The same initial criteria were used, but no adjustments were made for opposing pitcher quality or platoon split, since strikeout and walk rates are quick to stabilize. The table shows the differences in walk percentage and strikeout percentage, where negative numbers indicate that players were worse in matinees.

Walk and Strikeout Rate by Eye Color Category

Eye Color	PA	BB% Difference	SO% Difference
1	16,229	+0.25%	-0.26%
2	23,560	+0.47%	-0.23%
3	13,011	+0.76%	-0.40%
4	14,488	+0.30%	+0.47%
5	24,909	+0.52%	-0.24%
6	14,453	-0.07%	+0.13%
7	31,009	+0.28%	-0.54%
8	56,881	+0.21%	-0.01%
9	81,979	+0.33%	-0.47%

Across nearly all eye colors, hitters walk more (and strike out more) in the day. In terms of walks, the lightest-eyed players perform a bit better in the daytime than at night, and in many cases top the darker-eyed players. Light-eyed players do strike out more in the daytime than at night, but the differences are comparable to those posted by their dark-eyed counterparts. More and more, it doesn’t look like eye color, in and of itself, is a prevailing factor for any differences in day/night performance in major league baseball.

Lastly, for completeness, the day/night splits with catchers included appear in the table below.

All Position Players Day/Night wOBA Splits by Eye Category

Eye Color	PA	Day wOBA	Night wOBA	Difference (D-N)	Std. Dev.	95% CL Low
1	17,321	.3327	.3310	+1.7	5.4	(-9.0, +12.3)
2	28,641	.3362	.3340	+2.2	4.2	(-6.1, +10.5)
3	15,100	.3286	.3269	+1.8	5.8	(-9.6, +13.1)
4	17,349	.3420	.3442	-2.2	5.5	(-13.0, +8.5)
5	26,953	.3445	.3378	+6.7	4.4	(-1.9, +15.3)
6	15,432	.3246	.3202	+4.4	5.7	(-6.7, +15.6)
7	34,140	.3388	.3350	+3.8	3.9	(-3.8, +11.4)
8	65,738	.3331	.3321	+1.0	2.8	(-4.4, +6.5)
9	87,682	.3317	.3361	-4.4	2.4	(-9.1, +0.4)

What changes? Well, including catchers adds in nearly 32,000 PA (+11.5 percent), and increases the size each of the nine bins. The standard deviations shrink by fractions of a point apiece. Category 1 blues get worse in matinees, but Category 2 and 3 blues get better, and Category 6 green/brown types get better. The point estimates are even more divergent from the Bayesian prior. And still, the estimates are small relative to the larger standard deviations. There just isn’t statistical significance here.

Concluding Remarks

Why might the results run contrary to what several optometrists have said in the media? I think it comes down to a few points. One is an incredibly weird, shocking trick (via ESPN Dallas):

[Dr. Ison’s] solution for [Josh] Hamilton: Find a pair of sunglasses that he’s completely comfortable wearing while batting.

Dr. Ison noticed that in one of the Rangers’ recent day games in Atlanta, Hamilton was adjusting the sunglasses he was wearing twice during one at-bat and then with two strikes, took them off completely.

“He has to find a pair that he likes and that will be the right tint for him,” Dr. Ison said. “He just has to try some different kinds and figure out the right light transmission factor for him.”

All those dozens of articles written about the burden imposed by light eye color, and sunglasses are the solution? Maybe for some, but sunglasses aren’t a universal fix. Some hitters aren’t comfortable hitting while wearing sunglasses, as the nose piece blocks part of the hitter’s line of vision, and the darker tint can make it tough for some to track the ball. The greater point here is that hitters have so many choices today that it’s easier to make necessary adjustments. There are wraparound sunglasses, refractors, some eye black, lots of eye black, and those devilish red-tinted contacts. Lacking information on who was using what in which plate appearances may seem like a source for bias in this study, but I don’t think so. It’s reasonable to assume that each player made corrective choices that maximized comfort/effectiveness. Maybe there are natural disadvantages of light eye color, but the use of modern equipment helps neutralize them.

I also think another key is that major league players likely have other exceptional, counteracting aspects of vision going for them. A 1996 study showed that the vast majority of the tested 387 Dodgers major and minor leaguers had 20/15 vision or better, with many registering at 20/12.5. In terms of stereoacuity (detecting differences in depth between two objects), 58 percent rated as “superior,” which was over three times the proportion exhibited by the general population. Their contrast sensitivity was better than the baseline, too. Major league players are starting from higher levels of vision than the public at large and minor leaguers as well. (And there are opportunities to improve through perceptual learning.)

A missing piece here is whether light-eyed players have vision characteristics that are superior to those of dark-eyed players—this could show whether the bar for performance is set higher for lighter-eyed players to be major league quality. But lacking this information doesn’t take away from the finding that eye color is a non-issue across the league. So those bright blue eyes shouldn’t present an obstacle for Kris Bryant.

References and Resources

• Eye color data is in this Google doc
• Retrosheet events and games files
• Ted Turocy’s Chadwick Register
• James M. Stringham and Billy R. Hammond, Vision Science Laboratory, University of Georgia, Optometry and Vision Science, “The Glare Hypothesis of Macular Pigment Function”
• Sam Borden, The New York Times, “Light-Eyed Players Deal With Glare, and Doubts”
• David Waldstein, The New York Times, “Hitters With Blue Eyes Are Wary About Glare”
• Dave Cameron, FanGraphs, “Blue-Eyed Players Hit Just Fine in Day Light”
• David A. Mackey, Colleen H. Wilkinson, Lisa S. Kearns, and Alex W. Hewitt, Clinical and Experimental Ophthalmology, “Classification of iris colour: review and refinement of a classification schema”
• Mitchel Lichtman, MGL on Baseball, “Pinch-hitter, DH, and Other “Penalties” (revisited)”
• Tom Tango, Inside the Book Blog, “Do hitters and pitchers perform better during the day or at night?”