Tanaka Tues… Thursday?
Tuesday has always been my least favorite day of the week. Most people hate Mondays, but I always thought Mondays were better because it’s still a recovery from the weekend, so teachers would usually implement a review more so than a lecture or big assignments. When Tuesday came, those assignments rolled in and the weekend seemed forever away. Tanaka Tuesday saved me.
The phrase rolls off the tongue, and Twitter is always filled with fun memes and gifs. But besides being a whimsical alliteration, should we really be excited about Tanaka Tuesday?
Masahiro Tanaka’s career has been a bit of a rollercoaster (the pop-up carnival type, not one you’d find at Disney World). In 2014, the Yankees signed the Japanese superstar to a 7-year, $155,000,000 deal. Through the injuries and sometimes frustrating starts, you would be hard-pressed to find a fan that doesn’t think the signing is a net positive. His 3.63 career ERA is one of the best over that span, and he features one of the best splitters of this generation. He may not be the “ace” some thought he could be, but all in all, he is a very good starting pitcher.
There seems to be a sentiment amongst Yankees fans that Tanaka can only pitch on certain days or in certain conditions. “It’s gotta be 68 degrees. Wind blowing southwest. 2:00 pm. Hopefully, Masa wakes up on the left side of his bed.” All things that might affect his pitching performance. Regardless of the caveats, Tanaka Tuesday seems to be a day of excitement when fans think he’ll pitch well. This led me to ask a very simple question: “Does Masahiro Tanaka really pitch better on Tuesdays?”
First, I looked at each of his starts on Tuesdays. He certainly has had some good performances:
4/22/14 @BOS 7.1 IP, 7 H, 7 K, 2 ER
6/17/14 TOR 6 IP, 5 H, 10 K, 1 ER
6/9/15 WSH 7 IP, 5 H, 6 K, 1 ER
9/8/15 BAL 8 IP, 6 H, 10 K, 1 ER
7/5/16 @CWS 7.1 IP, 6 H, 6 K, 0 ER
But also some very forgettable ones:
5/10/16 KC 7 IP, 7 H, 4 K, 6 ER
8/2/16 @NYM 6.1 IP, 8 H, 4 K, 6 ER
6/6/17 BOS 5 IP, 5 H, 2 K, 5 ER
4/17/18 MIA 5 IP, 8 H, 5 K, 6 ER
When all is said and done, what’s the story? To answer this question, I decided to run a linear regression on when Tanaka pitches. For those who are not nerds like me, a linear regression is a mathematical formula which allows you to test variables against an outcome. In economics, it is commonly used to detect correlation and/or make projections. If you would like to know more about the math behind the results, a simple Google search could help, or I can answer questions in my Twitter DMs. In this case, the variables I am testing are the days of the week and home/away. The outcome I tested them on is ERA. It is important to note, this does not calculate what Tanaka’s ERA actually is on those days, it takes those real numbers and calculates a projection based on them.
The following table is a summary of the results.
|* denotes significance at 10% level
** denotes significance at 5% level
R^2 = 8.60%
You’ll notice Tuesday and Home are not listed variables. This is because they are calculated into the intercept. The interpretation of the intercept is “When Tanaka pitches on Tuesdays at Home, his ERA will be 3.93.” You’ll also notice some of the variables have negative coefficients. This does not make intuitive sense because a pitcher can obviously not have a negative ERA. These coefficients represent deviations from the intercept (when Tanaka pitches on Tuesdays at home). Therefore, the interpretation for Sunday as an example would be “When Tanaka pitches on Sundays at Home, his ERA will be 2.85 points more than if it were a Tuesday, AKA 6.78.” To give an example of when he pitches on the road, an interpretation would be “When Tanaka pitches on Saturdays on the road, his ERA will be 1.99 + 1.41 points higher than if he pitched on Tuesday at Home, AKA 7.33.” These interpretations can be followed for the entire chart.
One key mathematical aspect to understand is the significance level. Significance signals how certain you are in the coefficient’s value. A variable holding a 5% significance level means that 95% of the time, the coefficient’s value will be accurate. Once again, DM me if you want to know more. More importantly, the intercept and Away are not significant. This means that when Tanaka pitches on Tuesdays, home or away, it statistically has no effect on his ERA. Sorry to burst everyone’s bubble, but Tanaka Tuesday is a myth.
The other dates, however, do hold significance. In academia, 5% is the gold standard, but for our purposes, I included 10% significance. There are three dates when Tanaka pitches better: Monday, Thursday, and Friday. Thursday, he pitches the best with an ERA which is projected to be 2.55 points less than Tuesdays at home.
Finally, the R^2 listed is 8.6%. This means that 8.6% of the variation in Tanaka’s ERA is explained by the variation in the variables. In other words, the days of the week and whether he is home or away really don’t matter. Well, they technically do statistically, but there are MANY other factors that influence his ERA for a game. This should come as no surprise to anyone who knows baseball. Recently, we’ve heard about his fastball usage affecting his performance. Additionally, he has had elbow issues, the team he is playing matters, and countless other variables should come into the equation.
My goal here was to test whether the day of the week Tanaka pitches matters. Surprisingly, it does except for the one day everyone cares about, and he doesn’t even pitch his best on that day. In the end, it doesn’t seem to be a big deal and there is not a linear regression I could run that could explain away the excitement held by Yankees Nation on a Tanaka Tuesday.
For more on how I calculated these results, or a more thorough analysis, follow me on Twitter @Robrosene.
**Stats from MLB.com