First Foray Into Baseball Analytics: Pitch Sequencing

I've been enjoying sports analytics for a long while now, as they're the intersection of two of my favorite things: sports on one hand, and data, statistics, and and programming on the other. I started with baseball analytics, mostly thanks to the fine folks at Fangraphs, and I also quite enjoy basketball analytics, especially the work of Kirk Goldsberry, first at Grantland (RIP) and now at FiverThirtyEight. Ultimate frisbee, my favorite sport, is still lacking the level of data collection required for insightful analytics; this FiveThirtyEight piece details that.

The first baseball question I chose to tackle has to do with pitch sequencing - the order in which the pitcher and catcher choose to employ the pitcher's arsenal in order to get batters out. It is something that has some age-old adages (e.g. using the fastball to set up the change-up), and it seemed to like it should have a significant effect on outcomes. Eventually, I would to be able to answer questions such as:

• Which pitchers gain the most due to their sequencing, over what would be expected by the strength of their pitches alone?
• Can the effect of the catcher be separated from the role of the pitcher? 
• Are certain batters more or less susceptible to certain sequences, beyond their strength or weakness against specific pitches? 
• Are there any universally strong pitch sequences? Maybe for specific types of pitchers?

Before I tackle these harder questions, I realized I must start with a simpler one: Is there even a statistically significant effect of pitch sequencing? Can it be meaningfully distinguished from random selection from the independent pitches?

To do that, I started with the PitchFX database, which contains every pitch thrown in the past few MLB seasons, as well as its classification to one of around ten pitch types. Looking at the entire 2015 MLB season, I first calculated the individual probability of each pitch type being thrown:

Pitch ID	Pitch Description	Probability
FF	4-Seam Fastball	0.3629
SL	Slider	0.1463
FT	2-Seam Fastball	0.1365
CH	Change-up	0.1040
CU	Curveball	0.0783
SI	Sinker	0.0723
FC	Cut Fastball	0.0530
KC	Knuckle Curve	0.0211
FS	Split-finger Fastball	0.0154
KN	Knuckleball	0.0052
FA	Fastball	0.0036

I then created a new table in the database, to store pitch transitions. I defined a transition as two consecutive pitches within the same at-bat; a four-pitch at-bat would generate three transitions. Of course, this loses some information - one-pitch at-bats would not be examined, and the first and last pitch of each bat appear in the table only once, while the middle pitches appear twice. Still, I believe it's a fitting system. I then calculated the probability of each transition, building the markov transition table:

*****	FF	SL	FT	CH	CU	SI	FC	KC	FS	KN	FA
FF	0.5105	0.1433	0.0755	0.0951	0.0789	0.0177	0.0389	0.0203	0.0133	0.0014	0.0036
SL	0.3374	0.3397	0.1152	0.0645	0.0405	0.0658	0.0204	0.0039	0.0094	0.0000	0.0027
FT	0.1996	0.1331	0.4162	0.1142	0.0722	0.0001	0.0336	0.0148	0.0115	0.0000	0.0044
CH	0.3233	0.0873	0.1379	0.2536	0.0641	0.0681	0.0436	0.0166	0.0010	0.0002	0.0036
CU	0.3459	0.0842	0.1190	0.1124	0.2159	0.0506	0.0546	0.0000	0.0108	0.0019	0.0037
SI	0.0900	0.1419	0.0001	0.1087	0.0574	0.5170	0.0425	0.0239	0.0153	0.0000	0.0018
FC	0.2528	0.0613	0.0805	0.0876	0.0843	0.0544	0.3253	0.0293	0.0216	0.0000	0.0017
KC	0.3366	0.0372	0.0919	0.0994	0.0000	0.0776	0.0729	0.2809	0.0028	0.0000	0.0004
FS	0.2873	0.0711	0.0854	0.0096	0.0376	0.0602	0.0657	0.0027	0.3776	0.0000	0.0001
KN	0.1041	0.0011	0.0000	0.0037	0.0369	0.0000	0.0004	0.0000	0.0000	0.8328	0.0000
FA	0.3284	0.1155	0.1458	0.1001	0.0750	0.0245	0.0383	0.0027	0.0005	0.0000	0.1692

One expected outcome of this table are the high values on the diagonal - as a pitcher who can throw a specific pitch can certainly repeat it, while he probably only throws two to four other pitchers.

Next, I compared the observed dependent transitions with a hypothetical independent pitch transitions. The independent probability for each pair of pitches is the product of the two independent probabilities. For the dependent probability, I multiplied the probability of a transition starting with a certain pitch, by the probability of the second pitch given the first one. Thus, I created two tables of the same size, each with the joint probabilities of each pitch transition according to its model. To compare the two, I used Shannon's entropy - as entropy is maximized when probabilities are uniform, and I expected the dependent decisions to show more variability (due to some sequences being more preferable), I expected lower entropy from the dependent probabilities. These were the results:

Independent H(X,Y) = 5.49738472712

Dependent H(X,Y) = 5.14084599364

To test the significance, I performed a permutation test. I sampled individual pitches from the independent probabilities to create the same number of transitions as observed, calculated the entropy of each such permutation, and calculated the Z-score of the observed dependent entropy compared to the distribution of the permutation entropies. The results were striking: a Z-score of -102.57, which is off-the-charts low.

This is where I got suspicious. These results were too good to be true. I suspected it is either due to the extremely large sample size (the entire season gave me over 500,000 transitions), or because of the limitation on each pitcher's arsenal. Because each individual pitcher only throws a few pitches, he cannot make all transitions listed in the table - making the joint distribution skew sharper than it should. 

I decided to test individual players, to see if the results replicate. While it does not separate the hypotheses, as the sample sizes are indeed much smaller, it felt like a good start. Rather than randomly sample, I picked three groups of ten pitchers each: the ten pitchers with the most transitions last season, three around the average, and three around one standard deviation over the average. I then repeated the same individual and joint probability and entropy calculations, and the permutation tests:

Edit #1: it seems I was a little unclear. The permutation tests for each individual player were sampling from their individual probabilities - counting only the pitches they threw, to establish the frequency of each. That individual distribution is also the basis for the independent entropy (third column).

Group	Name	Indep. Entropy	Cond. Entropy	Z-Score	P-Value
Pitch transition count closest to mean (~688)  (until Josh Tomlin)	Francisco Rodriguez	3.7134	3.5884	-2.1538	0.0156
	Yimi Garcia	2.6504	2.4703	-1.4416	0.0747
	Sergio Romo	3.0703	2.9099	-1.4861	0.0686
	Derek Holland	3.3051	3.3169	0.4957	0.6900
	Hansel Robles	1.8342	1.8017	-0.2640	0.3959
	Carlos Villanueva	4.2170	4.1108	-0.8810	0.1892
	John Lamb	3.3414	3.2973	-0.4065	0.3422
	Joshua Fields	2.3622	2.3360	-0.1912	0.4242
	Santiago Casilla	4.0146	4.0413	0.8235	0.7949
	Josh Tomlin	3.6684	3.5650	-0.9883	0.1615
Pitch transition count closest to mean + std. dev (~1380) (until Tim Hudson)	Roenis Elias	4.2148	4.1512	-1.7099	0.0436
	Jake Peavy	4.4581	4.4121	-0.4792	0.3159
	Hisashi Iwakuma	4.4289	4.4015	-0.1079	0.4570
	Chad Bettis	4.1127	4.0334	-0.9856	0.1622
	Jaime Garcia	4.5430	4.4571	-1.3102	0.0951
	Williams Perez	2.5985	2.5346	-0.6638	0.2534
	Kevin Gausman	2.9166	2.8262	-1.0872	0.1385
	Michael Lorenzen	3.9086	3.7307	-1.9956	0.0230
	Kendall Graveman	3.8000	3.8172	0.6236	0.7336
	Tim Hudson	3.9299	3.9379	0.4617	0.6778
Max pitch transition count (2563-2831)	Collin McHugh	4.3544	4.2274	-3.2359	0.0006
	Jose Quintana	3.3734	3.3498	-0.2440	0.4036
	Christopher Archer	3.3490	3.2755	-1.9169	0.0276
	Cole Hamels	4.4435	4.4177	-0.9683	0.1664
	Clayton Kershaw	2.9702	3.0248	2.0182	0.9782
	Dallas Keuchel	4.3491	4.3080	-1.3321	0.0914
	Johnny Cueto	4.5603	4.5172	-1.3415	0.0899
	David Price	4.4113	4.3996	-0.2504	0.4011
	Edinson Volquez	3.7520	3.7481	-0.0093	0.4963
	Jake Arrieta	4.1939	4.2031	0.5471	0.7079

As is probably evident from the variability of the Z-scores, the results did not quite replicate. With an average z-score of -0.683, the p-value was 0.25, nowhere near significant (using a t-test with 29 degrees of freedom). To verify this result, I repeated this test for all 297 MLB pitchers at or above the average pitch transition count. The pitch transitions counts skew right, as many pitchers threw much more than the average, probably most of them starters and high-usage relievers. The results were similar - a mean Z-score of -0.77, which with the larger sample (df = 296) gave a p-value of 0.22.

While these results are somewhat discouraging, I intend to investigate further, to see if I can find a way to sufficiently distinguish between the independent and dependent transitions. First, I will check my math and code, and verify that my my methods were appropriate. I will then try to process another season or two, and see how that changes the results. In order to increase sample sizes, I'm also considering to attempt to cluster pitchers (perhaps by their individual pitch distributions) and testing them together, to see if such an examination by pitcher archetype makes sense. There are other confounding variables which might be harder to remove, such as the variation in location (more than merely pitch types), and the preferences of the batters. 

Either way, this has been very interesting, and great fun, and I'm looking forwards to continuing it!

Notes:

• This project would have been much more difficult and clunky without the help of Professor Michelle Greene, who teaches at Minerva, and another individual (whose consent I'm awaiting to put his name here). Thank you!
• This question has been on my mind for a while, and I found the time for it when I could also use it as my final project for my first semester at the Minerva Schools, where I'm studying.
• I will upload my code (Python and SQL) to github shortly.
• I'm aware how clunky the tables look; I need to find a better solution to post them as HTML, or perhaps write the whole post in some other editor and export the HTML here.
• If you've made it this far - I would love any comments or feedback!

Peace and Quiet in the Heart of the City

Note: like the previous post, this is another assignment for school, in blog post format. Enjoy!

The Living Innovation Zones (LIZ) program is initiative by the city of San Francisco to improve and iterate upon public space by better connecting it to the people and businesses nearby (SF…, n.d.). The program is designed to quickly adapt to rising needs, tackle urban design challenges creatively, and use space that currently goes unused (SF…, n.d.). In our research, my group and I visited several such installations. One, named Pause, challenges visitors to stop and take the time to think, but most people we saw passing by just enjoyed sitting on the benches. Another parklet, the Annie Street Plaza, was deserted when we visited; we imagined it might be more utilized on workdays, as a spot to have lunch outside of the nearby office buildings.

Even after several months in San Francisco, I have still not adjusted to how loud Market Street can be. Having lived in suburban towns for most of my life, the noise generated by the amount of pedestrians, not to mention the public and private transportation, is incredibly foreign to me. As I sauntered down Market, the inspiration for a quiet bubble struck me; what if people had a spot to sit down and enjoy a moment of silence as they make their way to work, or had the opportunity to collect their thoughts in peace before moving on with their day? Enter the 'quiet bubble':

Preliminary render of the proposed 'quiet bubble'

In order to design the bubble, I considered several constraints. It should not become an easy place for illicit activity to take place; therefore, the outer frame is built from glass, which is also very visually pleasing. Should the glass prove too weak, a metal reinforcement frame might be required. The semi-circular shape was chosen to help reduce noise on one side, and offer an economical use of space on the other, as we cannot take over the entire sidewalk. The bench was designed for comfort and simplicity – it should be a structure that welcomes the user for five to fifteen minutes at a time, so that many people can enjoy it. On the whole, I strove for a clean and simple design; visual parsimony, if you will.

When attempting to analyze the utility of such an installment, I began by considering the audience it would be for. My primary intended denizens are pedestrians who walk on Market Street to work, for lunch, or on their way home. It could also serve very well as a meeting or waiting point, as it is visually noticeable and offers the comfort of sitting. As this installment is designed to be placed on Market Street, it will certainly be used by members of the homeless community as well. I see that as a potential advantage; if it saves people from having to sleep outside in the rain, that is a very worthy use.

Proposed render on location at 1412 Market Street, San Francisco

The next step in assessing the utility would be to estimate how many people might choose to take advantage of the installation. A 2010 study by the San Francisco Planning Department found that approximately ten thousand people walk in each direction in the relevant area on Market on weekdays, with weekend figures being lower, approximately seven thousand people walking in each direction (Popper, 2010). If out of those, only one in one hundred decides to enjoy the bubble, for five minutes, we arrive at the bubble being occupied for:

(10,000 + 10,000 people) * (1/100 who would use it) * (5 minutes each) = 1000 minutes, or almost seventeen hours.

Weekend figures would be lower – approximately twelve hours. These estimates don’t account for any growth in the pedestrian traffic on Market street since 2010, which likely occurred. Moreover, 1412 Market Street is one of the least busy parts of the streets downtown – the area near Powell and Market, for example, features about twice the pedestrian traffic. Therefore, should the first such bubble prove successful, there is great expansion potential to other parts of Market Street.

Now that the collective utility of such a structure is established, I can examine the individual utility. The cost of using the bubble is in time alone; it is there, it is free to use, and I do not foresee any social stigma or cost from enjoying the bubble. On the other hand, there are many potential benefits. For a person with anxiety or crowd issues, having a small space to disconnect from the world momentarily might prove invaluable. Even without any special issues, having a place to focus or mentally prepare for a meeting or interview can be the difference between success or failure. Even without any specific purpose, it can simply be nice to take a break for a few minutes.

When discussing my proposal with my group, several new ideas came up. One was to make sure the bench is long enough to allow sleeping on, which I believe it is, but physical prototyping would be necessary to be sure. Another was about the noise permeability of the shape - with it being half-open, and without any active noise canceling, it might still allow too much noise to truly provide peace and quiet. In that scenario, the structure would have to be closed from the front, which would also necessitate a door. Some form of ventilation might also be required in that case; perhaps some vents that could be closed in the winter and opened in the summer. Should this proposal garner interest, I would be happy to render in these additional proposals, and begin evaluating this structure for integrity and its ability to reduce noise.

References:

Popper, A. (2010, March). Walking, Bicycling & Public Space on Market Street. Retrieved 8 November 2015, from http://www.bettermarketstreetsf.org/docs/MarketStreetReport.pdf

SF Mayor’s Office of Civic Innovation. (n.d.). What is a LIZ? | living innovation zones. Retrieved 8 November 2015, from http://www.sfliz.com/about/

Cultivating Culture: Uber vs. Lyft

Note: this was an assignment for a class, but as it was intended be written as a blog post, it might as well become one. Enjoy!

The service economy is ubiquitous. Need to get somewhere? Install Uber or Lyft and you’ll be on your way. Hungry? There are enough delivery services to use a different one every day of the week. Too lazy to do laundry or clean your apartment? Don’t worry, there’s an app for that. To differentiate themselves, service economy companies must either provide a superior product, cheaper prices, or build a unique culture around themselves. Through my experiences with Uber and Lyft, I will attempt to examine culture: how each company brands itself, why they chose so, and how those decisions affect the workers, who are the public faces of each company.

Uber is clearly the big brother to Lyft’s little brother act, and their websites provide powerful indications for how they carry themselves. Uber is all about professionalism, as their initial description on their websites claims, “Your ride, on demand. Transportation in minutes with the Uber app” (Uber, n.d.). Contrast that with Lyft’s statement: “Need a ride? Take Lyft for a welcoming, affordable, and memorable ride” (Lyft, n.d.). Uber strives to create an image of a professional chauffeur, who will be there whenever you might need him, and disappear afterwards. Lyft, on the other hand, tries to conjure images of calling your buddy at 2AM for a ride home from the bar. He’ll definitely be there, and will be happy to chat with you and ask how your night was. Uber have a newsroom (Uber, n.d.), while Lyft have a blog (Lyft, n.d.); the Lyft app is stylized in pink, while Uber is overwhelmingly black and white.

Chatting with drivers drives home the same notion. First and foremost, Lyft drivers appear to be much happier to talk! Some of them engage in conversation even without being prompted, behavior I found very rare with Uber drivers. Carlos estimates he was one of the first one hundred Lyft drivers in San Francisco, and while he used to drive for Uber as well, he stopped at some point. Lyft feels like a family to him: he mentions the friendly rivalry the “day walkers” have with the “nightcrawlers,” groups lunches in the middle of shifts, and a weekly Lyft driver happy hour. Daniel is a photographer, who drives at nights for supplementary income, or as he put it, “I drive so my girlfriend is less unhappy with me when I buy expensive photography equipment.” He mentioned that he too prefers driving Lyft, as passengers are nicer and more talkative. He says it’s simply more fun.

Lyft seek to differentiate themselves from uber by culture. As I found when examining the apps and websites, some of the culture stems from intentional decisions made by the two companies. Annuar, originally from Kazakhstan, drives for both, but notes that, “with Uber, I’m just another driver… for Lyft, I’m a friend.” Another former driver received a party pack from Lyft after reaching the one thousand ride milestone (Muender, 2014). Isn’t that awesome? However, some part of the culture also appears to be emergent. Annuar described it as a “pay it forward” culture: the first drivers were kind and friendly to the first passengers, who passed it on to their next drivers, and so on, even referencing the famous monkey learning experiment (which according to Maestripieri (2012), might not have occurred as famously described).

Annuar’s experience describes the network effects very clearly; a chain of drivers treating riders like friends, which causes these passengers to treat their next drivers similarly. Even with guidance from the company, this would never have worked without the cooperation of the drivers. The motivations on all sides are clear. For the drivers, work is fun when it doesn’t feel like work; driving friends around beats sitting in silence with strangers. Moreover, they probably get better tips, and and help build the Lyft brand. For the passengers, rides become enjoyable, rather than neutral. Technology obviously affects these interactions, as without it the drivers would be driving around like headless chickens, looking for someone to pick up. However, the effect does not have to be negative; Lyft provide a clear model for technology-fueled interactions can feel friendly and welcoming.

If Lyft’s culture is so superior, why does it lag far behind Uber? Uber is definitely better suited for those who prefer not to interact with strangers, or want to make use of the ride to think or work. Inertia is another powerful force; Uber came three years before Lyft, and made a very strong name for itself. Uber also offers a far wider range of services, particularly catering to more exclusive clientele: Lyft has no match for services such as Uber Select or Uber Black. Moreover, Uber allows calling regular taxis, for the more traditionally minded. Oh, and while the prices are similar, if there is a difference, Uber tends to be cheaper. Each category probably covers a significant amount of people; together, we can induce that they cover enough people to make Uber significantly farther reaching. Indeed, while both appear to be growing strong, Uber’s valuation is 27 times more than Lyft’s (Kelly, 2015). Some drivers also feel the financial power; Mohammad, who drives for both companies, mentioned that Uber is more profitable: “with Lyft I rarely leave the city, or have long drives. Uber often gives me longer trips, once I even took someone to Google, in Mountain View.”

For me, however, the culture of Lyft makes it a much nicer alternative. Beyond the good feeling of supporting the upstart (albeit a $3 billion one), riding a Lyft gives me more social utility – it just feels better. Annuar told me why he left Kazakhstan, and we bonded over our desire to work in software, but on a project with true meaning. Carlos gave each of us Lyft bandanas and a fantastic, fuzzy, pink Lyft mustache. Like a caring parent, Calvin made sure we got off from the right side of the car. Lyft succeeded in creating a culture that feels like they care, and for me that made the whole difference. 

Bibliography

Kelly, J. (2015, September 3). The Uber vs. Lyft War Has Been Won in Silicon Valley. Retrieved 26 October 2015, from http://www.vanityfair.com/news/2015/09/uber-vs-lyft-war-has-been-won

Lyft. (n.d.). A ride whenever you need one. Retrieved 26 October 2015, from https://www.lyft.com/

Lyft. (n.d.). Lyft Blog. Retrieved 26 October 2015, from http://blog.lyft.com/

Maestripieri Ph.D., D. (2012, March 20). What Monkeys Can Teach Us About Human Behavior: From Facts to Fiction. Retrieved 26 October 2015, from https://www.psychologytoday.com/blog/games-primates-play/201203/what-monkeys-can-teach-us-about-human-behavior-facts-fiction

Muender, G. (2014, December 3). Uber vs. Lyft: A former driver compares the two services. Retrieved 26 October 2015, from https://pando.com/2014/12/03/uber-vs-lyft-a-former-driver-compares-the-two-services/

Uber. (n.d.). Uber. Retrieved 26 October 2015, from https://www.uber.com/

Uber. (n.d.). Uber News, Events, Partnerships, Product Updates and More. Retrieved 26 October 2015, from http://newsroom.uber.com/

Life-Changing Dilemma (thanks to the Minerva Schools)

A year ago, I was pretty sure I'll be starting to study in 2014 or 2015, something in the general vicinity of math / computer science / statistics, at one of Israel's public universities (Tel Aviv University or the Hebrew University in Jerusalem, in all likelihood). Eight months ago, I had decided I'm not going to study in 2014, and that I shall travel for a few months (or more) before starting to study in 2015. Three months ago, give or take, I registered to universities in Israel, adding the Technion to the list of schools I might attend. I had almost went back from my trip early to interview for the Technion's excellence program, until deciding I'd rather travel some more. Over the past few weeks, I had come rather close to deciding I will study at Hebrew U, and pursue some unholy mathematics and cognitive science dual-major program, probably augmented with several computer science classes. I had consulted with friends, and started to plan how I might lay out the coursework. Last night changed everything.

I had applied to the Minerva Schools back in late January, as I was applying to universities in Israel. I don't remember how I even came to hear about them; friends, if one of you remembers posting about it on Facebook or talking to me about it, I probably owe you a beer. Much to the amusement of Eyal, with whom I was volunteering at Torres del Paine at the time (more on that soon), I spent quite a significant amount of our rest periods from the mountain dealing with the application procedure. I had a fair amount of work to do, little time, and the internet connection in Puerto Natales was quite unreliable. Once I finished their highly unique evaluation process, I generally set it aside; I felt I somewhat bombed one of the assignments, and besides, it was such a long shot. 

I received their e-mail as I was on the subway here in Buenos Aires on my way to meet Gal, a friend from the army I'm traveling with. The mobile internet was quite shoddy (either it's a repeating theme, or my standards are too high), and we met and started cooking dinner, so the notification left my mind for a while. As we sat down to eat, I realized I still haven't fully checked it, and the wi-fi in his hostel proved adequate. I was floored. For the rest of the meal (and night, and most of today), I still didn't really believe I was accepted, and only now is the shock finally starting to wear out. With it comes the harder part: do I go?

Why not? The program I'm considering at Hebrew U is really attractive to me. I love mathematics, and the faculty at the Hebrew U is incredible, and I find the cognitive science program to be a very interesting supplement, a way to expose myself to some topics I'm quite intrigued by (decision making, neurophsiology, linguistics, etc.). The programs there are established, and I generally know what I'm getting myself into. Living in Jerusalem sounds like a fun change of environment: new city, new friends, new atmosphere, but close enough to my friends and family. I should still be able to play Ultimate Frisbee with my club in Israel, and take care of my knee, should things go awry with it again. Last (and certainly not least) is the financial aspect: universities in Israel are significantly cheaper (Minerva will end up costing me around $30,000 a year including tuition, room and board, travel, etc.), and I could find work during the last year (or two?) of my degree, should I decide I want or need to.

However, the Minerva program sounds quite amazing. I quite connect to the idea of trying to refine higher education, and do it differently (and hopefully better). Small classes, seminars, a focus on skills and motivation (rather than just theoretical knowledge), and the company of unique and very bright people. The concentration of Computational Sciences is right up my alley, and the course topics seem to be exactly what I'm going for. Besides, the opportunity to be a part of something new, live in a different city each semester or two, and explore the world, learn languages... I'm not sure I could turn it down. It would be a very interesting social experience, as I imagine I'll be on the oldest there. I'm not quite sure how I feel about that yet. Moving around so much might also make finding serious relationships and making deep connections harder, but I would not let that deter me from trying.

The last thing on my mind might be FOMO - fear of missing out. If I try and see I don't enjoy it, I will be a year older, somewhat poorer, but I could go back to school in Israel knowing I followed the wild dream. Should I never try, I'm afraid I might not be able to forgive myself. It would make any and every hardship in university in Israel even harder to swallow. Don't I owe it to myself to try?

The Strange Kid

The strange kid would walk around town with his parents, reading the numbers of license plates as they went by. As he does not posses a superhuman memory (and rather, there is nothing quite superhuman about him), he does not remember it for himself. His relatives all seem amused whenever they recall this story, or remind him that his favorite books used to be encyclopedias, or other non-fiction works. Only in retrospect did he realize he has never asked any of his elders how they felt about it. He imagined they were proud, or at least, happy to see his parents’ affinity to numbers continuing another generation. Indeed it did: his favorite road-trip games were puzzling riddles and learning arithmetic tricks.

Later in his childhood, he was sent to a gifted class for his fourth grade studies. While he generally quite enjoyed it (long morning drives aside), he left after a year, due to his inability to handle a weird social situation that occurred. In retrospect, he could see it as foreshadowing many other parts of his adolescence, and in the great ‘what-if’ game of life, who knows where he would have been had he stayed there. Then again, he was in fourth grade. What kind of emotional maturity could be expected of him?

The weird pre-teen found his home in video-games and sports, more than anything else. While the latter were fun, and he enjoyed the activity and competition, he immersed himself within the former. He could easily tell you far more about companions such as Heroes, Crash Bandicoot, or Diablo, than he would be able to recall about many of his friends. While he certainly had some of those, they diminished in both quality and quantity as he moved from elementary school to the purgatory that is middle school. Of relationships, or any precursor thereof, there is little to talk about. Unfortunately, he was closer to his books and consoles than to any girls.

The eccentric teenager and his family moved halfway across the world. Perhaps the most telling sign of his social ineptitude was that only in retrospect did he realize how difficult the move was; at the time, he was blissfully unaware. During his freshman year he found himself with a circle of friends, and somehow drifted apart from them within less than a year. His Friday nights were spent having dinner with his family, and perhaps another family of friends, and afterwards retiring to play video games or watch a movie. He was not troubled or upset by it; for the most part, he simply did not know there are alternatives.

Romantically, things were not any better. While he met and briefly dated an interesting and exciting girl during his first year abroad, he let her get away over a silly incident that spiraled out of control. The future was not brighter. As he lacked friends and was inexperienced with emotions, he never quite knew what to do with them. Some signs of affection scared him away; to others he clinged mercilessly, blowing anything and everything out of proportion. It took him the better part of high school to gain some semblance of confidence (and a very limited one at that, as he still had issues with taking off his shirt at the pool), but it was all too little, too late, and even when things materialized, he barely got to experience them. A member of his freshman year circle of friends admitted to having a crush on him, for a long while. Never in a million years would our shining beacon of social competence have guessed it.

The peculiar adolescent did not have a better way with friends, either. He always felt somewhat of an outsider, second-rate to any other friends of his few friends. He was not an easy person to like. Loud, arrogant, and not incredibly kind, his actions tended to alienate himself, rather than bring people closer. He involved himself in many activities, taking positions of leadership in one or two, but always feeling a little bit outside. His video-game habit was ever stronger, and during his few years of high school, he spent an absurd amount of time playing World of Warcraft. It was absurd enough to suck away time from other activities (not to mention his schoolwork), yet not enough to truly master it.

Similarly, he probed many sports, enjoying each of them, but never immersing himself enough to reach any notable achievementד. He lacked single-minded focus and dedication, powers he would only acquire a few years later, when medical circumstances left him no choice in the matter.  While he eventually landed on a peculiar sport one he grew to enjoy immensely, even there he did not do all he could to better himself in to, 

in retrospect

much to his chagrin. Similarly, only during his final year abroad did he finally make some new friends he felt comfortable with. As always, his timing was impeccable, as soon afterwards they all graduated high school, and he returned to his country of origin.

The strange kid, the weird pre-teen, the eccentric teenager, and the peculiar adolescent will always be a part of me. However, no longer are they who I am, or rather, I am no longer any of them. Things got even worse before they got better; but better they did get, and while the 2015 model is far from perfect, he is much improved, or at least, vastly different. The details of journey here, which I would have never been able to make alone, will come soon. While change has to start from within, there is no way I would have been able to grow and evolve as I have without the help of some very dear people.

This post was inspired by Arcade Fire and by one of my favorite questions in OkCupid: “Would you rather be normal or weird?”

Have Travel Dilemmas, Will Ponder

Sometimes it seems to me as if the reason I've gone to the other side of the world is to ponder topics near and dear to my heart. I have written about memory and death, and of emotions evoked by experiences I encounter here. Alas, lately I have been pondering something I would have loved to avoid: when and why shall I return home.

I have been gone from home for almost five months now. My family and I started this trip together, in Florida, the Caribbean, and New York City. After staying for another two weeks in New York, I left for Buenos Aires, and I have been exploring Chile and Argentina (and Antarctica) ever since late October. I am truly having the trip of my life, at least so far; I have no intentions of this being my last long-term trip. And yet, life holds its cards close to heart, so it may be I am never afforded such an opportunity again. I have seen nature in its glory; hiked mountains beyond mountains; met incredible people from every corner of the globe; ate the food, drank the wine, and experienced the life. I have also delved into emotional thinking (and writing) on levels I have never reached before at home, and I am truly glad I have given myself the opportunity to do so.

If I return home, it will be mostly due to an acknowledgment that real life, the one I left behind, comes first. I applied to universities in Israel, and barring any surprises, will be accepted to all three schools I'm considering going to. Should I choose the Hebrew University in Jerusalem, it would be to study a Mathematics and Cognitive Science double major. In the Technion in Haifa or Tel Aviv University, my major would be Mathematics and Statistics. In the latter two, I am trying my luck with specialty programs: Tel Aviv's Lautman interdisciplinary studies program, and the Technion's excellence program. The problem stems from the fact those two programs want to interview potential students; while I'm not keeping my hopes up for Lautman, I'm quite confident I will be invited for interviews for the Technion's program. The program has quite a few advantages: First and foremost, freedom to choose your own course of studies, picking and choosing from different faculties and ignoring prerequisites. There are also several workshops and programs for the students, and scholarships for tuition and dorms. Lautman is both similar and different, but as I am not nearly as confident about it, I will spare the details.

My studies next year are not the only reason to return home, but they are what triggered the dilemma. Should I return home in late April, I might also take another few weeks to travel in Europe with a friend (I considered it, but I doubt I will fly off on another wholly different trip, such as the far east) I could also resume playing Ultimate, perhaps even in time for Windmill Windup or the European Ultimate Championships, should my knee oblige. Lastly, there is the ever-hanging sword of fiscal responsibility. I certainly could afford traveling until September; however, that would leave my with significantly less money saved for my first year of university. Should I return, I will probably find a job until I start studying, and coupled with the fact I will not be traveling, will result in a significant chunk of money saved.

On the other hand, the main reason not to return, is travel! Returning early means leaving South America in early April, to spend a couple of weeks in California (where I have not set foot since graduating high school back in 2008), and perhaps stop somewhere else in the states, before flying home out of New York City. That leaves me with barely another month with which to explore Argentina and Chile - not nearly enough. I could see more of the south, and perhaps taste the culture of the central regions, and the majestic deserts of the north; but by far and by large, there will be quite a lot left to see.

Without any time limits, I would hitch-hike my way up the Caraterra Austral, stopping a few times to hike in a few recommend hot-spots. I could then explore the island of Chiloe, famed for its wooden buildings and phenomenal seafood, and go climbing and hiking near Bariloche. I would be able to partake in urban and cosmopolitan Chile, visiting Santiago and Valpariaso, and see the wineries of Mendoza. Next I should be able to meet with a good friend from home, and meet up to see the magnificent deserts of northern Chile and Argentina. Beyond that, there are a great many other things to see, places to visit, and mountains to trek. To the north looms Bolivia, and its vastly different lifestyle and nature. Beyond that, Peru, with many more mountain ranges that yearn to be thoroughly hiked, and the cultural magic of the Inca. Further yet, Ecuador, and the opportunity to visit another of nature's marvels, the Galapagos Islands.

Moreover, a longer trip would leave me with more time in the states - freeing me to spend a few weeks to a month in California (and perhaps even longer - John Muir Trail, anyone?), and then perhaps make my way up the west coast, to see Portland, Seattle, friends, and natural treasures, before making my way home in time from the school year. Essentially, the opportunity to make an amazing trip even more exciting and fulfilling.

To summarize: on one hand, university programs, ultimate, short term travel, and fiscal responsibility. On the other, the opportunity to see even more of this splendid world, continue enjoying its glory, and grow and evolve with it. Which one shall it be?

An Emotional Rollercoaster As a Function

I'm currently volunteering in Torres del Paine national park, in Chilean Patagonia (I might actually have just finished my time there, but that's a whole other matter). The first couple of days of the shift I just finished were a hectic mess. The type of shitstorm possibly only when hormones, emotions, the Arctic Monkeys, and character traits (or flaws) get mixed up.

Part I: Increasing / Concave Up (first derivative positive, second derivative positive)
Suggested listening: I Bet You Look Good On The Dance Floor

I met her on the first night of the ship, sitting outside in the cooking area in camp. I went over to chat with a couple of Americans I remembered from the check-in to the campsite, and she was there too. At some point, an hour or two later, travel plans were discussed, and I mentioned that once I'm done in the park I'll probably head up north to Calafate and Chalten, a few hours away on the other side of the border with Argentina. She said that's exactly where she wants to go, and was hoping to find someone else to hitch-hike there with, as she (understandably) felt iffy about doing it alone. We chatted about it for another while, and as she had split of from her friends and was in no hurry to leave, we agreed to talk about it more the next morning.

The next day and a half were quite blissful. As she set up her tents next to mine, we both realized it's only for appearance's sake, even of those appearances were intended for her subconscious. We spent much of those days together, and it was quite comfortable and easy. The physical part was great, but it felt a bit more than that. The conversation was just very open and honesty, and I told her things I feel most people don't know about me. It felt good.

In retrospect, here's potential misstep number one. I cared. I care easily. While I don't have a trouble with casual sex, or just hooking up, especially if it's been established as that's where we're going. On the other hand, I still care about a woman more after sleeping with her. I generally grow fond of women somewhat easily and carelessly, and allow myself to build houses of cards in my mind. I easily saw myself traveling with her for a week, or maybe even a month, and having a blast. I got excited. It wasn't the first time this has happened to me, and probably won't be the last. Honestly, it's not that I don't want to care. I'd rather care than be disconnected, and feel it's a huge part of being human, and being me. On the other hand, maybe I need to be more gradual or reserved about it. I can't say I'm sure.

I remember telling her that "it won't always be this fun and easy, but we should try to remember how this feels now, for when the going gets harder." Fore, meet shadow.

Part II: Increasing / Concave Down (first derivative positive, second derivative negative)
Suggested listening: Fluorescent Adolescent

The evening of the next day, two Israeli girls came by with Jungle Speed. As you've probably never heard of it, it's an addictively fast card game, based on pattern matching and quickness of hand. As they played, I came and went, as I was busy baking bread, of all things - apparently I'm not bad at it. I noticed she was pretty friendly, possible flirty, with another American who joined the card game.

Here comes my second error. I let jealousy rear its ugly head. Even at the moment, I could tell myself on how many levels that's absolutely absurd. I've only know this woman for two days - as intensive as they might be, two days are still forty-eight hours. Beyond that, she was being excited and bubbly and nice, which are some of the qualities that led me to like her at first place. Further, when I think about it rationally, I'm very much opposed to jealousy. I truly want to give an open (or perhaps even poly) relationship a try, both to see how I like it, and perhaps to learn to work through some of these faults of mine. I'm not sure I could or should be the be-all-end-all object of someone's desires, and feel I have enough emotion to sustain more than one relationship.

I caught myself feeling it, and getting a little bit more touchy-feely than I should have. Once I realized what I'm doing, I excused myself, and recomposed. I realized I'm being ridiculous, and noted in my head to talk to her about it tomorrow. I felt that with how comfortable and easy our conversation has been, maybe she could help me work through it, and call me out on my nonsense. (You could argue this was another mistake, and I should have dealt with it by myself, but I believe in sharing and dealing together.)

Later that night, the other park rangers and us played quite a bit of cards. We also might have not been entirely sober. After several rounds of 'come-mierda' (the local version of 'asshole', played with the Spanish cards), and more drinking of all kinds, I was getting ready to call it a night. I could blame my possible lack of sobriety, but I'd be giving myself the easy way out - I mentioned to her that I want to talk to her about something, and that she should remind me tomorrow. I imagine we can all see where this is going: she insisted I tell her tonight, I wasn't wise enough to insist otherwise, and I told her. She seemed very understanding, and said she did notice I was acting oddly earlier. She told me that we'll talk tomorrow, and I should go to sleep if I'm tired, and she'll be over soon.

Part III: Decreasing / Concave Down (first derivative negative, second derivative negative)
Suggested listening: Snap Out Of It

It rained all night.

I woke up in my tent around six in the morning, alone, with my glasses still on. I remembered that I read for a while after getting back in, with my light still on, as I thought she might not have a light, and it would help her find her way in. Naïve up until the last moment.

As I woke up, the range of options ran through my head. Did she sleep in her tent? But her sleeping bag was in mine. Did she end up crashing in the house? I hope she didn't sleep on the floor. But where did she sleep? I stopped dealing with that train of thought, but nonetheless didn't fall back asleep. An hour or so later she came in, and told me she slept in the bed with another one of the guys. And made out with him.

I can't say I was angry. I truly wasn't. I was hurt though. After pondering it for a while, I realized it was because it came exactly after I told her about my slight jealous streak. I showed a vulnerability, and instead of receiving support, I got the exact opposite. I'm very open and candid, apparently at times to a fault.

She took a walk, and so did I, end I ended up talking about it with one of the Israelis from the night before. The Israeli was very kind and listened, and gave some well-needed advice, until at some point she came back. We went off to talk. She was very, very sorry, and talked about how she hurts before she gets hurt, how she says she hates drama, but just created a load of it, how she felt we were just hooking up, and more... I listened, and I understood, especially when she kept talking about how crazy she is, and her sexual history... I was hurt, and understanding, but I wasn't angry. I tried to understand, and as awkward as it was, I never asked her to leave or disappear,.

I talked to the other rangers, and they implored me to just put it behind it and leave it be. I'm pretty sure they also didn't understand about how I was so un-angry about the whole thing; it was certainly not the Chilean way to handle it.

Part IV: Decreasing / Concave Up (first derivative positive, second derivative negative)
Suggested listening: 505

I guess I might be somewhat of an emotional masochist, as I still saw myself traveling with her afterwards. It would have never been what it could have been at first, but I still saw it as being fun. I certainly would have learned something about myself from it.

The days afterwards were increasingly less awkward, as eventually one of her original friends also made it and stuck around with us for a few days. Apparently she's not the only source of drama - he broke up with his girlfriend of two years on the trail, and left her and her two friends. We played cards, cooked together, and generally lived together for those few days, and at some point it became less and less awkward.

It's interesting that it didn't make me run, or hate her, or get vengeful. I'm happy about that about myself. I feel that if we each only got one chance in life, nothing could ever succeed, and that it she's still a very interesting person. Crazy, but interesting.

Addendum I
I'll probably write about it more separately, but I've worked very hard over the past few years to develop an inner locus of control. It suits me incredibly well when doing things by myself - I don't think I would have successfully rehabbed from two knee surgeries (another topic for another time) if I didn't fully and truly believe that enough hard work will get me through. With emotional matters, though, the line is finer, as to whether or not that's positive or negative. Rationally, I understand this isn't my fault, at least not wholly and entirely. On the other hand, I couldn't stop myself from thinking that maybe had I not had that jealous streak, or had I waited to talk about it, or had I not cared, who knows where we'd be. That's life, though, isn't it?

Maybe I'm hard on myself so other people don't have to be? I wish I knew.

Addendum II
Up until now, I wasn't sure I'll post it.  It's highly ridiculous and deeply personal, and exposes more character flaws than I entirely feel comfortable with. I do want to learn and grow from it, and I felt it was a good writing experience, so on it goes. A week later, I guess the best way to describe how I feel about it would be to paraphrase the ending of Ocean's Eleven: I'm not sad about it, but I'm sure as shit ain't happy about how it turned out. It is a rather ridiculous story though, and in retrospect quite hilarious, so at least we've got that going.