Shiluach hakan as a segulah for having sons

Summary: A variant of it does have midrashic basis. But not precisely, I think. Furthermore, a little knowledge of statistics and Jewish fertility goes a long way.

Post: The pasuk, in last week's parsha, instructs us to send away the mother bird before taking the eggs.

6. If a bird's nest chances before you on the road, on any tree, or on the ground, and [it contains] fledglings or eggs, if the mother is sitting upon the fledglings or upon the eggs, you shall not take the mother upon the young.		ו. כִּי יִקָּרֵא קַן צִפּוֹר לְפָנֶיךָ בַּדֶּרֶךְ בְּכָל עֵץ אוֹ עַל הָאָרֶץ אֶפְרֹחִים אוֹ בֵיצִים וְהָאֵם רֹבֶצֶת עַל הָאֶפְרֹחִים אוֹ עַל הַבֵּיצִים לֹא תִקַּח הָאֵם עַל הַבָּנִים:
7. You shall send away the mother, and [then] you may take the young for yourself, in order that it should be good for you, and you should lengthen your days.		ז. שַׁלֵּחַ תְּשַׁלַּח אֶת הָאֵם וְאֶת הַבָּנִים תִּקַּח לָךְ לְמַעַן יִיטַב לָךְ וְהַאֲרַכְתָּ יָמִים:

This could be seen as a mitzvah kiyumis or a mitzvah chiyuvis, though the phrasing of the pasuk coupled with a specific gemara seems to strongly place it as a mitzvah kiyumis. Perhaps it even less than that, such that one should not seek it out, because this is contrary to the spirit of the mitzvah. (There is a qualitative difference between putting on a four cornered garment in order to wear tzitzis and getting divorced in order to be able to give a get, even if each is a mitzvah kiyumis.) Rabbi Slifkin recently wrote an article about the rationalist vs. mystical approach to this mitzvah, which appears to divide along these lines.

Now, the Torah says that the reward for it is long life. (Or, I would say, lengthy stay in eretz yisrael as opposed to exile. Compare the mitzvah of kibbud av va'em.) Yet the midrash (Devarim Rabba) heaps on other rewards as well. First, it calls this mitzvah one of kevodo shel olam and of tikun olam:

דבר אחר:
שלח תשלח אמר ר' אלעזר: 
לא היה צריך לומר כן, אלא אמר הקב"ה: הואיל ונתעסק בכבודו של עולם ובתיקונו של עולם, כדי שתינצל.

A bit later, some rewards:

דבר אחר:
שלח תשלח אמר רבי ברכיה: 
יש מזיק שקושט כחץ וטס כעוף. 

מנין? שנאמר: (תהלים צא) לא תירא מפחד לילה מחץ יעוף יומם. אמר הקב"ה: אם קיימת מצות שילוח הקן, אני מצילך מאותן.

דבר אחר: יש מצות שמתן שכרה עושר. 
ויש מצות שמתן שכרה כבוד. 

ומה מתן שכרה של מצווה זו? שאם אין לך בנים אני נותן לך בנים. 

מנין? שנאמר: שלח תשלח את האם. 
ומה שכר אתה נוטל? 
ואת הבנים תקח לך: 

As to whether it is kiyumis or chiyuvis:
דבר אחר:
שלח תשלח רבנן אמרי:
למה שני פעמים? 
שאם אירעה לך המצווה הזאת פעם שניה לא תאמר כבר יצאתי ידי חובתי, אלא כל זמן שתארע לידך אתה צריך לקיים אותה.

Well, not precisely. Whenever it comes to your hand, you are obligated to do it. So it is a kiyumis. But does this allow for the possibility of saying that you don't want the eggs? What is the hava amina? That you would take the eggs and not send away the birds? So perhaps the opposite.

More rewards:
דבר אחר:
שלח תשלח רבנן אמרי: 
אם שלחת מצות הקן את זוכה לשלח עבד עברי. 
מנין? שנאמר: (דברים טו) וכי תשלחנו חפשי מעמך.

דבר אחר: מהו שלח תשלח את האם? אם קיימת מצווה זו את ממהר לבוא מלך המשיח שכתוב בו שילוח. 
מנין? שנאמר: (ישעיה לב) משלחי רגל השור והחמור.
דבר אחר:
אמר ר' תנחומא: 
אם קיימת המצווה הזאת, אתה ממהר את אליהו הנביא זכור לטוב שיבוא, שכתוב בו שילוח, שנאמר: (מלאכי ג)הנה אנכי שולח לכם את אליה הנביא והוא יבא וינחם אתכם. 

מנין? שנאמר (שם) והשיב לב אבות על בנים.

I would guess that, in part, the driving force of this is that (a) this is one of the mitzvot for which explicit reward is stated in the Torah, along with kibbud av, and (b) it is one that is would be considered by the hamon am to be a light mitzvah, such that Chazal use this to show that we don't know mattan secharan shel mitzvot, as the reward is as great as kibbud av. This sets the stage for expanding on the rewards to the unstated realm.

Personally, in terms of these rewards, I would disagree with Rabbi Slifkin and not connect rationalist or mystical reasons to these rewards. I would attribute it instead to simple plays on words, which provide opportunities for midrashim methods to take effect.

Yet they say that the reward is children. Again:

ומה מתן שכרה של מצווה זו? שאם אין לך בנים אני נותן לך בנים. 

מנין? שנאמר: שלח תשלח את האם. 
ומה שכר אתה נוטל? 
ואת הבנים תקח לך

There is a danger of turning this mitzvah into a segulah. And indeed, it has become so. If so, put aside any arguments about whether we are supposed to look to fulfill it (the "mystical" approach), or rather when we want the eggs conduct ourselves in this particular manner to minimize the damage (the "rationalist" approach). Instead, anyone who is having difficulties having children will seek out this segulah.

There is no mitzvah to seek out rhinoceroses, yet:

Ground rhino horn is not used as an aphrodisiac, but is prescribed for everything from headache and toothache to infertility and fevers.

to the extent that they are on the critical list, as endangered species.

But if there is indeed a segulah effect to shiluach haken, even when takes action which goes against what seems to be the (rationalist) rationale for the mitzvah, namely compassion, then perhaps we should modify our theology. If Hashem desires and rewards this cruelty, then it would bolster the mystical position, that of the Zohar, that the purpose is cruelty in an effort to trigger Divine compassion, such that it is a good thing to fulfill it even where one does not need the eggs.

In a comment thread at Rationalist Judaism:

Just some of my personal experience with Shiluach Hakein. I arranged Shiluach Hakein for a friend of mine some ten years ago and he had his first child about a week shy of of nine months later, after eight or nine years of childlessness. I told this to Shiluach Hakein pioneer and author Rabbi Dan Schwartz of Jerusalem and he told me he has been told 1000 such stories (actually IIRC he said 1500 but I'll underestimate it to 1000) and in a very disproportionate amount of instances, the babies are boys. This seems to be consistent with the very literal meaning of "v'et haBANIM tikach". I assume that the number has increased in the past ten years.

The thing is, I am certain that Christians also have their miracle stories of this sort. For example, people try to bolster the Rabbi Meir Baal Hanes segulah with stories, but see how the Catholic equivalent, Saint Anthony, patron of lost articles, also has many stories bolstering his segulah. Yet, I am not about to become Catholic. And I am not about to let Small Miracles-type stories define my theology.

There are two aspects to this segulah story. One is the 1000 such stories, and the other is the disproportionate number of boys. The latter aspect is supposed to bolster the first aspect, to demonstrate that it is indeed miraculous and a fulfillment of the reward of the segulah, rather than random chance. But the answer to the first aspect is "Regression towards the mean" together with "selective reporting". And the answer to the second aspect is that this is not disproportionate, or rather that the disproportionality is precisely what we would expect if we understand Jewish fertility issues.

Let us begin with aspect (1). An example of regression toward the mean is:

Consider a simple example: a class of students takes a 100-item true/false test on a subject. Suppose that all students choose randomly on all questions. Then, each student’s score would be a realization of one of a set of i.i.d. random variables, with a mean of 50. Naturally, some students will score substantially above 50 and some substantially below 50 just by chance. If one takes only the top scoring 10% of the students and gives them a second test on which they again choose randomly on all items, the mean score would again be expected to be close to 50. Thus the mean of these students would “regress” all the way back to the mean of all students who took the original test. No matter what a student scores on the original test, the best prediction of his score on the second test is 50.

The equivalent here, by fertility, is that some people have no fertility problems, baruch Hashem, and some people do. There is an average. If you only take those who have fertility problems, and have them perform some segulah -- or, over the years, hundreds of segulot -- some will regress toward the mean of their own accord. And this is what you would expect, statistically. (Especially as those with fertility problems are often trying other, scientific methods, at the same time, where there is some chance of success each time.)

Combine this with selective reporting. If tens of thousands perform this segulah, and those who conceive excitedly contact the rabbi, but those who don't don't, then the rabbi will end up with a skewed picture of the effectiveness of this segulah.

That is the first aspect.

Aspect number (2) is the disproportional number of male children. While the midrash on Tazria speaks of segulot for specifically male children, I am not entirely convinced that this is the case of Devarim Rabba about shiluach haken. If it is, fine, but if not, don't invent new aspects not discussed by Chazal. But is there anything about Jewish fertility issues specifically that would cause male progeny, over female progeny?

Indeed there is. Males come from XY, while females come from XX. The mother provides an X, and so the gender of the child depends on if the father provides a sperm with an X chromosome or a Y chromosome.

Sperm with X chromosomes are more robust, and can thus remain in the womb for longer. With Y chromosomes are less robust, but are faster.

One of the most common fertility problems for Jewish people is a short cycle, such that by the time the woman goes to the mikvah after counting seven clean days, she is at the end of her fertile days, or past it. If so, if on some occasion the can become pregnant when coming back from the mikveh, then males are more likely. After all, it is not necessary for the sperm to remain in the womb waiting for the egg (X). Rather, there is a race for the sperm to reach the egg, and Y has an advantage. Therefore, that of people who called up this rabbi reporting success after difficulty conceiving, it is not surprising in the least that in a disproportionate number of instances, the baby is a boy.