The Talmud (Berachot 7a) tells us that Mi Yodeya was calculating the moment of God's anger:
אלא מלמד שהיה יודע לכוין אותה שעה שהקב"ה כועס בה
Rather this teaches that Yodeya was calculating that moment which God gets angry during.
But what would be the point of figuring out this moment? It can't be to use it against someone else, because the Talmud just a few lines later says that such a practice is improper:
ההוא מינא דהוה בשבבותיה דר' יהושע בן לוי הוה קא מצער ליה טובא בקראי יומא חד שקל תרנגולא ואוקמיה בין כרעי' דערסא ועיין ביה סבר כי מטא ההיא שעתא אלטייה כי מטא ההיא שעתא ניים אמר ש"מ לאו אורח ארעא למעבד הכי
The sectarian in the neighborhood of R. Joshua the son of Levi was tormenting him greatly with verses. One day [R. Joshua the son of Levi] took a rooster and placed it between the legs of the bed and gazed at it. He thought "when that moment comes I will curse him". When that moment came he had dozed off. He said "we see from here that it is not proper to do this".
Rather it must be that the purpose of calculating the moment of God's anger is to be able to emulate it. This falls under the positive commandment of והלכת בדרכיו, as enumerated in the eighth positive commandment according to Rambam:
להידמות בדרכיו הטובים והישרים שנאמר והלכת בדרכיו
To be similar to His good and just ways, as it says: "and you shall go in His ways".
However, in Guide for the Perplexed (1:54) we see the opposite – God's anger is not real anger, it is only an imitation of human anger:
His actions towards mankind also include great calamities, which overtake individuals and bring death to them, or affect whole families and even entire regions, spread death, destroy generation after generation, and spare nothing whatsoever. Hence there occur inundations, earthquakes, destructive storms, expeditions of one nation against the other for the sake of destroying it with the sword and blotting out its memory, and many other evils of the same kind. Whenever such evils are caused by us to any person, they originate in great anger, violent jealousy, or a desire for revenge. God is therefore called, because of these acts, "jealous," "revengeful," "wrathful," and "keeping anger" (Nah. i. 2) that is to say, He performs acts similar to those which, when performed by us, originate in certain psychical dispositions, in jealousy, desire for retaliation, revenge, or anger: they are in accordance with the guilt of those who are to be punished, and not the result of any emotion: for He is above all defect!
(Friedlander translation, my emphasis)
The resolution to this circular activity lies in the principle of לא דברה תורה אלא כנגד יצר הרע – "The torah spoke only against the Evil Inclination" (Kiddushin 21b). There are certain things that are simply too difficult for man to abide by. If they would be completely forbidden man would end up violating them. In these situations the Torah devises a way in which the thing can become permissible while still retaining the general prohibition.
In our case this works as follows: God would normally never get angry – indeed in the Talmudic passage in Berachot cited above, the Talmud was quite surprised that God could get angry:
ומי איכא רתחא קמיה דקודשא בריך הוא
Is there, in fact, anger by The Holy One Blessed Be He?
Man, left to his own devices, would naturally get angry, and it would be useless to completely forbid this. Instead, God takes on the human characteristic of anger and then commands man to imitate Him.
Now this would seem to not really solve the problem if man still ends up getting angry. But there's a catch. As explained in the chapter on anger in Orchot Tzadikim, there is a fundamental difference in God's anger abilities compared to man's anger abilities:
ובהשם יתברך נאמר ברוגז רחם תזכור וזה רחוק מאוד מדרכי בשר ודם
About God it says "in anger remember your mercy", but this is exceedingly far from the ways of man.
In other words, God can be both angry and merciful simultaneously while man cannot. Thus, when imitating God it is impossible for man to imitate Him fully and incorporate both the anger and the mercy. Man has to thus choose between these two middot, and we know that when anger and mercy conflict mercy should win out, as this is the prayer that God prays and the blessing that God received in Berachot 7a:
שיכבשו רחמיך את כעסך
that your mercy should conquer your anger
In conclusion, then, the anger of Mi Yodeya that you inquired about is not real anger. It is in fact mercy in the guise of anger as part of an elaborate trick of the Evil Inclination. As such you should have nothing to worry about.