Correlation does not imply causation - though it may be just that. It is not always easy to distinguish between two events that, while occurring simultaneously are in fact unrelated and those where one is the direct cause of the other. It is quite clear that the "super bowl indicator" where one can "predict" the direction of the stock market based on which conference the Super Bowl winning team came from is but a fluke despite its over 80% success rate over the past 50 years. On the other hand it has been proven over and over again that smoking and lung cancer are not merely related but the former causes the latter. It is the large reams of data in between that are not always easy to analyze. Should any significance be attached to the fact that a pitcher may have an ERA of 5.75 at home and 1.40[1] on the road? Is it the location of the game, are other factors at work or this just a number that upon further analysis has no real meaning?
"An ox that was a muad for its species but is not muad for other species, muad for people but not muad for animals, muad for minors but not muad for adults that which it is muad for it pays full damages and that which it is not muad for it pays half damages." (Bava Kamma 37a)
Up until this point we have learned that once an animal gores three times it becomes a muad requiring its owner to pay full damages on future gorings. However the Mishna teaches that we cannot look at the goring ox alone. There may be other factors at work whose contribution is such that they are the reason the animal gores and that full damages must be paid. An ox may attack only upon seeing other oxen or attack only non-oxen. If the animal develops a pattern to attack only people then if and when it attacks another animal such is considered out of character and only half damages are assessed. It is overly simplistic to classify animals as simply tam or muad. There are many variables at work many of which go beyond correlation towards causation. 
The Gemara records a fascinating debate as to our starting premise when an animal first becomes a muad. Rav Zveed is of the view that once an animal gores three times it considered a muad for all goring. Only if and when it establishes a pattern that it only attacks in certain ways would we remove the muad status for those that the animal does not attack. On the other hand Rav Pappa asserts that the muadstatus must be demonstrated for each and every class of damages. When an animal establishes a pattern of attacking other oxen it becomes muad for oxen, when it attacks kids it becomes muad for kids and so on and so forth. Unless it establishes a pattern of attack for each class it remains a tam for such a class and only half-damages would be assessed.  
Not only do we need to look at what an animal may attack we must be cognizant of when it attacks. "They asked Rabbi Yehuda; if it gores on Shabbat but not on the weekday [what is its status]? He said to them for goring done on Shabbat he pays full damages, for goring done on the weekday he pays half damages." The Mishna assumes that Shabbat and the attacking ox are not merely correlated but it is Shabbat that causes the ox to attack. Rashi and Tosafot offer differing, but not necessary conflicting, reasons as to why this may be so. Rashi explains that because on Shabbat the animal (and his owner[2]) are not working and with little to do the animal is more likely to attack others. Too much free time does no one much good. 
Tosafot explains that since people dress differently on Shabbat - "your dress on Shabbat should not be like your dress on the weekday" (Shabbat 113a) - the unusual clothing might entice the ox to attack. 
Putting this all into practice is not simple. The Gemara queries a series of cases wondering into which category an attack might fall. For example an animal attacked in the following pattern; ox, ox, ox, donkey, camel. There is no question this animal is a muad regarding other oxen but might we also say that we can view the last attack on the ox as the first of series of attacks on three different animals making one a muad for all? Or what about an animal that attacks on Shabbat, Shabbat, Shabbat, Sunday and Monday? May we say that third Shabbat attack is also the first of the attacks on three different days and it is a muad for all [3] days of the week?
The Gemara does not have an answer for these scenarios, which would mean that in practice the victim would not be able to collect damages. Hamotzee mechaveiro alav harayah, one who wants to extract money from a friend must bring evidence. With no evidence available in these cases there is nothing to collect.   
While for urbanites such discussion may seem a little too much like hair splitting that has more to do with our lack of daily contact with animals nor familiarity with the complex nature of animals. Ox, sheep, cows, goats and the like [4] generally cannot be classified as wild or tame but like humans are often responding to environmental cues. It is our job to be aware of those cues and act accordingly. 
[1] For those who do not follow baseball, ERA is earned run average and reflects the number of runs a pitcher gives up per nine innings. The lower the number the better. You can see more here.
[2] Recall our previous discussion as to the role of the owner in attacks by his animal such that attacks might be ascribed to the owner as much as to the animal.
[3] All agree that beyond Shabbat there is no compelling argument to allow one to place the days of the week into their own category. Whether it gores on Sunday or Wednesday makes no difference. 
[4] Wild animals such as lions, bears, tigers and snakes are always considered muad.