The probability will also deceive people. How can the performance of the football team look better?Use Simpson Paradox

In daily work and life, we often like to analyze some issues through probability, but do you know that probability can also be deceived.

For example, if we have a poor football team, now we want to make his results look better, what should we do? Of course, training should be strengthened, but in addition to this, there is a faster way to act, that is, the calculation method of changing the winning rate. How to change? Let us have an example to explain. Suppose we now have two football teams, one has a poor record, we name them "sea cucumber team", and the other football team's record is much better. We named it "Rose Team". Let's talk about the record of the sea cucumber team. Within a year, the sea team fought 240 games at home, of which 114 games were victory. In addition, 60 games were played in the away game, of which 6 were victory.

According to the one -year performance of the sea cucumber team, we can calculate his winning percentage. The winning rate of its home battle is 47.5%and the win rate of away games is 10%.

Now let ’s take a look at the Rose team’ s record. The Rose team fought 60 games at home within a year, of which 42 games were successful. In addition, there were 240 games on the away battle, of which 48 games were victory. Based on this, we can also calculate the results of the Rose team. Her home battle rate is as high as 70%, and the away battle rate for the away game is 20%. It can be seen that whether it is at home or away, the winning rate of the Rose team is much higher than that of the sea cucumber team. Even if the away game is not very high, the Rose team is twice as high as the sea team's winning percentage. In the face of such achievements, the sea cucumber team is obviously embarrassing, but there is no need to worry, there is a way.

If the sea cucumber team wants to make your performance look good, it is actually very easy. It only needs to mix the results of the main and away games together.

Adding the main and away game together, the sea cucumber team participated in 300 games within a year, winning 120 games. Looking at the Rose team again, it also participated in 300 games within a year, with a total of 90 victories. Based on this summary data, the winning percentage of the sea cucumber team became 40%, while the roses' winning rate became 30%, and the sea cucumber team surpassed the roses. Is it very interesting? Whether it is a home battle or away, the winning rate of the Rose team will exceed the sea team, but after adding the main away away, the winning rate of the sea cucumber team is higher than that of the Rosho team. Why is this?

Obviously, in the above issues, we were deceived by probability.

In the world, Edward Simpson took the lead in discussing this probability issue in detail, so this problem was called "Simpson Paradox". We know how to deceive the probability, but how is the probability of deceiving us? Observe the previous examples, you will find that the sea cucumber team has conducted a large number of home games, and the Rose team conducted a large number of away games. We all know that home operations are relatively easy and easier to win. That is to say In the issue of probability, doing more easy things can effectively increase the overall probability. Understand this, we can apply it to all aspects of life.

Suppose that the leaders now let you and several other sales departments make a promotional solution and determine the pros and cons of each plan through the final sales completion rate, then we can use the Simpson paradox.

It is very difficult to stand out in the production of the promotional plan, but we can try to increase the sales completion rate in the sales link. During the implementation of the promotional plan, promotion outlets will be set up in different places, and the sales of some areas should be better than other areas, so we should set up promotion outlets in these places. Come up. There are many similar examples, such as which subjects should we focus on when studying? Of course, it is those disciplines that are easier to improve scores, so as to effectively drive the total score. In the same subject, those question types that are easier to raise are our focus.

Sometimes, even if the Simpson paradox is applied, what should I do if I still fail to obtain the probability advantage?

Taking the previous football team problem as an example, if the main and away battle field of the sea cucumber team and the rose team is not too much, even if the Simpson paradox is used, it cannot make the records look good. Layout probability, such as trying the division of winter and summer scenes, such as the division of the rainy match and the sunny game, spend more effort, you can always find some classification methods to make the record look good. However, this is just a disordered method. If you can't really improve the strength of the team, the shame will still be torn off. Now we know that the probability is also deceiving, so before analyzing the problem through probability, we must first figure out what the probability in front of us represents.

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