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Revelation of Lanchester equation

2020-12-07 02:55:59 Xiao Guodong's I private plot

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Lanchester Equation (Lanchester equation) It's a British engineer, Frederick · Lanchester (Frederick Lanchester) During world war I (1916) A series of differential equations have been developed to describe the combat effectiveness of both sides .

Also known as Lanchester's law (Lanchester's Law), among , Lanchester is sometimes translated as Lanchester .

So what exactly does this equation say , What enlightenment can it bring us ?

Two main points of Lanchester Equation

We've all heard one sentence , be called " Kill the enemy one thousand , Self damage eight hundred ", This is usually used to describe a situation where there is a close match , But if there is a gap between the two sides , At this time, what was the result of the battle between the two armies ?

For example , If there's a Red Army versus a blue one , For the Red Army 200 people , The blue army 100 people , The individual strength of both sides is equal , In terms of numbers, the Red Army 2 : 1 dominant , So what will be the result of the war between the two armies ?

natural , The Blues have no hope of winning , But the blues decided to fight with the Red Army , 100 All men die in battle , So how much damage can the blues do to the Red Army ?

You can think about the answer for yourself first , Look down again , Verify whether your idea is reliable .

First , One of the pitfalls is that , Since the individual strength of both sides is equal , You may be rash to conclude that : The Blues have sacrificed themselves 100 people , That's why I lost the Red Army's 100 people , The blue army was wiped out , The Red Army has only 100 people , The blues were defeated in the end , It's just because of the disadvantage of numbers .

But actually it's not like this , And these are two very important points Lanchester has revealed for us :

  1. Combat effectiveness and number of people square In direct proportion to
  2. The loss of the larger party is much lower than that of the smaller one

Why is that? ? Let's make a detailed calculation and you will probably understand .

A specific combat calculation

First of all, the initial comparison between the two armies is 2 : 1, Then the individual strength of both sides is equal , So the firepower comparison is the number of people , It's also 2 : 1, But the comparison of the overall combat effectiveness ? No more 2 : 1, It is 4 : 1 !!

Why? ? Now suppose both sides shoot each other , And then the hit rate is 20%, After all, the strength of individual soldiers is equal ; And then simply assume that if you hit, you kill the other person .

shooting 20% Can be interpreted as , One out of five can hit , Or five people shooting at the same time , There's a man who can hit , It's the same effect anyway .

The initial situation was like this :

 Lanchester Equation (Lanchester equation)  Example of initial engagement

And then through a round of shooting , Let's calculate the war situation :

The number of times the Red Army can kill the blues is : 200 × 20% = 40;

The number of times the blues can kill the Red Army is : 100 × 20% = 20;

The remaining quantity of the Red Army is : 200 - 20 = 180;

The number of Blues left is : 100 - 40 = 60;

After a round of fighting , That's how it turned out ( Black means lost personnel ):

 Lanchester Equation (Lanchester equation)  An example of a round of engagement

Do you see any problem at this time ? In the first place , Both sides are still 2 : 1 A comparison of the number of people , After a round of shooting , The balance of the rest of the population degenerates into 3 : 1 了 (180 : 60), The comparative disadvantage of the blues has been magnified !

On the other hand , What about the war damage ? Just look at the comparison of the loss of people , 40 : 20 still 2 : 1, But the big problem is , The blues are a small team , It's still a big loss , The loss is as high as the overall 40% (40 : 100); And the Red Army , It's just 10% (20 : 200)!

It's not very nice to say , It's just like this , The blue side is almost half destroyed !

The game goes on , The second round of shooting , And the war :

The number of times the Red Army can kill the blues is : 180 × 20% = 36;

The number of times the blues can kill the Red Army is : 60 × 20% = 12;

The remaining quantity of the Red Army is : 180 - 12 = 168;

The number of Blues left is : 60 - 36 = 24;

After the second round of fighting , This has become the case ( Grey means the people lost this round , Black means the first round of loss ):

 Lanchester Equation (Lanchester equation)  Example of a two round engagement

The blues were almost beaten to pieces , The loss rate of this round is as high as 60% (36 : 60)! remainder 60 More than half of the people have been wiped out !

The number of people lost this round accounted for the original total number of people 36% (36 : 100), And the overall battle damage is as high as 76%(36% + 40%), That is, more than three-quarters of the population has been eliminated !

And the Red Army ? The rate of loss is 6.7%(12 : 180), Compared to the last round of 10% It's also down !

The number of people lost this round accounted for the original total number of people 6% (12 : 200), And the total war damage is only 16%(6% + 10%), Less than one in six !

And now the numbers of both sides have come to 7 : 1 (168 : 24)! The number of people in the blue army continues to deteriorate , And the deterioration has accelerated !

Now we have a third round of engagement , Keep counting the war :

The number of times the Red Army can kill the blues is : 168 × 20% = 33.6 ≈ 34;

The number of times the blues can kill the Red Army is : 24 × 20% = 4.8 ≈ 5;

The remaining quantity of the Red Army is : 168 - 5 = 161;

The number of Blues left is : 24 - 34 = -10;

You can see , The blues are not enough for each other , After the third round, he was killed by the regiment ( Light grey means the people lost this round , Grey means the second round of losses , Black means the first round of loss )::

 Lanchester Equation (Lanchester equation)  An example of a three round engagement

The loss for the blues this round is 100%, The overall loss has also reached 100%.

And the Red Army , The loss of this round is 3%(5 : 168), Compared to the last round of 6.7% It's accelerating the descent .

The result is not surprising at all , Because the blues are accelerating their collapse , Therefore, the ability to cause damage to the other side is naturally a rapid decline !

The battle is finally over , The total loss of the Red Army is 20 + 12 + 5 = 37, The overall loss rate is 18.5%.

Obviously , At first you might have intuitively imagined the sacrifice of the Blues 100, I also fantasized that I would kill each other 100 The human situation didn't happen ! The red side only sacrificed 37 It's just people , Although the individual strength of both sides is equal , But there is no one to one exchange ratio , The loss of the blue army is far more than that of the Red Army in terms of number and ratio , It's much more than what both sides started with 1 : 2 The situation of .

therefore , Through the calculation of the above specific example , Let's go back to the two main points of Lanchester's equation :

  1. Combat effectiveness and number of people square In direct proportion to
  2. The loss of the larger party is much lower than that of the smaller one

Don't you think it's no longer difficult to understand ?

The key is firepower

In the above example , Let's assume that the individual's firepower is equal , So the calculation is only related to the number of people , But the decisive factor in combat effectiveness is firepower . If the numbers of the Red Army and the blue army are still 2 : 1, But if the blue individual's firepower is stronger than the Red Army's , Compared with the Red Army 2 : 1, that 200 People's Red Army at this time and 100 The total firepower of man's blue army is about equal , Now the two armies are at war , The Red Army can't take advantage of it .

If the Red Army still wants to get firepower at this time 2 : 1 The advantages of , So as to establish combat effectiveness 4 : 1 The absolute advantage of , If the Red Army doesn't plan to upgrade its individual firepower , Then we have to raise the number to 400.

Examples of actual combat

The above is a theoretical calculation , A false example , So in actual war , What's the situation ?

Take an example of the war of liberation , The famous battle of Menglianggu , Chen Yi 、 Hua Ye, under Su Yu's command, completely annihilated the Kuomintang “ The first of the five main forces ” The compilation of 74 t . At that time, the National Army 74 Zhang lingfu, the division commander, went deep alone , Captured by huayo , Focus quickly 5 Twice the force of the other side " Dumpling style " Encirclement and annihilation .

although 74 The Division has all the beautiful equipment , Individual firepower is the PLA side 3 Times. , So the overall firepower ratio is 5 : 3, According to Lanchester Equation , Combat power is the square of firepower , So that is 25 : 9, near 3 : 1, Therefore, the PLA's combat effectiveness is excellent , eat 74 It's no surprise that teachers .

<< Sun Tzu's art of war >> In the said : More is more , Less is more .

In fact, throughout the history of PLA stations , Especially the early Eighth Route Army , The period of the Red Army , Under the leadership of Mao Zedong , It has always been stressed that , Concentrate superior forces to fight annihilation . Although most of the time , The overall strength is not as good as the other side , But we have concentrated our superior forces locally , It's still possible to win , And the price we pay is small , Slowly, it reversed the whole situation .

Another extreme example is a battle that Britain once fought in Zimbabwe , The British Army just 50 people , It killed Zimbabwe, almost 3000 people ! What's going on here ? It turns out that the British Army's machine guns , But Zimbabwe is still a traditional grassland tribe that uses traditional weapons , Of its traditional weapons " fire " Facing the new machine gun is almost equivalent to 0, At this time, no matter how many people there are, it will not help in terms of combat effectiveness .

Revelation

that , What enlightenment can this Lanchester equation bring to us in our daily work ?

natural , We should focus on improving our personal " fire ", The ability to do things , When we're twice as good as each other , We may be four times as effective as each other in doing things .

In turn, , We should be right " fire " Keep an eye on the gap between levels . You read a hundred books , They read two hundred books , You think your gap is just 1 : 2, But it may not be , On the cognitive level , You're probably crushed .

From a team perspective, it's , If you can expand your team , The combat effectiveness of the team increases by the square .

Of course , Here's a premise , You can integrate the team , Form a joint force with each other instead of shifting responsibilities , Cause internal friction .

Han Xin leads the army , It is said that Liu Bang asked him , How much can you bring , Han xin said : the more , the better . From the connotation of Lanchester Equation , It makes sense .

In Physics , Momentum and kinetic energy are both related to speed , Momentum is proportional to speed , But kinetic energy is proportional to the square of the velocity , Twice the speed , " The amount " It's still twice as high , " can " It's already four times as big ! We should be aware of this effect .

Last , Even if you're just playing games , This equation can also give us a lot of enlightenment . For example, in a lot of war games , If your hero still can't kill the other side , The result must be that you are constantly being fucked by the other party , Keep losing blood !

It's not just about killing each other , Most of the time, it's the way to stop loss ! therefore , The more effective way is to concentrate our superior forces , Get rid of them quickly , It's almost the best way .

contrary , Getting caught up in all kinds of hard work is no different from fighting for consumption . Besides , If our own strength is far behind ? That's Thirty-six Strategies. It's better to leave , It's better to avoid fighting and preserve your strength .

It's no shame to be obscene , The result of hard work is failure , And the sacrifice is disproportionate , The loss caused by the other party is far greater than that caused by you . Such a sacrifice is not tragic , It's stupid !

remember : I'm not afraid to die, but I'm still going to die , Winning battles depends on calculation, not bravery ! Courage alone , A cavity of blood to charge , You may be just giving away your head !

Matthew effect (Matthew Effect)

In the previous calculation , We see a phenomenon , As the war goes on, the backward side , Disadvantages will be magnified , The backward side will be more and more backward , Finally, he was wiped clean by the leading Party .

This similar phenomenon , stay << Bible · New Testament · Matthew >> There's a saying in it : " Where there is , And double it for him to call him superfluous ; There is no the , Even what he has will be taken ".

“For whosoever hath, to him shall be given, and he shall have more abundance: but whosoever hath not, from him shall be taken away even that he hath.” Gospel of Matthew

This kind of " The richer the richer , The poorer the poor " It's also known as Matthew effect (Matthew Effect).

Ancient Chinese classics << Lao tze >> There is also such a sentence in it :

The way of heaven , To make up for a loss . The human way is not , Not enough is enough .

These effects are similar to those revealed by Lanchester equation . And this effect is undoubtedly cruel to the weak individuals who live in this society !

One side , We may need to avoid confrontation with the strong , Because we know very well , The weak have no chance of winning , And they lose more in conflict !

But on the other hand , Some competition is inevitable , If we can't get stronger , We're not being pushed away linearly , It's a parabola of being thrown away , We were sped away !

This is a Law of square !

It's not just getting weaker , It's getting weaker and weaker ! Looking at the gap statically may be problematic , Simple intuition can also be unreliable , If you extrapolate, you will find that things may be unexpected , The real gap is often much larger than the static gap on paper !

The good news is , Getting stronger is also getting stronger , So how to choose , I believe you already have the answer in your heart !

That's all about Lanchester equation .

Additional notes : This article is published on Weibo @ Silicon Valley Wang Chuan The relation between Matthew effect and Lanchester equation mentioned above is enlightening , Some examples are from its talk show .

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