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 :

- Combat effectiveness and number of people
**square**In direct proportion to - 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 :

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 ):

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 ):

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 )::

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 :

- Combat effectiveness and number of people
**square**In direct proportion to - 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 .