Numpty >> friday october 29 - 15:27, Edited friday october 29 - 15:43

If I'm thinking of healing a player for a match I do find it a bit tricky working out how long I can leave him before treatment so I can save on the costs. Most likely other people have the same problem so I thought I would show you how.

Calculating the latest possible time to heal my player so he's ready for a match

This is easier to explain with an example and then I will provide a more general formula at the end. 

Firstly I need to calculate the time from the start of my match to the end of the injury. Because that's the amount of time that I will need to reduce the injury by. 

You should calculate this in hours and convert any minutes to a decimal.  The match is at 13:16 and my player is injured until 17:57 on the same day as the match. So the injury time saved by treatment needs to be at least 4 hours 41 minutes, which is 4.7 hours as a decimal. 

If I heal the player at the last possible moment then: 

Injury time remaining before treatment

•  = Injury time remaining after treatment + 4.7 hours (time saved by treatment)
• TB = TA + 4.7 

I currently have HC level 9 which has a 'speed up healing' rate of 51%, and also have staff level 9 with time remaining after treatment of 45%. These figures are available in the Health Centre overview page. 

The HC healing rate of 51% gives a remaining healing time of 49% after treatment. 

So now we get:

Injury time remaining after treatment 

•  = Injury time remaining before treatment * 0.49 * 0.45
• TA = TB * 0.49 * 0.45
• TA = TB * 0.2205 

Reformatting we get:

• TA = (TA + 4.7) * 0.2205   
• TA = (4.7 * 0.2205 ) / (1 - 0.2205 )
•     = 1.3295 hours

This is the remaining time of the injury after treatment, so I need to heal the player a minimum of 1 hour 20 minutes before the start of the match, which is with 6.03 hours of the untreated injury remaining.  

To double check this then the time remaining after treatment

•  = 6.03 * 0.49 * 0.45 = 1.3296 hours

Here is a more general formula:

Minimum Treatment Time Before Match 

•  = [IU - MT] * H / (1 - H)    
• With H = (1 - HC) * S

Where:

•   IU = Injured Until, the normal time without treatment 
•   MT = Match Time, the time you want the player to be recovered
•   HC = Health Centre 'speed up healing' rate as a decimal
•   S  = Staff injury time after treatment as a decimal

With HC 10 and Staff level 10

Since HC 10 (54%) with staff 10 (40%) is probably the most common facility the general formula simplifies to:

Minimum Treatment Time Before Match 

•  = [IU - MT] * 0.2255  

Aad Mansveld >> friday october 29 - 16:11

Math professor Numpty

CristianS9 >> friday october 29 - 19:01

Thank you, @Numpty. It appears that you have put some effort on this!

Lee >> saturday october 30 - 10:36

Wow Numpty, you must have been really bored! :)

I just look at the healing time on the Health Centre page.

Numpty >> saturday october 30 - 12:46

Normally so do I @Lee.

Sometimes that's enough. But sometimes I can save significant treatment costs by working things out. 

For me the question is often do I need to pay for treatment today or can I wait until tomorrow and risk it being too late. If I'm not sure and I want the player for a certain match then either I have to pay for the extra day, stay up very late or get up very early. That's really not much fun.

So sometimes it's much easier to work it out exactly.

holt >> sunday october 31 - 17:22

You should shift this to the General section, it would get lost here.

Numpty >> sunday december 11 - 22:01, Edited sunday december 18 - 12:37

Health Centre Injury Rates

Regarding injury rate, the 2 levels difference is only a guide that seems to have become part of RS folklore. It's useful but may not be perfect. For the HC I think it's better to use the actual numbers given in the reference table.   

The injury prevention rate is a probability and can be expressed as a simple fraction for each level:

• (level -2)/(level -1)
• which gives 1/2, 2/3, 3/4, 4/5, 5/6 etc. 

Example difference between levels

For HC level 8 this prevents 6/7 of potential injuries so you get 1 out of every 7 - and HC level 10 prevents 8 out of every 9 injuries. 

The difference between the 2 levels is you would get 7 injuries (HC 10) for every 9 (HC 8), so it effectively reduces the injury rate by 2/9 or 22.2%.

Similarly going from HC 10 (8/9) to HC 11 (9/10) effectively reduces the injury rate by a further 1/10 or 10%. And going from level 12 (10/11) to level 13 (11/12) reduces the rate by 1/12 or 8.3%. So every HC level gives a diminishing return. 

We haven't been given any figures for the academies, it simply says 'increased injury chance' at each level but I imagine it works using similar ratios.  

Numpty >> sunday december 18 - 11:49, Edited monday december 19 - 10:33

Health Centre Levels

I decided to put this into a reference table so it's a little easier to understand. 

This is from the Health Centre help, with the percentages expressed as a simple fraction:

https://rockingsoccer.com/en/soccer/help/facilities/facility-fysio

Injury prevention rate 

• Level 1 and 2 - Zero
• Level 3 - 1/2
• Level 4 - 2/3
• Level 5 - 3/4
• Level 6 - 4/5
• Level 7 - 5/6
• Level 8 - 6/7
• Level 9 - 7/8
• Level 10 - 8/9
• Level 11 - 9/10
• Level 12 - 10/11
• Level 13 - 11/12
• Level 14 - 12/13
• Level 15 - 13/14
• Level 16 - 14/15

Actual Injury rate (non-prevented injuries)

• Level 3 - 1/2
• Level 4 - 1/3
• Level 5 - 1/4
• Level 6 - 1/5
• etc.

One level difference

As explained by the example in the previous post, this is the reduction in the injury rate between each health centre level:

• 3 to 4 - 1/3
• 4 to 5 - 1/4
• 5 to 6 - 1/5
• 6 to 7 - 1/6
• 7 to 8 - 1/7
• 8 to 9 - 1/8
• 9 to 10 - 1/9
• 10 to 11 - 1/10
• 11 to 12 - 1/11
• 12 to 13 - 1/12
• 13 to 14 - 1/13

Two level difference

• 3 to 5 - 2/4 
• 4 to 6 - 2/5
• 5 to 7 - 2/6
• 6 to 8 - 2/7
• 7 to 9 - 2/8
• 8 to 10 - 2/9
• 9 to 11 - 2/10
• 10 to 12 - 2/11
• 11 to 13 - 2/12
• 12 to 14 - 2/13

Three level difference

• 3 to 6 - 3/5
• 4 to 7 - 3/6
• 5 to 8 - 3/7
• 6 to 9 - 3/8
• 7 to 10 - 3/9
• 8 to 11 - 3/10
• 9 to 12 - 3/11
• 10 to 13 - 3/12
• 11 to 14 - 3/13

Four level difference

• 3 to 7 - 4/6
• 4 to 8 - 4/7
• 5 to 9 - 4/8
• 6 to 10 - 4/9
• 7 to 11 - 4/10
• 8 to 12 - 4/11
• 9 to 13 - 4/12
• 10 to 14 - 4/13

For clarity, this is the difference in the expected injury rates between HC levels and not between HC and training levels. 

As can be seen from the table going from HC 5 to HC 6 has the same effect as going up 2 levels from HC 9 to HC 11 - a reduction of 1/5 or 20% in the injury rate. Similarly, going from HC 4 to 6 is the same as going from HC 7 to 11 - a reduction of 2/5 or 40%.

So a 4 level difference at higher HC levels has a similar effect to a 2 level difference at lower HC levels. Whether that's the same for training centre levels is not known. 

Numpty >> sunday december 18 - 13:07, Edited monday december 19 - 10:50

Proposed TC Injury Rate

Proposed increases in the injury rate with each training centre level. 

This is all rather speculative, and even if not correct is probably indicative of what happens.

I have proposed 2 slightly different models, my reasons behind them are as follows:

The HC injury reduction rate and corresponding TC increase rate must follow a similar, reverse, pattern. If the TC rate increased faster than the HC reduction rate then injuries would start to multiply with each TC level and I don't think we see that. It could, of course, be a little lower. 

Vincent likes patterns involving simple multipliers and fractions and it makes sense if the TC injury increases follows a very similar pattern to both the TC training rate and the HC reduction rate. My preferred model uses an identical pattern to the TC training rate and a similar pattern to the HC reduction rate.  

1. Proposed TC Injury Multiplier (Preferred)

• Level 1 - x1 (The basic Injury rate probability)
• Level 2 - x2
• Level 3 - x3
• Level 4 - x4
• Level 5 - x2 
• Level 6 - x6
• Level 7 - x7
• Level 8 - x8
• Level 9 - x9
• Level 10 - x10
• Level 11 - x11
• Level 12 - x12
• Level 13 - x13
• Level 14 - x14
• Level 15 - x15
• Level 16 - x16

2. Proposed TC Injury Multiplier (Alternate)

I don't know where the '2 level difference' came from. Perhaps this was information from Vincent at some point in the past? If it is indeed the case and not just RS folklore, then this alternate proposal follows the 2 level rule exactly, so if you keep 2 levels apart the effective injury rate remains identical.  (Level 4 onwards)

• Level 1 - x 1/4
• Level 2 - x 1/2
• Level 3 - x 3/4
• Level 4 - x1 (The basic Injury rate probability) 
• Level 5 - x2
• Level 6 - x3
• Level 7 - x4
• Level 8 - x5
• Level 9 - x6
• Level 10 - x7
• Level 11 - x8
• Level 12 - x9
• Level 13 - x10
• Level 14 - x11
• Level 15 - x12
• Level 16 - x13

(For direct comparison with the first model then multiply all numbers by 4.)

How does this work in practice?

If we work with my preferred model, let's say that over the course of a number of matches that the basic injury probability at TC level 1 would give you 100 potential injuries. Then TC level 5 would give you 500 potential injuries and so on. 

Without a HC then none of the potential injuries get prevented and they all become actual injuries. So with no HC you would get 10 times more injuries with TC 10 than with TC 1. 

With a HC then most of the potential injuries get prevented. You simply reduce the potential injuries by the given fraction. A few examples keeping a 2 level difference:

• TC 2 & HC 0 = 100 x 2 = 200 injuries
• TC 5 & HC 3 = 100 x 5 x 1/2 = 250 injuries
• TC 6 & HC 4 = 100 x 6 x 1/3 = 200 injuries
• TC 8 & HC 6 = 100 x 8 x 1/5 = 160 injuries
• TC 10 & HC 8 = 100 x 10 x 1/7 = 143 injuries
• TC 12 & HC 10 = 100 x 12 x 1/9 = 133 injuries

So with this model the injury rate falls off slightly if you keep 2 levels apart at the higher levels. Is this what we see?

If we attempt to stay with a consistent injury rate of around say 150-200 injuries, then we get this:

• TC 2 & HC 0 = 100 x 2 = 200 injuries
• TC 4 & HC 3 = 100 x 4 x 1/2 = 200 injuries
• TC 5 & HC 4 = 100 x 5 x 1/3 = 167 injuries
• TC 6 & HC 5 = 100 x 6 x 1/4 = 150 injuries
• TC 7 & HC 5 = 100 x 7 x 1/4 = 175 injuries
• TC 8 & HC 6 = 100 x 8 x 1/5 = 160 injuries
• TC 9 & HC 6 = 100 x 9 x 1/5 = 180 injuries
• TC 10 & HC 7 = 100 x 10 x 1/6 = 167 injuries
• TC 11 & HC 7 = 100 x 11 x 1/6 = 183 injuries
• TC 12 & HC 8 = 100 x 12 x 1/7 = 171 injuries
• TC 13 & HC 8 = 100 x 13 x 1/7 = 186 injuries
• TC 14 & HC 9 = 100 x 14 x 1/8 = 175 injuries
• TC 15 & HC 10 = 100 x 15 x 1/9 = 167 injuries

Of course, this model may be wrong. It suggests that you need around 1 HC level to cover 2 TC level upgrades. This may not be what we see.

Any comments and opinions appreciated.

Numpty >> monday december 19 - 03:01, Edited monday december 19 - 11:24

3. Hedging your bets?

Finally, a third model that works out at somewhere in between the other 2. This model keeps an identical increase/reduction rate between the TC level and the same HC level. So if you keep the TC/HC level the same then the injury rate doesn't change. (Works for all levels except L2)

• Level 1 - x1 (The basic Injury rate probability)
• Level 2 - unclear
• Level 3 - x2
• Level 4 - x3
• Level 5 - x4 
• Level 6 - x5
• Level 7 - x6
• Level 8 - x7
• Level 9 - x8
• Level 10 - x9
• Level 11 - x10
• Level 12 - x11
• Level 13 - x12
• Level 14 - x13
• Level 15 - x14
• Level 16 - x15

I'll let other decide which model they think works best.