Greetings ladies and gentlemen,

I was wondering 5 seconds ago if IP boosts are worth the RP.
I am going to compare this, with buying a 6300 IP champion.
So let's calculate it:

Data
2 wins boost = 160 RP
50 wins boost = 2560 RP

1 day boost = 290 RP
30 day boost = 3490 RP

A 6300 IP champion = 975 RP

Win-boosts
1 win bonus in normal ~ 145 IP
1 win bonus in ranked = 166 IP
1 loss bonus = 0 IP

Day-boosts
1 win (of 45 min) bonus = 104 IP
1 loss (of 45 min) bonus = 63,2 IP


Calculations
First comparison
Let's take a closer look:

A champion has an IP worth of: 6300/975 = 6,46 IP/RP
That means, each point of RP equals 6,46 IP


2 Win-boosts
So let us look at the win boosts:

The 2 wins boost costs 160 RP and grants:
145 * 2 = 290 IP in normal games
166 * 2 = 332 IP in ranked games

That means that the IP you get per RP is:
290/160 = 1,8 IP/RP in a normal game
332/160 = 2,1 IP/RP in a ranked game

The amount of IP you get from buying a champion = 6,46 IP/RP, that means that 2-win boosts are NOT worth it.


50 win-boosts
A 50 win boost costs 2560 RP and grants:
145 * 50 = 7250 IP in a normal game
166 * 50 = 8300 IP in a ranked game

That means that the IP you get per RP is:
7250/2560 = 2,83 IP/RP in a normal game
8300/2560 = 3,24 IP/RP in a ranked game

The amount of IP you get from buying a champion = 6,46 IP/RP, that means that 50-win boosts are NOT worth it.


1 Day boost
A 1 day boost costs 290 RP and grants 104 IP per win, and 63,2 IP per loss.
In order to make it equal 6,46 IP/RP, means that you need to play:
290 * 6,46 / 104 = 18 matches and win them all
290 * 6,46 / 63,2 = 29,64 matches and lose them all

That means that you need to spend:
18 * 45 minutes = 13,5 hours in one day if you win everything, to make it equal a champion.
29,64 * 45 minutes = 22,23 hours in one day if you lose everything, to make it equal a champion.

Since we sleep at least 8 hours a day and work/should be working 8 hours a day, it means that the 1 day boost is NOT worth it.


30 Day boost
A 30 day boost costs 3490 RP and grants 104 IP per win and 63,2 IP per loss.
In order to make it equal 6,46 IP/RP, means that you need to play:
3490 * 6,46 / 104 = 216,8 matches and win them all
3490 * 6,46 / 63,2 = 356,7 matches and lose them all

That means you need to spend:
216,8 * 45 minutes = 162,6 hours in 30 days if you win everything, to equal a champion
356,7 * 45 minutes = 267,5 hours in 30 days if you lose everything, to equal a champion

That means you need to spend:
162,6/30 = 5,42 hours a day if you win everything
267,5/30 = 8,92 hours a day if you lose everything

As long the amount of hours spend < 8 hours, it is realistic (since you are 8 hours sleeping and you should be working 8 hours aswell, leaving 8 hours a day for LoL).

That means that the 30 day boost is worth it if you know how to play.


Conclusion
The win-boosts are trash, which you shouldn't buy at all unless you want to rush your rune pages.
The day boosts are much better, the following have been calculated in the background to be worthy:
7 days if you pretty much win everything
14 days if you win about 70% of the time
30 days if you win more than 40% of the time

If a champion has a sale of 50% off, then the sale is definately worth it over any boost.

I hope this helped you, if it did, you are welcome to +rep me any time :D

Thank you all for reading and may you waste as little RP as possible :P
-Meiyjhe