If you just had one expense once a year of $1200, you would put in $100 a month. The average balance is going to be $600 in that case - the 0 and $1200 months average to $600, as do the $100 and $1100, the $200 and $1000, and so on. If you had one expense twice a year of $600 and put in $100 a year it will average to $300. You have a mix of 3/6/12 months - does 8 months seem reasonable as an "average" frequency? If so, there should be about a 4 month slush all the time.

Now instead of one expense averaged over 12 months, imagine 12 accounts, each needing $100 a month. If you started at zero, you would put in $1200 the first month and immediately spend it. One account would go from +100 (its share of what you put in) to -1100 while the rest are all at +100. Overall your balance would be zero. Then the next month you would again deposit 1200 and spend 1200, bringing one account to -1000, one to -1100, and the rest to +200. You average to zero actually on deposit because some of the "accounts" have negative balances and some have positive.

But aren't doing that. You "caught up" the months you were behind. So it would be like putting in $1200 for the first account, $1100 for the second, $1000 for the third and so on - a total of $7800. Then you take out $1200 and go down to 6600. The next month you put in $1200 and take out $1200 but you will always have that $6600 amount in there. All of the accounts will have positive balances - averaging $550 in this example.

If you just had one expense once a year of $1200, you would put in $100 a month. The average balance is going to be $600 in that case - the 0 and $1200 months average to $600, as do the $100 and $1100, the $200 and $1000, and so on. If you had one expense twice a year of $600 and put in $100 per month it will average to $300. You have a mix of 3/6/12 months - does 8 months seem reasonable as an "average" frequency? If so, there should be about a 4 month slush all the time.

Now instead of one expense averaged over 12 months, imagine 12 accounts, each needing $100 a month. If you started at zero, you would put in $1200 the first month and immediately spend it. One account would go from +100 (its share of what you put in) to -1100 while the rest are all at +100. Overall your balance would be zero. Then the next month you would again deposit 1200 and spend 1200, bringing one account to -1000, one to -1100, and the rest to +200. You average to zero actually on deposit because some of the "accounts" have negative balances and some have positive.

But aren't doing that. You "caught up" the months you were behind. So it would be like putting in $1200 for the first account, $1100 for the second, $1000 for the third and so on - a total of $7800. Then you take out $1200 and go down to 6600. The next month you put in $1200 and take out $1200 but you will always have that $6600 amount in there. All of the accounts will have positive balances - averaging $550 in this example.

If you just had one expense once a year of $1200, you would put in $100 a month. The average balance is going to be $600 in that case - the 0 and $1200 months average to $600, as do the $100 and $1100, the $200 and $1000, and so on. If you had one expense twice a year of $600 and put in $100 a year it will average to $300. You have a mix of 3/6/12 months - does 8 months seem reasonable as an "average" frequency? If so, there should be about a 4 month slush all the time.

You would only average to zero if you let some of the accounts have negative balances. But the point about saving is there are no negative balances.

If you just had one expense once a year of $1200, you would put in $100 a month. The average balance is going to be $600 in that case - the 0 and $1200 months average to $600, as do the $100 and $1100, the $200 and $1000, and so on. If you had one expense twice a year of $600 and put in $100 a year it will average to $300. You have a mix of 3/6/12 months - does 8 months seem reasonable as an "average" frequency? If so, there should be about a 4 month slush all the time.

Now instead of one expense averaged over 12 months, imagine 12 accounts, each needing $100 a month. If you started at zero, you would put in $1200 the first month and immediately spend it. One account would go from +100 (its share of what you put in) to -1100 while the rest are all at +100. Overall your balance would be zero. Then the next month you would again deposit 1200 and spend 1200, bringing one account to -1000, one to -1100, and the rest to +200. You average to zero actually on deposit because some of the "accounts" have negative balances and some have positive. 

But aren't doing that. You "caught up" the months you were behind. So it would be like putting in $1200 for the first account, $1100 for the second, $1000 for the third and so on - a total of $7800. Then you take out $1200 and go down to 6600. The next month you put in $1200 and take out $1200 but you will always have that $6600 amount in there. All of the accounts will have positive balances - averaging $550 in this example.