There's not a big difference between $87,075,264 and $80,875,264 for a multi-billionaire NBA owner, until you show him the tax bill that comes with it. With the new luxury tax tiers that come into play this season, teams are charged for every dollar over the tax threshold of $71,748,000 as follows:

Tier 1: $1.50 for every dollar from $71,748,001 up to $76,747,999=$7,499,998.50 Tier 2: $1.75 for every dollar from $76,748,000 up to $81,747,999=$8,749,998.25 Tier 3: $2.50 for every dollar from $81,748,000 up to $86,747,999=$12,499,997.50 Tier 4: $3.25 for every dollar from $86,748,000 up to $91,747,999=$16,249,996.75 Contributions from Dunking on a 6 ft rim!

There's an additional tier(s) but it doesn't pertain to the Heat. With Mike Miller still on board the Heat had 13 guaranteed contracts for a total payroll of $87,075,264 ($15,327,264 over the tax threshold) and still had two roster spots open. In that instance the tax bill would total $29,813,605.5 (tier 1+tier 2+tier 3+$1,063,611.25[of a taxable $327,265 at $3.25]). Now to business. Had the Heat kept Miller they'd be paying a payroll of $87,075,264 + a tax bill of $29,813,605.5 for a grand total of $116,888,869.5. Keep three things in mind:

There are still two roster spots available. Micky Arison, owner since the '95-'96 season, has paid a total of $33M in luxury tax in 17 seasons, including this past '12-'13 season of $13.3M in tax. Had Mike Miller been kept Arison would have paid almost if not all of that ($30M-$33M) after just the '13-'14 season. The Heat would have another taxable $4,672,735 (at a rate of $3.25 per dollar) to work with in salary to fill two roster spots before hitting the 5th tier of luxury tax at $3.75.

After paying $90,252,678 in team salary this past season, the Heat were looking at a payroll of $116,888,869.5 for 13 players for the upcoming season. That's why it had to be Mike Miller and not Joel Anthony who had to get amnestied. Miller's salary was the difference between paying $3.25 per dollar for any new addition to the team to paying $1.75 per dollar (the Heat only have $872,735 to work with, not even enough for two rookie contracts, before paying $2.50 per dollar; unless they shed salary off their books) for said addition. Had Anthony been amnestied instead, the Heat would be facing a payroll of $83,275,264 ($11,527,264 over the tax threshold). In that instance the tax bill would total $20,068,159.25 (tier 1+tier 2+$3,818,162.5[of a taxable $1,527,265 at $2.50]). Had the Heat amnestied Anthony they'd be paying a payroll of $83,275,264 + a tax bill of $20,068,159.25 for a grand total of $103,343,423.25 and another taxable $3,472,735 (at a rate of $2.50 per dollar) to work with in salary to fill three roster spots before hitting the 4th tier of luxury tax at $3.25.

Currently, the Heat are $9,127,264 over the tax threshold with 12 guaranteed contracts and the non-guaranteed contract of Jarvis Varnado at $788,872. They have $872,735 in salary to work with before falling under the 3rd tier of luxury tax. Adding a veteran at a minimum 1 year deal or even Varnado (though his projected salary is $788,872, for tax purposes, it is counted at the two-year minimum of $884,293; the same as a veteran addition) would leave the Heat at 13 players and $11,558 into the 3rd tier of luxury tax at $2.50 per dollar. As you can see, the only way to improve player personnel, fill out the roster and remain in the 2nd tier of the luxury tax is to trade Joel Anthony.

Keep in mind, a team receiving Joel Anthony is not interested in acquiring him for the sole purpose of his services but rather the incentive(s) to take on his contract. Philly must add salary to their payroll or otherwise pay their roster a prorated bonus if they do not meet the salary floor. Perhaps for their 1st round pick obligation from the 2012 NBA Draft Day deal to be removed (the Heat aren't getting a 1st round pick anyway but it saves Philly two future 2nd rounders) and some other sweetener, cash considerations, etc. to take on Joel Anthony. Trading Anthony and receiving no salary in return would wipe $3,800,00 off the books and give the Heat $4,672,735 in salary to work with to fill four roster spots while remaining inside the 2nd tier of luxury tax. This is where the addition of Greg Oden comes in.

I ran the numbers and the most the Heat could offer Oden while remaining in the 2nd tier of luxury tax is $2,413,969 of their mini-MLE. Now this is assuming that:

Joel Anthony is traded The Heat pick up the contract of Jarvis Varnado at $788,872 (for tax purposes, his salary is counted at the two-year minimum of $884,293) A veteran (your choice) is signed to a 1 year minimum deal (must be a 1 year deal without a player/team option otherwise the salary cap hit is no longer just $884,293) A rookie contract is added to round out the 15. For this I used James Ennis at $490,180.

Contributions from Albert Random.

All of these transactions put the Heat at $9,999,999 over the luxury tax threshold which is the max allowed under the 2nd tier luxury tax of $1.75 per dollar for a tax bill of $16,249,996.75 and a payroll of $81,747,999 culminating in a grand total of $97,997,995.75.

To conclude,

Keeping Mike Miller & Joel Anthony would have cost $116,888,869.5 and beyond. Amnestying Joel Anthony and keeping Mike Miller would have cost $103,343,423.25 and beyond. Amnestying Mike Miller and trading Joel Anthony while adding Greg Oden, Jarvis Varnado's non-guaranteed contract, a veteran on a 1 year minimum deal and a rookie contract would cost $97,997,995.75.

Note: Team salaries/taxes are not final until the season is over. They are adjusted throughout the season pending addition(s)/subtraction(s)/suspension(s) and the league's escrow fund. Scenarios that I presented involving amnesty do not take into account the money/offset that the Heat would still owe to said player.

I want to thank Surya Fernandez for reaching out to me after reading a comment I left on his article and for the opportunity to contribute on a FanPost for HotHotHoops.