By Jeff Hwang

June 14, 2006

Down two games to one in the NBA Finals, the Miami Heat are looking to become only the eighth team in NBA Finals History to come back from a 2-1 deficit to win the series. Jeff Hwang makes you a hypothetical bet that the Heat will, in fact, win the NBA title. Should you take it?

Q: Will the Heat win the NBA Finals?

A: Of course they will.

Watching Dwyane Wade and the Miami Heat -- already down two games to none to the Dallas Mavericks -- rise from the dead to take Game 3 of the NBA Finals in a most stunning fashion Tuesday night on Disney’s (NYSE: DIS) ABC, I had an epiphany: The Heat are going to win it all.

Never mind that only seven teams in the 59-year history of the NBA Finals have come back from a 2-1 deficit to win the title. But if my vision sounds ridiculous, I should point out that there is some precedence for such an epiphany. I had a similar moment a couple of years ago during the 2004 American League Championship Series between the Boston Red Sox and the New York Yankees. With the Sox down three games to none, and down a run going into the bottom of the ninth inning, the Yankees’ Tony Clark fumbled a ground ball, evoking memories of the Red Sox’s Bill Buckner in the 1986 World Series. In that instant, I just knew that, not only were the Red Sox going to win that game, but that they were also going to win the last three games of the series and become the first team in Major League history to overcome a 3-0 deficit (see Will the Red Sox Make the World Series?).

And, as we now know, that’s exactly what happened.

So in the spirit of crystallized moments and investing games, let’s make a hypothetical bet: If the Heat go on to win the series, I will give you $15; if the Mavericks win, you will give me $5.

Should you take this bet?

The real question: How much is the bet worth?

At least one Heat Hater has told me that I have a better chance of winning Harrah’s (NYSE: HET) World Series of Poker than the Heat do of winning the series (in other words, not good). However, whether you should take the bet isn’t as clear cut as who you think will win. The real question here isn’t actually who will win the series, but whether or not you are getting value from the deal.

What you want to know is how much the bet is actually worth. And what is clear is that the size of the competitive advantage can have a fairly dramatic affect on the value of that bet.

The approach

The first factor of note is that I am laying you $15:$5 or 3:1 odds on this bet. What this means is that you would have to believe that Heat have a 1-out-of-4 or 25% chance of winning the series in order for this bet to be EV (expected value) neutral. Moreover, the Heat would have to have a greater than 25% chance of winning in order for you to be getting the best of this bet.

That said, we need to estimate the Heat’s chances of winning the series. And probably the easiest way to do this is to estimate the probability of the Heat winning Game 4, Game 5, Game 6, and Game 7, and then add up the probabilities of all of the potential sequences in which the Heat don’t lose two games (i.e. they win). There are four ways the Heat can win the series, and that is to win the next three games (W-W-W), or lose one game and win the other three (W-W-L-W, W-L-W-W, L-W-W-W).

In addition, to come up with a fair value range, we will set a base case where both teams are evenly matched, the “Epiphany Case” (Heat has better chance of winning each game,” and the bad case (the Mavericks are the better team).

Base Case

In our base scenario, we’ll assume that the teams are evenly matched, and that the home team has a 60% chance of winning each game. Game 4 and Game 5 are in Miami, with the potential Game 6 and Game 7 being in Dallas. Thus the probability of Miami winning Game 4 is 0.6 (60%), 0.6 in Game 5, 0.4 in Game 6, and 0.4 in Game 7. Conversely, the probability of Miamilosing Game 4 is 0.4, 0.4 in Game 5, and 0.6 in both Games 6 and 7.

We get the probability of each sequence by multiplying the probability of each individual outcome in that sequence. Adding up the results of each sequence yields the probability of the Heat winning the series under these assumptions. In this case, the probability of the Heat winning is 0.3072, or 30.7%.

The “Epiphany Case”

Of course, it wouldn’t be much of an epiphany if I thought Heat and the Mavericks were going to perform evenly. For one thing, it is arguable that the Heat outplayed the Mavs for most of Game 1, and Game 3 as well. The Heat are capable of playing much better than they have. Moreover, we should account for the “Dwyane Wade” effect -- that is, the effect of D. Wade being and acting like the best player on either team, as he was in Game 3. Plus there is also the momentum factor -- it will be tough for a team to recover after losing a game the way the Mavs lost Game 3, after leading by 13 points with just over six minutes left to play.

So in the “Epiphany Case”, we’ll assign the Heat a 70% chance of winning Game 4 at home, a 65% chance of winning Game 5, a 40% chance of winning Game 6, and a 45% chance of winning Game 7. Under these assumptions, the Heat have a 38.4% chance of winning the series.

Bad Case

On the other hand, it’s possible that Dallas is simply the better team. Let’s assume that the Heat have a 0.5 chance of winning Game 4, a 0.45 chance of winning Game 5, a 0.35 chance of winning Game 6, and a 0.4 chance of winning Game 7. In this scenario, the Heat have only a 20.7% chance of winning.

Interpreting the results

The prize pool here is $20 -- your $5 bet plus my $15. So if the Heat and Mavericks are evenly matched, and the Heat have a 30.72% chance of winning the series, then your bet is worth ($20)(0.3072) or $6.14. If the Heat have a 38.405% chance of winning the series, as in the “Epiphany Case”, then your bet is worth ($20)(0.38405) or $7.68. Alternatively, in the case where the Mavericks are simply the better team, then your bet is worth ($20)(0.20725) or only $4.15.

Basically what this means is that, if you only had to put in $4.15 to win my $15, you would take the bet no matter what you thought of the Heat’s chances. However, Heat Haters would expect to lose 17% [($5 - $4.15) / $5] by taking the bet at $5.

On the other hand, if you thought the Heat matched up evenly with the Mavericks -- or better -- than you are getting good value at the $5 price I offered you. In this case, you have an expected return of 22.3% [($6.14 - $5) / $5] if you think the Heat and Mavericks are evenly matched (base case), and a 53.6% expected return [($7.68 - $5) / $5] in the “Epiphany Case.”

The size of the competitive advantage matters

There are a couple of things to take from this. One is that highly divergent opinions lead to highly divergent valuations. A Heat Hater would certainly balk at paying the $7.68 “Epiphany Case” price for my $15 payoff, much less $6.14 or even the $5 I offered. A Heat Hater would likely pay no more than $4.15 for a $15 payoff. On the other hand, an “Epiphany Case” believer would gladly take the $5 bet, as that price offers considerable value and even margin-of-safety to the “evenly-matched” scenario. He might even pay $6.14, a price that still offers some leeway to his most optimistic beliefs.

This should help explain why stock prices are so volatile.