In a recent thread by Lev Facher on the playoffs being a Crapshoot, I wrote a comment looking at it from a probabilistic point of view. Several people suggested I pull it out to a full post. I want to mention straight up that danmerqury deserves a lot of credit as well for the thinking here.
So first off a few simple terms. We'll assume team A plays Team B, and we'll assume the probability of team A winning a game against team A is P(A), and by definition P(B) the probability of Team B winning P(B) = 1-P(A).
e.g. if team A has a 0.6 (60%) chance of winning Team B has a 40% chance.
That should be fairly straightforward.
The more difficult question is what probability should we assign P(A). Well one simple way might be to look back across the season. If you're a .600 team you should win 60% against a random team. The challenge is it's not a random team. If both teams are in the playoffs they have a .500 winning percentage as a minimum. If both team A and team B had .600 winning percentages, then P(A) and P(B) can't be both 60%. More likely it's a straight 50/50 shot.
Let's assume S(A) = winning percentage of team A during the Season, S(B) = winning percentage of Team B during the season, this might be a reasonable function
P(A) = 0.5 + (S(A) - S(B))
So if S(A) = 0.6 and S(B) = 0.5, then P(A) = 0.6. This is reasonable, since B is an average team, and so the probability of A winning is the same as their season average. So let's take some very realistic season percentages for two playoff teams S(A) = 0.6 and S(B) = 0.55 then P(A)=0.55. This seems reasonable to me, the better team has a higher probability of winning but it's still below their season average winning percent (because they're playing a better than average team)
If you use this model and if you look at any reasonable winning percentages over a reasonable sample, it's hard to envisage a team on average having much more than a 60/40 advantage, and it seems to me a 55/45 advantage is probably a reasonable edge in a lot of cases.
So let's run this through all the possibilities (I won't go into the detailed Math, but you can use the BINOMDIST function in Excel)
Similar Teams | Marginal Edge | Normal Edge | High Edge | |
Probability of A Winning | P(A)= 0.5 | P(A)=0.525 | P(A)=0.55 | P(A) = 0.6 |
Win 1 Game Series | 50.0% | 52.5% | 55.0% | 60.0% |
Win 5 Game Series | 50.0% | 54.7% | 59.3% | 68.3% |
Win 7 Game Series | 50.0% | 55.5% | 60.8% | 71.0% |
So a couple of interesting things come through when you look at this:
With a normal edge you're only really about a 60/40 chance to win a series. Even with a high edge it's only 70/30. Also note that the argument that a 7 game series is much less of a crapshoot does not hold water. With a normal edge, it only increased the probability of the better team winning by about 2%.
Now let's look at the probability of the best team in baseball winning the World Series, let's assume they have a high edge against all 3 teams they face (this is somewhat extreme, but let's assume it anyway, say the 2000 Mariners). They have to win a 5 game, a 7 game, and another 7 game. That is 68.3%*68.3%*71% = ~33%. Now that's better than the average 12.5% for the last 8, but note about 2/3 of the time the best team in baseball does not win the World Series (it's likely even higher, because I picked the high edge).
In the above analysis, what happens if we have an Ace, say a Jon Lester, who really alters your odds. What does he really give you. I ran the numbers for a 5 game series, assuming that P(A)=0.55 for non-Ace games and P(A)=0.7 when your Ace pitches. This is the upper end in my opinion; for reference I think we and the Red Sox won about 60% of the games Lester pitched. Let's also assume the pitcher goes in game 1 and 4 (on short rest, with no downside).
if you run the numbers (and I've not shown the detailed calcs), it shows a 70% chance of winning the 5 game with an unbelievable Ace vs. 59% if you had a 55/45 edge in all games, so you gain about 11 percentage points, or put another way you increase your chance of winning the playoff by about 20% from what you had before.That ace gives you an edge, but it's hardly decisive. By the way, I didn't run it for 7 game series, but it would be marginally less unless you could get your ace out 3 times.
So what's the conclusion here? It's obviously not quite a crapshoot, but it's really not far off. And for the press who said "the A's have to win the World Series and anything less is a disappointment" - well that's just baloney.