FanPost

Are the Playoffs a Crapshoot? A probabilistic model

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.