THE BOOK--Playing The Percentages In Baseball

Thursday, February 24, 2011

How many teams in MLB playoffs? Part 2

By Tangotiger, 03:50 PM

All data is from Stanley Cup seasons 1987-2010, when the NHL had 4 rounds of best-of-7. Excluded is the 1995 Cup 48-game season (and naturally the lockout year). That gives us 22 Stanley Cups.

In each season, I ranked the teams by points (1 through 30). In all 22 seasons, the Stanley Cup was won by a team that finished in the top 8 in the standings. The team that led the league in points won 7 of the 22 Cups, or 31.8%.

Let’s focus on the teams that led the league. Here’s how many rounds they won:
4: 7 times (and won the Cup)
3: 1 times (lost in Finals)
2: 5 times (lost in Final 4)
1: 4 times (lost in Final 8)
0: 5 times (eliminated first round)

Boring stuff to skip
Suppose the #1 team has a 75.1% chance of winning each series. The chance of them winning 4 consecutive series is 75.1% ^ 4 = 31.8%. So, given 22 seasons, we’d expect 7 Stanley Cups, just like it really happened.

The #1 team made the Cup finals 8 of 22 seasons (or 36.4%). In order for that to happen, they’d have to have a chance of winning each series 71.4%.

The #1 team reached the Final Four 13 of 22 seasons (or 59.1%). In order for that to happen, they’d win each series 83.9% of the time.

The #1 team won at least one series 17 of 22 seasons (or 77.3%). That is its chance of winning that first series.

Putting it together, the #1 team has around a 77% of winning each series.

A three-round Cup run
If the NHL was down to a 3-series Cup run (8 teams, or 12 teams with byes for the top 4), the #1 team would need to win 3 series of 4-of-7. That would imply they’d win the Cup .77^3 = 46% of the time according to the boring stuff above.

An alternative way to look at it is that the 17 times that the #1 team entered the playoffs in the Final 8 round, they won 7 times. 7/17 = 41%.

Conclusion
An NHL fan is suggesting that the #1 team should win the Cup 32% of the time if they want a 16-team playoffs, and 41% of the time if they want an 8- or 12-team playoffs.

My question: how many MLB teams would you need in the playoffs in order to get a 32% or 41% chance of the #1 team in MLB of winning the World Series? How many in the NBA? The NFL?

Who wants to do the legwork on presenting the matching data for these sports?

• Sabermetrics • Talent_Distribution • Other Sports • Football • Hockey

#1 Tangotiger (see all posts) 2011/02/24 (Thu) @ 15:55

I think I remember reading that Tiger Woods won one-third of his tournaments at his peak?

How often did Federer and Nadal and Sampras win?

Is it fair to say that we want the #1 team to win about one-third of the time?

#2 J-Doug (see all posts) 2011/02/24 (Thu) @ 16:04

Sounds about right. Isn’t the opening Vegas line on MLB playoff teams to win the Series usually somewhere around 2:1 and 3:2?

#3 J-Doug (see all posts) 2011/02/24 (Thu) @ 16:04

Should have been clear, line for the fave.

#4 NaOH (see all posts) 2011/02/24 (Thu) @ 16:24

In the Wild Card era, the team with the game’s best record has won three of the 16 World Series played, a 23% rate. Of the 13 times the team with the best record in the game didn’t win the Series, there were 4 times that team did reach the Series but lost (’95, ‘99, ‘03, ‘04). Had they succeeded, the rate would have been 44%.

I don’t know if 16 postseasons is ample data, but it seems like after accounting for luck and other unforeseeable vagaries that the 12-team postseason in MLB is close to the right number to get the #1 team winning a third of the time.

#5 Tangotiger (see all posts) 2011/02/24 (Thu) @ 17:17

NaOH: ok, so 7 of 16 went to the final round, or 44%.

In the NHL, 8 of 22 went to the final round, or 36%. That’s a 4-round tournament. If we made it a 3-round tournament, then 8 of 17 went to the final round or 47%.

It seems therefore that an 8-team tournament in the NHL is equivalent to an 8-team tournament in MLB.

Since NHL fans prefer 8, 12, or 16 teams in the playoffs (with 12 being the median), then having 12 teams in MLB playoffs would be perfectly fine.

Great job, thanks!

#6 J-Doug (see all posts) 2011/02/24 (Thu) @ 17:57

NaOH: Sorry to nitpick, but 3/16 = 19%… unless I’m missing something.

#7 NaOH (see all posts) 2011/02/24 (Thu) @ 18:23

Absolutely correct, J-Doug. Thanks for catching that.

#8 Davor (see all posts) 2011/02/25 (Fri) @ 08:03

With unbalanced schedule, we should be looking at the best team in each league (conference). No to mention that often the difference between the first and second team is 2 wins or less.
How would data look if first teams from both leagues (conferences in NHL) are considered and the numbers are then divided by 2 (effectively saying that best teams from both leagues/conferences are equals)?

#9 Davor (see all posts) 2011/02/25 (Fri) @ 09:57

To answer my own question:
NHL, since 1987, without 1995, No.1 seeds from both conferences (I took best record when they weren’t ranked within conferences):

4 wins: 8 (18%)
3 wins: 4 (9%)
2 wins: 9 (20%)
1 win: 12 (27%)
0 wins: 11 (25%)

3 times best teams from both conferences reached finals (that is, No.1 seed knocked out No.1 seed).

So, 27 % (12 of 44) reached final round, but only one of them lost from “inferior” opponent (Boston from Edmonton in 1990, ranked 2nd in Clarence Campbell conference).
If we take 3-round tournament, 12 of 33 (36%) reached finals.
All three times No.1 seeds met, points leader won (twice in 7 games, once in 6, all 1 or 2 goal games).

So, teams ranked No.1 in other conference:

4 wins: 1 (5%)
3 wins: 3 (14%)
2 wins: 4 (18%)
1 win: 8 (36%)
0 wins: 6 (27%)

Surprisingly (for me), best team in the “other” conference has less than 20% chance of reaching finals in 4-round tournament, and 25% chance of reaching finals in 3-round tournament.

For hockey, my theory that both No.1 seeds are similar in quality seems to be wrong.

#10 Davor (see all posts) 2011/02/25 (Fri) @ 12:02

MLB, od 1995 best in both leagues:

3 wins: 6 (19%)
2 wins: 5 (16%)
1 win: 10 (31%)
0 wins: 11 (34%)

Best teams in other league won 3 WS, like the best teams, but reached WS just one other time. Both times best teams in both leagues met, second-best won.

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THE BOOK--Playing The Percentages In Baseball

Thursday, February 24, 2011

How many teams in MLB playoffs? Part 2

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