By Max Kaplan
The baseball playoff system is messed up. It’s a statistician’s worst nightmare. As both an Angels diehard and a statistician, I have descended into despondency.
After six months and 162 games of baseball, a 5-game coin flip decides the fate of the eight playoff teams. The Los Angeles Angels, considered by many to be the best team in baseball and considered by most to be a better team than the Kansas City Royals, were knocked out in only three games after leading the league with 98 regular season wins. That’s three games – the same length as the common regular season sweep.
I’m going to try to “fix” the randomness and unfairness of a short playoff series. And by doing so, I hope to resurrect the Angels 2014 World Series hopes.
How many games would we need in a playoff series to be fairly confident that the better team moves on? According to my calculations below, that number is 1,101.
And maybe after watching Josh Hamilton go 0 for 3,500 at-bats, Mike Scioscia would finally have a large enough sample size to bench him…
How Many Games Would We Need?
There is Too Much Parity in MLB for a 5-Game Series
There is a relatively small difference in Win Pct. between the best playoff teams (.605) and the worst playoff teams (.543). It would take 18 games to expect the Angels to win just 1 more game than the Royals.
But 18 games are not even close to enough – we need consider randomness. The Pirates, Giants, and A’s all finished with the same record, and the Royals only finished one game better. Even after 162 games, the Pirates, Giants, or A’s might actually be better than the Royals. Each team may just have gotten lucky or unlucky in a few games, and we don’t have enough information to rank them. The closer that the teams end up in the standings, the less sure we are that one team is better than the other.
The “Best-of” Series Format Does Not Work
We start to see that a Best-of-5 series is not only random, but it’s a literal coin flip. In fact, the “Best-of” concept is flawed unto itself. If we had a Best-of-161 game series and the Angels beat the Royals 81 wins to 80 losses, we still wouldn’t really know which team were better. But if the Angels won the first 10 games of the series, we could probably just end it there. Statistics doesn’t favor “close wins” in that winning a series by a small margin is not statistically strong evidence that the team is better.
Did the Royals ALDS Sweep Prove They Were the Better Team?
To answer the question, we bring in the binomial test, which is a simple statistical test that can tell us how confident we are that one team is better than the other.
After the Royals went 3-0 against the Angels, the binomial test puts 75% confidence that the Royals were the better team. Of course, we are less confident in a series that reaches Game 4 or Game 5.
Let’s look at the confidence percentages for Best-of-5 and Best-of-7 series, calculated using R:
Confidence that the Better Team Won
When we reach the rubber match of Game 5 in the ALDS or Game 7 in the ALCS or World Series, we learn nothing statistically about whether one team is better than the other, since someone must win. This is the intuition why we have 0% confidence that the winning team was better.
The Infinite Playoff Series – The Ideal Playoff Format
How would a statistician decide how many games to play? Just play an indefinite series. Keep playing games until one team asserts itself clearly as the better team.
In this case, we would keep playing games until we reach some confidence threshold that one team is better. In statistics, we often use 95% certainty as the cutoff. That corresponds to the records below. This is the winning team’s record so that the “better” team moves on at least 95% of the time.
Records That Would End the Series
…and the list goes on
Obviously, it takes a lot more than best-of-5 or best-of-7 series to conclude that one team is indeed better. The easiest and shortest way to win is a 6-game sweep. Otherwise, it’s going to be a loooong series.
How many games until the Angels move on to the ALCS?
In the case of the Angels and the Royals, if we use their regular season records as their true ability, we can assume the Angels would win about 52.4% of the games. I ran 1,000 simulations of this to see how long the average series would last before a team got “far enough” ahead to end it.
Turns out, we would need, on average, 1,101 games to be played before we could confidently say with 95% certainty that the Angels (or Royals) are far enough ahead to move on. That’s the equivalent of about 6.8 seasons of baseball.
Using this system, we’d finally be able to fairly determine the winner of the 2007 ALDS from 7 years ago, when the Angels were swept 3-0 in the first round by the Boston Red Sox. Gary Matthews, Jr., Garret Anderson, and Casey Kotchman would all be in the box score, and Vladimir Guerrero would be approaching the all-time HR record by now.
One of the simulations took 10,470 games to decide the winner. That is about 65 seasons. So maybe I’m being a little unreasonable, but the alternative is to continue to let inferior teams move on to the next round. The Angels deserve better…