(57) Playoffs part I: The law of large numbers

Tiff asked me a long time ago why, IMO, the Cards can win convincingly in the regular season and then play so poorly in the playoffs.  I had 2 ideas at the time – luckily she asked me before Interleague play started, because right now I am inclined to say that the AL is just flat out better than the NL.  But, sticking to my original arguments, I will say that (1) the bigger the sample (more games) the more likely you are to accurately determine the best team, and (2) the Cards are fundamentally built to win in the regular season and this usually does not translate well into playoff success.

We all have heard the phrase, "The season is a marathon, not a sprint."  This is a valid statement and is often used in reference to a losing streak.  Ironically, this phrase is of some use to Cards fans currently to comfort us coming off of a 8-game losing streak.  The point is that no matter how bad we are doing currently, or have been lately, it is a long season in which you can work out kinks, reemerge from slumps, and just generally endure bad luck.  No matter how good any team is, baseball happens, and no one wins 162 games in a season. 

The long season translates into the law of large numbers (for you math / statistics geeks out there, like me) in that, the more trials you have, the more likely the results are to resemble the phenomenon you are trying to measure.  The large number of repetition reduces the effect of "luck" and streaks.  For example, take a series of coin tosses.  We all know that, with a fair coin, you have a 50% chance of getting heads or tails.  However, it would not be too weird for you to get all heads if you only flipped the coin 3 times.  But if you flipped the coin 100 times, it would be extremely strange if you got 100 heads.  More likely would be to have something close to 50 heads and 50 tails plus or minus a few.  Within the 100 flips there may have been several streaks – 4 heads here, 3 tails here, 10 tails, 7 heads, etc. – but in the end they cancel each other out.  In 1000 flips, you are likely to be even closer to 50% than you were in 100 flips, and so on.  It works with any probability.  The more trials you have, the better you can approximate the "true" probability from your sample.  This can be applied to baseball as well.

In the regular season we have 162 games vs. only 19 games in the playoffs (really, we should count these individually as 5, 7, and 7 since each series decides once and for all who continues and who dies).  So if team A is better than team B, we are much more likely to see that over 162 games vs. either 5 or 7 games, and the difference in accuracy between these two samples is anything but trivial.  Hence the large impact of "luck" and "hotness" and "streakiness" that permeate the post season.  These streaks are meaningless over the long season, just as the 3 game sweep of the Cards by the Cubbies will be meaningless when we finish the regular season 15 games ahead of them.  Given that the Cardinals are the best team, they are exponentially more likely to demonstrate that over 162 games than any 5 or 7 game series.

See the next post for part II: Built for the long haul.

2 Comments

Marc,
Hey, guess what….I can comment on your site again!

I loved this post….very well written and touched on a lot of good points that I think you’re right about. In fact, I was thinking the other day that for the last two years the Cardinals have been the best team and lost in the playoffs. So, maybe this year if they aren’t the best team, they will win?? :) Ok, maybe not, but we can hope.

I most agreed with your comment on pitching. That’s why we got beat by the Astros. Pitching. Sure, Albert extended it one more game, but it came down to pitching. That’s why I think come the trade deadline we really need another arm. We have enough offense to produce if we have the pitching to keep the other team’s offense down.

The only way I would want another bat is if it comes attached to a killer outfielder arm. I can’t remember the last time I saw one of our LF/RF nail a runner at home.

Tiffany

http://redbirdfever.mlblogs.com/

I’m glad you can comment again!! I was starting to wonder if it was even worth keeping my blog… I couldn’t get any comments, and then I couldn’t log in at all!

I’m glad you liked the post, it only took about 2 months to get around to writing it :)

I made some edits, finished my thought on the team structure, and broke it into parts for easier reading. Hope this is what you were looking for.

I believe as you do regarding pitching being our priority. I think we need improvement everywhere, but 1 starting pitcher goes a looooooong way. If you don’t believe me, rewatch games 2 and 6 of the NLCS.

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