The baseball season comes down to series of weighted coin flips. It might seem overly simplistic, but over a season the good teams win around 60 percent of their games (a 97.2 win pace), while the bad teams win around 40 percent of their games, a 64.8 win pace.
Most teams lie somewhere in the middle, where the Rays are projected. Most projections that are currently out have the Rays winning between 81 and 85 games. The Rays are expected to be flipping a slightly weighted coin. 162 games is a lot, and sounds like it should remove a lot of the variance. It should reason that teams end up where they deserve.
It is only nature to wonder why the Texas Rangers won 95 games despite having a run differential of +8, which equates to an 82-win rate by pythagorean win percentage. On the other side of the coin, the Rays won 68 games while having a run differential of -41, which would equate to a 77-win season by pythagorean win percentage.
The Rangers over-performed by 13 wins and the Rays under-performed by nine wins. There are factors outside of luck, to be sure, but to not recognize as most of the difference not come from luck would be disingenuous.
For this exercise I’m going to take a fictional team that has exactly a 50 percent chance to win every game. To simulate the season, I will flip a coin 162 times. Heads will be a win and tails will be a loss. This team would be expected to win 81 games while losing 81 games.
81 would be the mean outcome, but due to variance will not be the outcome in most trials.
Warning: math ahead.
Variance = N n (1-n)
N = Number of trials
n = Probability of successful outcome (0.5 = 50%)
The variance for a 162 trial sample is 40.5.
Standard deviation is the square root of variance. The standard deviation of a 162 trial sample would be 6.36.
What are the chances that this team wins x games?
P(x) = N!/(x!(N-x)) n^x (1-n)^(N-x)
P(x) = Probability of success
N = Number of Trails (162)
n = Odds of success (0.5 = 50%)
x = Number of successes (wins)
The mean outcome of 81 wins only occurs 6.25 percent of the time. The 75-87 range, plus or minus six, occurs 69.23 percent of the time. Over 30 percent of the time, the wins will be distributed outside of that 12 win range.
69 and 93 wins were used as the cutoff, because that’s where the odds fell below one percent for any individual outcome. However, 68 and fewer occurs 2.46 percent of the time. The same is true for 94 or more. This team that is flipping coins has a 9.07 percent chance of ending the season with 90+ wins.
The Gambler’s fallacy of expecting things to even out because something has happened more often than would be expected is not true. Past events do not alter the future odds when they are static. Banked wins matter. Once you start the season getting ahead or behind will have a large effect on where you end. If you start the season 7-0 like the Orioles did last year, or 0-6, this will move the mean outcome three to three and a half wins to end the season.
How does this apply to the Rays?
The Rays are currently projected to win a few more than they lose and have a chance to compete for the wild card. 162 games sounds like a lot, but in the grand scheme of things, it really isn’t. There is still a ton of variance that exists in a sample this small.
It is unlikely but still possible the Rays will win 90+ games if they play like a .500 team similar to the Rangers last season. As a group, they will have to overperform their median outcomes. Some individual players will have to put up career years.
The good news is, as a whole, they are on the right side of 30. Improvement or career years wouldn’t shock anybody from just about any of their younger players. Evan Longoria, Xavier Cedeno, and Danny Farquhar are the only Rays players over 30 years old.
The Rays’ front office has done a good job of building up depth where they can while having many of their best prospects only a call away in Triple-A Durham. Nothing will prevent the team from really hurting if someone like Kevin Kiermaier misses significant time again.
Not all of the 2016 68-win campaign can be attributed to luck, but a certain part can. They played badly at times, especially during the 3-24 stretch.
In life, you only get to run it once. You will be remembered on that binary outcome of wins and losses. Whether you deserve it or not, time will remember what happened. Hopefully the 2017 Rays will put some wins on the board.