Go grab 10 quarters, a piece of paper and a pen.
Okay, now I want you to take the first quarter and flip it 100 times.
Write down how many times Coin #1 came up heads and how many times it came up tails.
Now, set that quarter aside and repeat the process for Coins #2 through 10.
There’s a good chance that one or more of those quarters had results that were not an even 50/50 split.
In fact, I wouldn’t be surprised if one of those quarters had either heads or tails coming up 55 times. Heck, maybe even 60. Or more!
Now I want you to take that quarter that appears to be coming up heads or tails more often.
Hold it up in the air. Examine it. Look at it. Talk to it. Praise it.
I’m about to ask you to flip it another 100 times, because clearly this quarter is gifted and we’d like to see it showcased.
But before you do that, let me ask you this question – what are you expecting the quarter to do in the second half of this experiment?
Do you expect it to continue it’s run of a high frequency of heads (or tails)? Or do you expect it to be about an even 50/50 split because, hell, that’s how flipping coins works?
The reason I ask is because every year we get the same level of dumbness surrounding the Major League Baseball Home Run Derby.
People get up in arms about how participating in the Home Run Derby somehow ruins sluggers for the second half of the season.
It’s nonsense for the same reason as my quarter example above.
Batters who take part in the Home Run Derby are, naturally, going to be the guys who are among the league leaders in Home Runs headed into the All-Star Break.
What does it take to lead the league in Home Runs? Well, some combination of an actual innate ability to hit for power, yes. But also some degree of luck – a random element that gives you a higher rate of success in driving the ball out of the ballpark than you normally might.
That nudge is enough to get you among the league’s leaders and, most likely, nominated for the Home Run Derby.
What happens after the Home Run Derby isn’t that a batter’s swing is “ruined” from having participated in the contest.
What happens is that the batter was playing a bit above his actual abilities for the first 3 months of the season and, in the 2nd half, played closer to their actual abilities.
In the quarter example above, we may have had a quarter that came up heads 60% of the time in the 1st half of the experiment. In the 2nd half, it’s probably going to come up heads on 50% of our tosses. It’s not that the quarter was ruined by being selected to participate in anything before the 2nd half of the experiment. It’s just that, it’s a quarter, and it has a certain level of expectation for how often it will come up heads or tails. 50%.
Participants in the Home Run Derby are no different.
I went into Baseball Reference and grabbed some of the league’s top Home Run hitters in the first half of the season from 2012 through 2014.
For 2012, I grabbed the 21 players who had 17 or more HR. For 2013, the cut-off was 21 players who had 18 or more. And for 2014, it was 22 who had 17 or more. (I originally grabbed the Top 25, but then it turned out that because of tie-breakers I had to include either more or less and I sided with less because this sample size of 64 players is enough to prove a point.)
For each of those 64 players, I calculated their Home Run Rate for the First Half of the season. Home Run Rate was defined as Home Runs divided by At Bats. (I wanted to exclude walks, because what are the chances of driving a ball out of the park when the bat is on your shoulder?)
I did the same for the Second Half of their seasons.
My sample size was reduced because of players who just didn’t have many At Bats in the Second Half due to an injury and therefore would have made this experiment less worthwhile. Troy Tulowitzki’s sample size of 5 at bats in the Second Half of 2014, for example? Not very reliable.
I decided that 100 At Bats in the Second Half was a nice enough sample size and made that my final cut-off.
So the final tally was a sample of 58 players.
If what I’m saying is wrong, then you’d expect a player’s Home Run Rate to remain more or less constant. How they hit in the First Half should be completely consistent with their Second Half.
But if what I’m saying is right, and a player tends to lead the league in the First Half because of some element of “good luck” that leads to them playing above their true level, then you’d expect their Second Half rate to be lower. (By the way, I expected this to be true in well over half of my 64 player sample.)
If players who were among the First Half leaders in Home Runs tend to have higher Home Run Rates in the Second Half, then I’m just completely wrong about everything and I need to re-consider everything in my life.
So what happened to these guys?
Out of the 58 players examined, 76% saw their Home Run Rate decrease in the Second Half.
Well, that’s fine about my theory of strong First Halves not being something you should rely on to predict a strong Second Half. (Unless you’re prediction is just the rate should go down if it was exceptionally strong in the First Half, in which case, yes, I agree with you.)
But this still doesn’t tackle the whole “Home Run Derby Effect”, right?
Out of my sample of 58 players, 12 of them were participants in the Home Run Derby.
So was there any difference in the frequency of regression among that group of 12 Home Run Derby participants versus the 46 who were not participants?
Out of the 12 Home Run Derby participants, 83% saw their Home Run Rate decrease in the Second Half.
Is 83% significantly different than 76%? I’m inclined to say no. 12 is a small(ish) sample size. If only one of those 12 switched over, we’d be at 75% instead of 83%, so things can change pretty quickly there.
An interesting thing that perhaps illustrates the point. If we take this list 58 players and sort them by First Half Home Run Rate, the top 14 on the list had a downward trend in the Second Half 100% of the time. The bottom 14 on the list? They only had a downward trend 71% of the time.
Of the sample of 58, the average player had a Second Half Home Run Rate that was 79% of their First Half Home Run Rate. The average player included had a First Half Home Run Rate of 6.5% compared to 5.0% in the Second Half.
So if you are worried about your favorite player being included in the Home Run Derby and messing up his swing, check yourself.
From the NL Central, the Chicago Cubs‘ third baseman Kris Bryant and first baseman Anthony Rizzo as well as the Cincinnati Reds‘ third baseman Todd Frazier.
While it’s true that all three will probably see their Home Run Rates decrease in the Second Half of the season, it has nothing to do with the Home Run Derby and everything to do with the fact that, up to this point, they’ve been playing a little bit above their true abilities. And that’s part of why they were invited to participate in the first place.