## Year of the Pitcher?…Think Again

WASHINGTON D.C., August 10^{th} – Five no-hitters. Two of them perfect games. A third perfecto lost. And then there was Brandon Morrow, losing his no-hitter with two outs in the ninth. The 2010 season has been branded as the Year of the Pitcher. But statistical evidence points in a different direction.

RS | RS/G | Z-score | Change | Change% | ABS % | |

2000 |
24971 | 10.28 | 3.34 | N/A | N/A | N/A |

2001 |
23199 | 9.55 | 0.72 | -0.73 | -7.10 | 7.10 |

2002 |
22408 | 9.22 | 0.46 | -0.33 | -3.46 | 3.46 |

2003 |
22978 | 9.46 | 0.40 | 0.24 | 2.60 | 2.60 |

2004 |
23375 | 9.62 | 0.97 | 0.16 | 1.69 | 1.69 |

2005 |
22326 | 9.19 | 0.57 | -0.43 | -4.47 | 4.47 |

2006 |
23599 |
9.71 |
1.30 | 0.52 | 5.66 | 5.66 |

2007 |
23322 |
9.60 |
0.90 | -0.11 | -1.13 | 1.13 |

2008 |
21939 |
9.03 |
1.14 | -0.57 | -5.94 | 5.94 |

2009 |
22419 |
9.23 |
0.43 | 0.20 | 2.21 | 2.21 |

2010 |
14813 |
8.88 |
1.69 | -0.35 | -3.79 | 3.79 |

STDEV |
0.28 |
-0.14 |
-1.37 |
3.81 |
||

AVERAGE |
9.35 |

This chart summarizes the runs-scored data for the 2000-2010 seasons. While the runs scored per game figure for this season is clearly the lowest in the set, there are multiple available factors that determine that it’s a normal fluctuation.

The first is the basic standard deviation. The average of the set is approximately 9.35 RS/G, and the standard deviation is approximately 0.28 RS/G. The z-score column indicates a particular point’s distance from the mean in terms of the standard deviation. Ninety-five percent of the time, a point is expected to be within two standard deviations from the mean, or have a z-score between 0 and 2. As we can see from the chart, the 2010 season fits neatly into that range, with a z-score of approximately 1.7.

The second is the percentile change between each season’s RS/G figure. If we take the absolute value of each percentile change, we find that each year, the runs-scored total differs from the previous year’s total by about 3.81% in one direction or the other. This season hits that mark almost exactly, featuring a 3.79% drop from the previous year.

And there isn’t a definitive trend, either. Of the ten points in the data sent for changes, six were drops from the previous year, and four were increases, leading to the basic average of -1.37%, which equals about -0.14 RS/G over the course of a season.

In conclusion, statistical factors point in the direction of this season being a normal fluctuation in terms of runs scored. We’ve certainly seen dominance from the mound, and this could turn out as being the most pitching-heavy season in recent memory, but it’s well within normal, and could easily go right back the other way at the drop of a hat.

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Are strike zones being enforced in a similar way to years past or is there an effort to call a smaller strike zone this year?

I’m sorry, but this is an ill informed use of an inappropriate test for the question at hand. You’re calculating Z-scores to use as evidence that a sample set has a true mean (mu), a process that is completely backward. Even if applied correctly, with your nine degrees of freedom, the 95% confidence interval would be at 2.26 standard deviations not 2, but regardless, is violated by your observation from 2000. In fact, there is less than 1% chance that we get an RS/G of 10.28 in 2000 if there is a true, unchanging, RS/G baseline of 9.35. This should be a red flag for your method. On top of that, let’s consider these data for the narrative behind them. Should we expect RS/G to remain constant? I’d say no. Over a ten year stretch, it’s probably safe to assume more than half the hitters and pitchers have changed. To gut-check this assumption, I took a quick look at the leader boards for 2009 and 2000 for hitting and pitching and at most saw one or two names in each category that were the same. So at the very least, the hitters and pitchers producing the most runs have changed. Add to that that rules change and new stadiums are built, and it’s easy to see why scoring should not be a constant across time. And doesn’t it feel like there are more good pitchers now? Luckilly, we have trend stats to check.

I can see that you have some understanding that there is noise to any data point by your use of standard deviation. As such, I am doubly confused that you dismiss a trend because in four of the ten years, the RS/G went up on the previous year instead of down. Did you make a graph of these data? It looks like there’s a trend there. I ran the numbers using simple regression, which is by no means a perfect tool for analyzing this sample, but will allow for a trend (z-scores don’t).

The results: a coefficient of -.07 for time. This indicates that, over the period you look at, the trend was that each year RS/G went down by said amount. That’s not an unsubstantial number; it suggests that, over a 14 year period, we’d expect scoring to drop by a full run per game. And to re-introduce confidence intervals, with the data at hand, we can be more than 95% certain that there is a downward trend w/r/t scoring.

This says nothing about whether 2010 is The Year of the Pitcher, though. By your method, it seems to me that you are concerned with whether there is an observably different level of pitching talent this year than in the previous nine years. There are statistical tools that will allow us to look for “breaks” in data sets that are largely dependent on time, and that would be the appropriate tool to use here. There are several problems with this though: (1) being that you wouldn’t be separating out the talent of pitchers from hitters and (2) being that in this sample size and without several years of data after 2010, it would be almost impossible to isolate this break, to name two of them.

In the end, this YotP question is semantic, really. It is perfectly fine to call this The Year of the Pitcher based only on the fact that scoring is the lowest it’s been in a decade. The “why” question of pitcher talent needs only apply if you want it to. We can’t say that this year’s scoring level isn’t luck based, but we don’t correct WAR production for BABIP either. If you’ve produced, it doesn’t matter for analyzing the past whether it was due to luck or not. There is no question that, so far this year, pitching has been successful at a rate that is better than pitching has been successful across whole years previously. To that extent, it has been The Year of the Pitcher.

Anyway, best of luck in your future calculations.

Cheers,

Jason

Nick – I have no idea, but I haven’t seen any evidence to support the notion that a smaller strike zone is being called.

Jason – I only searched for a simple trend, didn’t run a regression. Thanks for the heads-up on that. I don’t recall claiming that RS/G should remain constant, I only said that it should constantly fall in a specific range. You’re right in that we can call this the Year of the Pitcher, because of the low run totals. I suppose that my point was more along the line “this isn’t that far out of the ordinary”, or that “this is probably not sustainable.” Thanks for the advice on my method, I’ll try to apply some of that in the future.

Thanks,

Arjuna

Arjuna – I know you didn’t explicitly claim that RS/G should remain constant, but the necessary implication in running a t-test is that there is a true mean. The first statement you make, that this is not “that far out of the ordinary,” is a fair point but is in contradiction with any belief that there isn’t a trend. This year’s data point is second furthest out of the ordinary as you define it. It’s less out of the ordinary than 2000, but it’s still more out of the ordinary (further from the sample mean) than any other data point. Your second statement, “this is probably unsustainable,” is pretty contingent on whether this level of scoring is out of the ordinary or what we’d expect. If we think that there has been a trend of RS/G decreasing and don’t see any reason that the hitters should get better or the pitchers should get worse next year, then there is no reason for this to be unsustainable. It’s probably slightly more likely that RS/G will be higher next year, but with all the noise and a somewhat observable trend, there is almost as good chance that it will go down again. I’m just not sure we should speculate out of sample with this kind of data. The explanatory value of time isn’t high enough to bet one way or the other. Anyway, I appreciate all the healthy discussion.

The mere fact that this IS the lowest RS/G in the last decade, would mean this IS the year of the pitcher. I don’t think anyone ever contended that pitchers are having an unprecedented domination of hitters to the extent that it’s a statistical anomaly. I think the phrase “year of the pitcher” fits perfectly with the fact that, yes, RS/G is down compared to recent years and, yes, there have been an odd amount of perfect games/no-hitters.

Don’t get me wrong, i’m impressed with the statistical analysis, and i actually found it pretty intriguing. I just don’t think it does anything to disprove this being a year of the pitcher. In fact, I think it did more to prove that it really IS the most pitcher friendly year of the last decade.

This seems like a good place to post a theory about why runs are down this year. With the advent and improvement of pitch tracking abilities, I wonder if pitchers are increasingly taking advantage of this new information to exploit the vulnerabilities of hitters. What do you think?

jd1234 – I don’t think that advanced data is a major factor. I don’t really know if anything is a major factor. However, I’m inclined to be skeptical, as I doubt that there’s been a league-wide renaissance in terms of paying attention to advanced methods.

“In conclusion, statistical factors point in the direction of this season being a normal fluctuation in terms of runs scored. ”

No, they absolutely don’t. Statistical factors point that this COULD be a normal fluctuation. Not that it is. That is an important distinction.

Arjuna – I put your numbers in a spreadsheet and got a different average and standard deviation. Did you use a larger data set to get those two numbers?

Additionally, I think Rich C. gets at an important point: you should probably look at this year as a fluctuation from the past and then ask whether this year is likely in context of what we knew ahead of time. We could get pretty Bayesian here, but let’s keep it simple. The first and most important question is: what is a baseline year? To do this, we need a sample set. OK, we have one. Now, do you include 2000 when forming your a priori hypothesis? I wouldn’t — ten years and nine years are completely arbitrary, so we can decide to call the past nine years an era and see whether this year is a break if we want. You did, so let’s look at that first.

If you average 2000-2009 to get a baseline year, the probability of getting 8.88 runs or fewer per game in 2010 is considered to be about 4% (mean 9.49, SD .357). If you exclude 2000 from your data set, which seems like a number from the height of the steroid era to me, your Gaussian probability of seeing fewer than 8.88 runs per game is about 1.5% (mean 9.40, SD .238).

Essentially, we need to define what we think a normal year is before we test The Year of the Pitcher. In order to ask if this question, it’s necessary to have an opinion as to the baseline we’re comparing against, and you can choose any criteria you want for that baseline, especially in a statistically messy data set like baseball necessarily produces. Looking at anything longer than 3 or 4 years is probably silly, in fact (here it would be helpful to look at player attrition rates for guidance). That said, I feel pretty comfortable at choosing to look at a decade, then throwing out 2000 as The Year of the Hitter, which is a bigger outlier than this year.

So, with 2000 included, we are 96% sure that underlying factors have shifted in the direction of pitching. With 2000 excluded, we are better than 98.5% sure that underlying talent levels have shifted. We can’t know how much it has shifted using this method, but, as you can see, we are pretty sure that it has. (Key caveats remain that this is an incomplete season, and we haven’t looked at whether run scoring increases as the year goes, etc.)

Isn’t RS/G a measure of pitching+defense? I’m still relatively new to sabermetrics, but wouldn’t a better measure be to subtract out the Defensive Runs per game to get Pitching Runs per game? While I know that defensive metrics aren’t up to par, this would help normalize each year.

Also, it might be good to look at the pooled FIP, xFIP, etc. of all qualified pitchers, weighting by IP and ignoring the constant added per year to scale to ERA.

Defensive metrics measure a player’s distance above/below average. So for every year, the sum of all defensive runs should be 0. However, I think the decrease in runs scored results more from an increased focus on defense than improved pitching talent.