Weird Pitching Decisions Almanac in 2010 December 24, 2010
Posted by tomflesher in Baseball.Tags: baseball-reference.com, Carl Pavano, Cheap Wins, Clayton Kershaw, Colby Lewis, Cubs, Felix Hernandez, Francisco Rodriguez, Hiroki Kuroda, Jeremy Affeldt, John Lackey, Justin Verlander, Mariners, Phil Hughes, Red Sox, Rodrigo Lopez, Roy Oswalt, Royals, Tommy Hanson, Tough Losses, Tyler Clippard, vulture wins
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I’m a big fan of weird pitching decisions. A pitcher with a lot of tough losses pitches effectively but stands behind a team with crappy run support. A pitcher with a high proportion of cheap wins gets lucky more often than not. A reliever with a lot of vulture wins might as well be taking the loss.
In an earlier post, I defined a tough loss two ways. The official definition is a loss in which the starting pitcher made a quality start – that is, six or more innings with three or fewer runs. The Bill James definition is the same, except that James defines a quality start as having a game score of 50 or higher. In either case, tough losses result from solid pitching combined with anemic run support.
This year’s Tough Loss leaderboard had 457 games spread around 183 pitchers across both leagues. The Dodgers’ Hiroki Kuroda led the league with a whopping eight starts with game scores of 50 or more. He was followed by eight players with six tough losses, including Justin Verlander, Carl Pavano, Roy Oswalt, Rodrigo Lopez, Colby Lewis, Clayton Kershaw, Felix Hernandez, and Tommy Hanson. Kuroda’s Dodgers led the league with 23 tough losses, followed by the Mariners and the Cubs with 22 each.
There were fewer cheap wins, in which a pitcher does not make a quality start but does earn the win. The Cheap Win leaderboard had 248 games and 136 pitchers, led by John Lackey with six and Phil Hughes with 5. Hughes pitched to 18 wins, but Lackey’s six cheap wins were almost half of his 14-win total this year. That really shows what kind of run support he had. The Royals and the Red Sox were tied for first place with 15 team cheap wins each.
Finally, a vulture win is one for the relievers. I define a vulture win as a blown save and a win in the same game, so I searched Baseball Reference for players with blown saves and then looked for the largest number of wins. Tyler Clippard was the clear winner here. In six blown saves, he got 5 vulture wins. Francisco Rodriguez and Jeremy Affeldt each deserve credit, though – each had three blown saves and converted all three for vulture wins. (When I say “converted,” I mean “waited it out for their team to score more runs.”)
Diagnosing the AL December 22, 2010
Posted by tomflesher in Baseball, Economics.Tags: 2010, American League, baseball-reference.com, R, regression, statistics, Year of the Pitcher
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In the previous post, I crunched some numbers on a previous forecast I’d made and figured out that it was a pretty crappy forecast. (That’s the fun of forecasting, of course – sometimes you’re right and sometimes you’re wrong.) The funny part of it, though, is that the predicted home runs per game for the American League was so far off – 3.4 standard errors below the predicted value – that it’s highly unlikely that the regression model I used controls for all relevant variables. That’s not surprising, since it was only a time trend with a dummy variable for the designated hitter.
There are a couple of things to check for immediately. The first is the most common explanation thrown around when home runs drop – steroids. It seems to me that if the drop in home runs were due to better control of performance-enhancing drugs, then it should mostly be home runs that are affected. For example, intentional walks should probably be below expectation, since intentional walks are used to protect against a home run hitter. Unintentional walks should probably be about as expected, since walks are a function of plate discipline and pitcher control, not of strength. On-base percentage should probably drop at a lower magnitude than home runs, since some hits that would have been home runs will stay in the park as singles, doubles, or triples. Finally, slugging average should drop because a loss in power without a corresponding increase in speed will lower total bases.
I’ll analyze these with pretty new R code behind the cut.
What Happened to Home Runs This Year? December 22, 2010
Posted by tomflesher in Baseball, Economics.Tags: baseball-reference.com, forecasting, home runs, R, regression, standard error, statistics, time series, Year of the Pitcher
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I was talking to Jim, the writer behind Apparently, I’m An Angels Fan, who’s gamely trying to learn baseball because he wants to be just like me. Jim wondered aloud how much the vaunted “Year of the Pitcher” has affected home run production. Sure enough, on checking the AL Batting Encyclopedia at Baseball-Reference.com, production dropped by about .15 home runs per game (from 1.13 to .97). Is that normal statistical variation or does it show that this year was really different?
In two previous posts, I looked at the trend of home runs per game to examine Stuff Keith Hernandez Says and then examined Japanese baseball’s data for evidence of structural break. I used the Batting Encyclopedia to run a time-series regression for a quadratic trend and added a dummy variable for the Designated Hitter. I found that the time trend and DH control account for approximately 56% of the variation in home runs per year, and that the functional form is
with t=1 in 1955, t=2 in 1956, and so on. That means t=56 in 2010. Consequently, we’d expect home run production per game in 2010 in the American League to be approximately
That means we expected production to increase this year and it dropped precipitously, for a residual of -.28. The residual standard error on the original regression was .1092, so on 106 degrees of freedom, so the t-value using Texas A&M’s table is 1.984 (approximating using 100 df). That means we can be 95% confident that the actual number of home runs should fall within .1092*1.984, or about .2041, of the expected value. The lower bound would be about 1.05, meaning we’re still significantly below what we’d expect. In fact, the observed number is about 3.4 standard errors below the expected number. In other words, we’d expect that to happen by chance less than .1% (that is, less than one tenth of one percent) of the time.
Clearly, something else is in play.
Home Run Derby: Does it ruin swings? December 15, 2010
Posted by tomflesher in Baseball, Economics.Tags: Baseball, baseball-reference.com, Chris Young, Corey Hart, David Ortiz, Hanley Ramirez, home run derby, home runs, Matt Holliday, Miguel Cabrera, Nick Swisher, Vernon Wells
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Earlier this year, there was a lot of discussion about the alleged home run derby curse. This post by Andy on Baseball-Reference.com asked if the Home Run Derby is bad for baseball, and this Hardball Times piece agrees with him that it is not. The standard explanation involves selection bias – sure, players tend to hit fewer home runs in the second half after they hit in the Derby, but that’s because the people who hit in the Derby get invited to do so because they had an abnormally high number of home runs in the first half.
Though this deserves a much more thorough macro-level treatment, let’s just take a look at the density of home runs in either half of the season for each player who participated in the Home Run Derby. Those players include David Ortiz, Hanley Ramirez, Chris Young, Nick Swisher, Corey Hart, Miguel Cabrera, Matt Holliday, and Vernon Wells.
For each player, plus Robinson Cano (who was of interest to Andy in the Baseball-Reference.com post), I took the percentage of games before the Derby and compared it with the percentage of home runs before the Derby. If the Ruined Swing theory holds, then we’d expect
The table below shows that in almost every case, including Cano (who did not participate), the density of home runs in the pre-Derby games was much higher than the post-Derby games.
| Player | HR Before | HR Total | g(Games) | g(HR) | Diff |
| Ortiz | 18 | 32 | 0.54321 | 0.5625 | 0.01929 |
| Hanley | 13 | 21 | 0.54321 | 0.619048 | 0.075838 |
| Swisher | 15 | 29 | 0.537037 | 0.517241 | -0.0198 |
| Wells | 19 | 31 | 0.549383 | 0.612903 | 0.063521 |
| Holliday | 16 | 28 | 0.54321 | 0.571429 | 0.028219 |
| Hart | 21 | 31 | 0.549383 | 0.677419 | 0.128037 |
| Cabrera | 22 | 38 | 0.530864 | 0.578947 | 0.048083 |
| Young | 15 | 27 | 0.549383 | 0.555556 | 0.006173 |
| Cano | 16 | 29 | 0.537037 | 0.551724 | 0.014687 |
Is this evidence that the Derby causes home run percentages to drop off? Certainly not. There are some caveats:
- This should be normalized based on games the player played, instead of team games.
- It would probably even be better to look at a home run per plate appearance rate instead.
- It could stand to be corrected for deviation from the mean to explain selection bias.
- Cano’s numbers are almost identical to Swisher’s. They play for the same team. If there was an effect to be seen, it would probably show up here, and it doesn’t.
Once finals are up, I’ll dig into this a little more deeply.
Quickie: Ryan Howard's Choke Index October 25, 2010
Posted by tomflesher in Baseball.Tags: baseball-reference.com, binomial distribution, Choke Index, Phillies, Ryan Howard, statistics
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The Choke Index is alive and well.
Previous to 2010, Ryan Howard of the Philadelphia Phillies hit home runs in three consecutive postseasons. He managed 7 in his 140 plate appearances, averaging out to .05 home runs per plate appearance. Not too shabby. It’s a bit below his regular season rate of about .067, but there are a bunch of things that could account for that.
This year, Ryan made 38 plate appearances and hit a grand total of 0 home runs in the postseason. What’s the likelihood of that happening? I use the Choke Index (one minus the probability of hitting 0 home runs in a given number of plate appearances) to measure that. As always, the closer a player gets to 1, the more unlikely his homer-free streak is.
The binomial probability can be calculated using the formula
Or, since we’re looking for the probability of an event NOT occurring,
or
using his career postseason numbers. That means that Ryan Howard’s 2010 postseason Choke Index is .858. Pretty impressive!
The 600 Home Run Almanac July 28, 2010
Posted by tomflesher in Baseball, Economics.Tags: 600 home runs, A-Rod, Alex Rodriguez, Babe Ruth, Barry Bonds, Baseball, baseball-reference.com, Hank Aaron, Jim Thome, Ken Griffey Jr., Manny Ramirez, probability, Sammy Sosa, statistics, Willie Mays
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People are interested in players who hit 600 home runs, at least judging by the Google searches that point people here. With that in mind, let’s take a look at some quick facts about the 600th home run and the people who have hit it.
Age: There are six players to have hit #600. Sammy Sosa was the oldest at 39 years old in 2007. Ken Griffey, Jr. was 38 in 2007, as were Willie Mays in 1969 and Barry Bonds in 2002. Hank Aaron was 37. Babe Ruth was the youngest at 36 in 1931. Alex Rodriguez, who is 35 as of July 27, will almost certainly be the youngest player to reach 600 home runs. If both Manny Ramirez and Jim Thome hang on to hit #600 over the next two to three seasons, Thome (who was born in August of 1970) will probably be 42 in 2012; Ramirez (born in May of 1972) will be 41 in 2013. (In an earlier post that’s when I estimated each player would hit #600.) If Thome holds on, then, he’ll be the oldest player to hit his 600th home run.
Productivity: Since 2000 (which encompasses Rodriguez, Ramirez, and Thome in their primes), the average league rate of home runs per plate appearances has been about .028. That is, a home run was hit in about 2.8% of plate appearances. Over the same time period, Rodriguez’ rate was .064 – more than double the league average. Ramirez hit .059 – again, over double the league rate. Thome, for his part, hit at a rate of .065 home runs per plate appearance. From 2000 to 2009, Thome was more productive than Rodriguez.
Standing Out: Obviously it’s unusual for them to be that far above the curve. There were 1,877,363 plate appearances (trials) from 2000 to 2009. The margin of error for a proportion like the rate of home runs per plate appearance is
Ordinarily, we expect a random individual chosen from the population to land within the space of 
That means that all three of the players are well without that confidence interval. (However, it’s likely that home run hitting is highly correlated with other factors that make this test less useful than it is in other situations.)
Alex’s Drought: Finally, just how likely is it that Alex Rodriguez will go this long without a home run? He hit his last home run in his fourth plate appearance on July 22. He had a fifth plate appearance in which he doubled. Since then, he’s played in five games totalling 22 plate appearances, so he’s gone 23 plate appearances without a home run. Assuming his rate of .064 home runs per plate appearance, how likely is that? We’d expect (.064*23) = about 1.5 home runs in that time, but how unlikely is this drought?
The binomial distribution is used to model strings of successes and failures in tests where we can say clearly whether each trial ended in a “yes” or “no.” We don’t need to break out that tool here, though – if the probability of a home run is .064, the probability of anything else is .936. The likelihood of a string of 23 non-home runs is
It’s only about 22% likely that this drought happened only by chance. The better guess is that, as Rodriguez has said, he’s distracted by the switching to marked baseballs and media pressure to finally hit #600.
Cheap Wins July 16, 2010
Posted by tomflesher in Baseball.Tags: baseball-reference.com, Bill James, Brian Bannister, Cheap Wins, Joe Saunders, John Danks, John Lackey, R.A. Dickey, Ricky Romero, Roy Halladay, Tim Lincecum, Tim Wakefield, Tough Losses, Yovani Gallardo
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The opposite of the Tough Loss discussed below (which R.A. Dickey unfortunately experienced tonight in a duel with Tim Lincecum) is a Cheap Win. Logically, since a Tough Loss is a loss in a quality start, a Cheap Win (invented by Bill James) is a win in a non-quality start – that is, a start with a game score of below 50 (or, officially, a start with fewer than 6.0 innings pitched or more than 3 runs allowed).
The Chicago White Sox’ starter, John Danks, picked up a Cheap Win in Thursday’s game against the Twins. Although he pitched six innings, he gave up six runs (all earned) in the second inning, leading to an abysmal game score of 33. Danks had two of last year’s 304 Cheap Wins. Ricky Romero led the pack with six, and Joe Saunders and Tim Wakefield were both among the six pitchers with five Cheap Wins. Even Roy Halladay had two.
Through the beginning of the All-Star Break, there have been 136 Cheap Wins in 2010. That includes one by my current favorite player, Yovani Gallardo. John Lackey is already up to 5, and Brian Bannister is knocking on the door with 4.
It’s hard to read too much into the tea leaves of Cheap Wins, since they’re not all created equal. In general, they represent a pitcher sliding a little bit off his game, but his team upping their run production to rescue him. To that end, Cheap Wins might be a better measure of a team’s ability than Tough Losses, since, while Tough Losses show a pitcher maintaining himself under fire, Cheap Wins represent an ability to hit in the clutch (assuming that run production in Cheap Wins is significantly different from run production in other games). That’s hard to validate without doing a bit more work, but it’s a project to consider.
More on Home Runs Per Game July 9, 2010
Posted by tomflesher in Baseball, Economics.Tags: Baseball, baseball-reference.com, Chow test, home runs, Japan, Japanese baseball, R, Rays, regression, replication
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In the previous post, I looked at the trend in home runs per game in the Major Leagues and suggested that the recent deviation from the increasing trend might have been due to the development of strong farm systems like the Tampa Bay Rays’. That means that if the same data analysis process is used on data in an otherwise identical league, we should see similar trends but no dropoff around 1995. As usual, for replication purposes I’m going to use Japan’s Pro Baseball leagues, the Pacific and Central Leagues. They’re ideal because, just like the American Major Leagues, one league uses the designated hitter and one does not. There are some differences – the talent pool is a bit smaller because of the lower population base that the leagues draw from, and there are only 6 teams in each league as opposed to MLB’s 14 and 16.
As a reminder, the MLB regression gave us a regression equation of
where 
Just examining the data on home runs per game from the Japanese leagues, the trend looks significantly differe
nt. Instead of the rough U-shape that the MLB data showed, the Japanese data looks almost M-shaped with a maximum around 1984. (Why, I’m not sure – I’m not knowledgeable enough about Japanese baseball to know what might have caused that spike.) It reaches a minimum again and then keeps rising.
After running the same regression with t=1 in 1950, I got these results:
| Estimate | Std. Error | t-value | p-value | Signif | |
| B0 | 0.2462 | 0.0992 | 2.481 | 0.0148 | 0.9852 |
| t | 0.0478 | 0.0062 | 7.64 | 1.63E-11 | 1 |
| tsq | -0.0006 | 0.00009 | -7.463 | 3.82E-11 | 1 |
| DH | 0.0052 | 0.0359 | 0.144 | 0.8855 | 0.1145 |
This equation shows two things, one that surprises me and one that doesn’t. The unsurprising factor is the switching of signs for the t variables – we expected that based on the shape of the data. The surprising factor is that the designated hitter rule is insignificant. We can only be about 11% sure it’s significant. In addition, this model explains less of the variation than the MLB version – while that explained about 56% of the variation, the Japanese model has an 
There’s a slightly interesting pattern to the residual home runs per game (
it isn’t as pronounced, this data also shows a spike – but the spike is at t=55, so instead of showing up in 1995, the Japan leagues spiked around the early 2000s. Clearly the same effect is not in play, but why might the Japanese leagues see the same effect later than the MLB teams? It can’t be an expansion effect, since the Japanese leagues have stayed constant at 6 teams since their inception.
Incidentally, the Japanese league data is heteroskedastic (Breusch-Pagan test p-value .0796), so it might be better modeled using a generalized least squares formula, but doing so would have skewed the results of the replication.
In order to show that the parameters really are different, the appropriate test is Chow’s test for structural change. To clean it up, I’m using only the data from 1960 on. (It’s quick and dirty, but it’ll do the job.) Chow’s test takes
where 
The critical value for 90% significance at 4 and 192 degrees of freedom would be 1.974 according to Texas A&M’s F calculator. That means we don’t have enough evidence that the parameters are different to treat them differently. This is probably an artifact of the small amount of data we have.
In the previous post, I looked at the trend in home runs per game in the Major Leagues and suggested that the recent deviation from the increasing trend might have been due to the development of strong farm systems like the Tampa Bay Rays’. That means that if the same data analysis process is used on data in an otherwise identical league, we should see similar trends but no dropoff around 1995. As usual, for replication purposes I’m going to use Japan’s Pro Baseball leagues, the Pacific and Central Leagues. They’re ideal because, just like the American Major Leagues, one league uses the designated hitter and one does not. There are some differences – the talent pool is a bit smaller because of the lower population base that the leagues draw from, and there are only 6 teams in each league as opposed to MLB’s 14 and 16.
As a reminder, the MLB regression gave us a regression equation of
where 
Just examining the data on home runs per game from the Japanese leagues, the trend looks significantly different. Instead of the rough U-shape that the MLB data showed, the Japanese data looks almost M-shaped with a maximum around 1984. (Why, I’m not sure – I’m not knowledgeable enough about Japanese baseball to know what might have caused that spike.) It reaches a minimum again and then keeps rising.
After running the same regression with t=1 in 1950, I got these results:
| Estimate | Std. Error | t-value | p-value | Signif | |
| B0 | 0.2462 | 0.0992 | 2.481 | 0.0148 | 0.9852 |
| t | 0.0478 | 0.0062 | 7.64 | 1.63E-11 | 1 |
| tsq | -0.0006 | 0.00009 | -7.463 | 3.82E-11 | 1 |
| DH | 0.0052 | 0.0359 | 0.144 | 0.8855 | 0.1145 |
This equation shows two things, one that surprises me and one that doesn’t. The unsurprising factor is the switching of signs for the t variables – we expected that based on the shape of the data. The surprising factor is that the designated hitter rule is insignificant. We can only be about 11% sure it’s significant. In addition, this model explains less of the variation than the MLB version – while that explained about 56% of the variation, the Japanese model has an 
There’s a slightly interesting pattern to the residual home runs per game (
it isn’t as pronounced, this data also shows a spike – but the spike is at t=55, so instead of showing up in 1995, the Japan leagues spiked around the early 2000s. Clearly the same effect is not in play, but why might the Japanese leagues see the same effect later than the MLB teams? It can’t be an expansion effect, since the Japanese leagues have stayed constant at 6 teams since their inception.
Incidentally, the Japanese league data is heteroskedastic (Breusch-Pagan test p-value .0796), so it might be better modeled using a generalized least squares formula, but doing so would have skewed the results of the replication.
In order to show that the parameters really are different, the appropriate test is Chow’s test for structural change. To clean it up, I’m using only the data from 1960 on. (It’s quick and dirty, but it’ll do the job.) Chow’s test takes
Back when it was hard to hit 55… July 8, 2010
Posted by tomflesher in Baseball, Economics.Tags: Baseball, baseball-reference.com, home runs, R, regression, sabermetrics, Stuff Keith Hernandez Says, talent pool dilution, Willie Mays, Year of the Pitcher
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Last night was one of those classic Keith Hernandez moments where he started talking and then stopped abruptly, which I always like to assume is because the guys in the truck are telling him to shut the hell up. He was talking about Willie Mays for some reason, and said that Mays hit 55 home runs “back when it was hard to hit 55.” Keith coyly said that, while it was easy for a while, it was “getting hard again,” at which point he abruptly stopped talking.
Keith’s unusual candor about drug use and Mays’ career best of 52 home runs aside, this pinged my “Stuff Keith Hernandez Says” meter. After accounting for any time trend and other factors that might explain home run hitting, is there an upward trend? If so, is there a pattern to the remaining home runs?
The first step is to examine the data to see if there appears to be any trend. Just looking at it, there appears to be a messy U shape with a minimum around t=20, which indicates a quadratic trend. That means I want to include a term for time and a term for time squared.
Using the per-game averages for home runs from 1955 to 2009, I detrended the data using t=1 in 1955. I also had to correct for the effect of the designated hitter. That gives us an equation of the form
The results:
| Estimate | Std. Error | t-value | p-value | Signif | |
| B0 | 0.957 | 0.0328 | 29.189 | 0.0001 | 0.9999 |
| t | -0.0188 | 0.0028 | -6.738 | 0.0001 | 0.9999 |
| tsq | 0.0004 | 0.00005 | 8.599 | 0.0001 | 0.9999 |
| DH | 0.0911 | 0.0246 | 3.706 | 0.0003 | 0.9997 |
We can see that there’s an upward quadratic trend in predicted home runs that together with the DH rule account for about 56% of the variation in the number of home runs per game in a season (
Then, I needed to look at the difference between the predicted number of home runs per game and the actual number of home runs per game, which is accessible by subtracting
This represents the “abnormal” number of home runs per year. The question then becomes, “Is there a patt
ern to the number of abnormal home runs?” There are two ways to answer this. The first way is to look at the abnormal home runs. Up until about t=40 (the mid-1990s), the abnormal home runs are pretty much scattershot above and below 0. However, at t=40, the residual jumps up for both leagues and then begins a downward trend. It’s not clear what the cause of this is, but the knee-jerk reaction is that there might be a drug use effect. On the other hand, there are a couple of other explanations.
The most obvious is a boring old expansion effect. In 1993, the National League added two teams (the Marlins and the Rockies), and in 1998 each league added a team (the AL’s Rays and the NL’s Diamondbacks). Talent pool dilution has shown up in our discussion of hit batsmen, and I believe that it can be a real effect. It would be mitigated over time, however, by the establishment and development of farm systems, in particular strong systems like the one that’s producing good, cheap talent for the Rays.
