As much as I love the Angels, I can’t take Jered’s side on this one.

Today, I was browsing the voting results from the various awards being voted on. Each league’s Cy Young award voting included the requisite two closers. No surprises there. There was also a beautiful case study of the AL Cy Young winner, **Felix Hernandez**, versus **Jered Weaver**. They had identical records (13-12) in an identical number of starts (34) and similar strikeouts (233 for Weaver versus 232 for Hernandez). What explains Hernandez’ winning total of 167 points contra Weaver’s fifth-place 24?

A few things come to mind:

**Hernandez went longer.**In the same number of games, wins, and losses, King Felix pitched 249 2/3 innings, whereas Weaver pitched 224 1/3. Those extra 25 1/3 innings show not only that Hernandez was considered more reliable by his manager but that he was, in fact, more reliable (since the extra innings didn’t result in his stats taking a hit). Hernandez also pitched a formidable 6 complete games with one shutout, whereas Weaver had no pips in either category.**Hernandez was more effective.**Felix gave up fewer runs (80 versus 83) and had a much higher proportion of unearned runs – fully 21.25% of his runs were unearned, whereas Weaver had about 9.6% of runs unearned. That means that more of Hernandez’s runs are attributable to defensive mishaps than Weaver’s. That leads to Felix with a miniscule 2.27 ERA, much lower than Weaver’s respectable 3.01, and 6 wins above replacement compared with Weaver’s 5.4.**Hernandez was marginally more effective.**He had six Tough Losses and no Cheap Wins, while Weaver had five Tough Losses and one Cheap Win. Felix couldn’t rely on his team to supply him with significant run support, while Weaver got that support in his one cheap win.- However,
**Hernandez’s control wasn’t as good.**Felix walked 70 batters for a control ratio (Strikeouts over walks) of .30 and threw 14 wild pitches. Jered, on the other hand, walked only 54 batters, for a control ratio of .23, and only 7 wild pitches. Still, it seems reasonable to assume that control suffers exponentially as innings increase, so part of the apparent lack of control can be explained by Hernandez’s extra innings.

Overall, Felix’s marginal value over Weaver more than explains the difference in voting.

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How can I quantify that? Well, it seems to me that a sign of quality as a starter is the vaunted quality start (game score above 50, or six innings with three or fewer runs allowed, depending who you ask), and a sign of quality as a reliever is the save. Thus, a good utility pitcher is one who can muster at least one quality start and at least one save in a given season. It’s not perfect, since it relies on the manager being willing to insert a primary starter at the right point in a game to earn a save (or starting a primary reliever, as Joe Girardi did with **Brian Bruney** back in 2008). Nonetheless, eight pitchers managed that feat this year.

By far the most versatile was **Hisanori Takahashi** of the Mets. Tak managed six quality starts, a handful of appearances as a left-handed specialist, and eight saves when he stepped in as the Mets’ closer after **Francisco Rodriguez** became unavailable.

**Mike Pelfrey** also represented for the Mets, although he made only one relief appearance (in the crazy 20-inning game against the Cardinals).

**Matt Garza** of the Rays made some news this July when he showed his versatility by starting and saving games in the same series.

The other five pitchers were **Bruce Chen**, **Nelson Figueroa**, **Tom Gorzelanny**, **Matt Harrison**, and **David Hernandez**.

Shockingly, **Carlos Zambrano** wasn’t among the pitchers listed, even though he spent some time in the bullpen for the Cubs and some time as a starter. (Big Z was briefly the highest-paid setup man in the league.)

My guess for the 2011 season? **Neftali Feliz** of the Rangers was among the best closers this year but has the ability to start games as well. Most likely, though, it’ll be someone like Pelfrey, who was pressed into service in relief for an extra-inning game.

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Let’s talk about the average utility pitcher, which is a phrase I just made up to avoid saying “position player called on to pitch” over and over again.

**He’s a journeyman**.**Felipe Lopez**, who pitched for the Cardinals on April 17 in a 20-inning game against the Mets, has played for six teams since 2001.**Joe Inglett**played for three different teams since 2006, and he pitched for the Brewers in a loss on July 27. Backup catcher**Kevin Cash**has pitched for five teams since 2002, including Houston, where he pitched in a loss on May 28.**He’s expendable.****Jonathan Van Every**, who pitched for Boston in a May 8 loss to the Yankees, has played 39 games over three seasons of bouncing between the minors and the majors.**Bill Hall**, his teammate, pitched on May 28 (in a different game than Cash did!) and played six utility positions for Boston during 2010 – second base, third base, shortstop, and all three outfield positions – in addition to pitching.**Joe Mather**, who pitched in the same game as Lopez and took the loss, played all three outfield positions and both infield corners. These are guys who are marginal enough that they have to learn a million positions just to be on the roster.**He played for Boston at some point.**Okay, okay, Inglett, Miles, Marte and Mather never did. Fine. But Van Every and Hall both pitched for Boston, Cash has done two unrelated stints with the Red Sox, and Lopez ended the season as Terry Francona’s utility man. That’s quite the coincidence, wouldn’t you agree?

Before anyone gripes, there’s one other type of utility pitcher, but he wasn’t represented this season. That, of course, is the star who gets his jollies pitching. This includes two prime varieties: the Wade Boggs, (wily vet who taught himself a knuckleball), and the **Jose Canseco** (idiot who hurts himself).

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*not a guarantee

The Spectrum Club is the elite group of players who play, in one season, at both ends of the Defensive Spectrum. At the end of a season, a player is inducted if he pitches in at least one game and appears as designated hitter in at least one game. As it stands, that leaves about ten pitchers who only served as placeholder DHs but never made a plate appearance on the rolls, but that’s okay.

Three players have joined the Spectrum Club twice – **Jeff Kunkel** in 1988 and 1989 for Texas, **Mark Loretta** in 2001 for the Brewers and 2009 for the Dodgers, and Wade Boggs in 1997 for the Yankees and 1999 for Tampa Bay. Baltimore leads the club in inductees with six.

This year’s first inductee is **Aaron Miles** of the Cardinals, who actually pitched twice (August 3 in a loss to Houston and September 28 in a loss to Pittsburgh). Making it more impressive, Miles DHed only once, in an interleague win over Kansas City on June 26. Miles is an experienced pitcher, having tossed twice in 2007 and once in 2008. Tony Larussa has quite the commodity there, and I bet he wishes he’d had Miles on hand for that crazy 20-inning game against the Mets on April 17.

The second player to join the club is **Andy Marte** of Cleveland. Marte DHed twice, once on July 10 in a loss to the Rays and once on September 7. His single inning pitched came as part of the Best Game Ever, a July 29 loss to the Yankees in which the Yankees lost their DH and Marte struck out **Nick Swisher**.

Who’s the smart money on for Spectrum Club inductions in 2011? **Joe Mather** and **Felipe Lopez** are both reasonable hitters and both pitched for Tony Larussa in the Mets-Cardinals game. If Lopez stays with the Red Sox, he might be called on to DH an odd late game, and Terry Francona has been known to use position players in emergencies. **Ike Davis** may well be asked to DH interleague games for the Mets, and he was a closer in college, so he’d be a solid emergency reliever. If I had to guess, though, I’d figure that the next Spectrum Club inductee will be **Nick Swisher** getting his second induction for the Yankees.

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The absolute leader this season was not **Kevin Youkilis** or **Brett Carroll** but **Rickie Weeks**, who led with 25 HBP in 754 plate appearances. Put another way, Weeks got hit in 3.32% of his plate appearances. That’s almost once every 30 plate appearances, or nearly four times the MLB-wide rate of 0.83% of the time. (Incidentally, that’s total HBP divided by total plate appearances. The more skewed mean percentage is 0.58%.) What leads to such a high number of plunkings?

I would assume that a few things would go into the decision to hit a batter intentionally:

- Pitchers are less likely to be hit by other pitchers.
- If a hitter is likely to get on base anyway, he’s more likely to be hit – you don’t lose anything by putting him on base, and you control the damage by limiting him to one base.
- If a batter is likely to hit for extra bases, he’s more likely to be hit.
- If a batter is likely to steal a base, he’s less likely to be hit, but there is an offsetting effect for caught stealing.
- American League batters are more likely to be hit because of the moral hazard effect of pitchers not having to bat.

With that in mind, I set up a regression in R using every player who had at least one plate appearance in 2010. I added binary variables for Pitcher (1 if the player’s primary position is pitcher, 0 otherwise) and Lg (1 if the player played the entire season in the American League, 0 otherwise), then regressed *HBP/PA* on *Pitcher, Lg, BB, HR, OBP, SLG, SB,* and *CS*. The results were somewhat surprising:

Call: lm(formula = hbppa ~ Pitcher + Lg + BB + HR + OBP + SLG + SB + CS) Residuals: Min 1Q Median 3Q Max -0.0154027 -0.0059081 -0.0018096 0.0001845 0.1397065 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 6.847e-03 9.815e-04 6.975 5.77e-12 *** Pitcher -5.399e-03 9.136e-04 -5.909 4.81e-09 *** Lg -1.614e-03 7.054e-04 -2.289 0.0223 * BB -1.412e-05 3.257e-05 -0.434 0.6647 HR 1.122e-04 7.956e-05 1.411 0.1587 OBP 8.570e-03 3.477e-03 2.465 0.0139 * SLG -3.451e-03 2.468e-03 -1.398 0.1624 SB -6.749e-05 8.693e-05 -0.776 0.4377 CS 1.770e-04 2.646e-04 0.669 0.5036 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.01042 on 935 degrees of freedom Multiple R-squared: 0.08839, Adjusted R-squared: 0.08059 F-statistic: 11.33 on 8 and 935 DF, p-value: 2.07e-15

Created by Pretty R at inside-R.org

That’s right – only *Pitcher, Lg, HR,* and *SLG* are even marginally significant (80% level). *BB, SB,* and *CS* aren’t even close. Why not?

Well, for one, the number of stolen bases and times caught stealing are relatively small no matter what. There probably isn’t enough data. For another, there simply probably isn’t as much intent to hit batters as we’d like to pretend.

Second, American Leaguers are **less** likely to be hit. This baffles me a little bit.

Also, keep in mind that this model shouldn’t be expected to, and cannot, explain all or even most of the variation in hit batsman. The R-squared is about .09, meaning that it explains about 9% of the variation. It ignores probably the most important factor, physics, entirely. (That is, the model doesn’t have any way to account for accidental plunkings.) As a side note, other regressions show there might be an effect for plate appearances, meaning you’re more likely to get hit by chance alone if you take enough pitches.

Finally, there are some guys who manage to do the opposite of Weeks’ feat. Houston outfielder **Hunter Pence** went 156 games and 658 plate appearances without getting plunked at all. Honorable mentions go to **Raul Ibanez**, **Scott Podsednik**, **Victor Martinez**, and **Omar Infante**, all of whom went over 500 plate appearances without a beaning. Now THAT’S plate discipline.

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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.”)

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In Kenley’s case, that’s not entirely surprising, since he was a catcher until this season. His numbers weren’t great, but he was competent. What surprised me was that 75 pitchers since 2000 have finished the season with a perfect batting average. 9 were from this year, including **Clay Buchholz** and his distant cousing **Taylor Buchholz**. **Evan Meek** and **Bruce Chen** matched Jansen’s two plate appearances without an out. None of the perfect batting average crowd had an extra-base hit except for Chacin.

Since 2000, the most plate appearances by a pitcher to keep the perfect batting average was 4 by **Manny Aybar** in 2000.

At the other end of the spectrum, this year only three pitchers managed a perfect 1.000 on-base percentage without getting any hits at all. **George Sherrill** and **Matt Reynolds** both walked in their only plate appearances; **Jack Taschner** went them one better by recording a sacrifice hit in a second plate appearance.

Finally, to round things out, this year saw **Joe Blanton** and *Heureusement, ici, c’est le Blog*‘s favorite pitcher, **Yovani Gallardo**, each get hit by two pitches. Gallardo had clearly angered other pitchers by being so much more awesome than they were.

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There are several parameters that are of interest when discussing the distribution of events. The first is the mean. This year’s mean was 5.43, meaning that of the players with at least one plate appearance, on average each one hit 5.43 homers. That’s down from 6.53 last year and 5.66 in 2008.

Next, consider the variance and standard deviation. (The variance is the standard deviation squared, so the numbers derive similarly.) A low variance means that the numbers are clumped tightly around the mean. This year’s variance was 68.4, down from last year’s 84.64 but up from 2008’s 66.44.

The skewness and kurtosis represent the length and thickness of the tails, respectively. Since a lot of people have very few home runs, the skewness of every year’s distribution is going to be positive. Roughly, that means that there are observations far larger than the mean, but very few that are far smaller. That makes sense, since there’s no such thing as a negative home run total. The kurtosis number represents how pointy the distribution is, or alternatively how much of the distribution is found in the tail.

For example, in 2009, **Mark Teixeira** and **Carlos Pena** jointly led the American League in home runs with 39. There was a high mean, but the tail was relatively thin with a high variance. Compared with this year, when Bautista led his nearest competitor (**Paul Konerko**) by 15 runs and only 8 players were over 30 home runs, 2009 saw 15 players above 30 home runs with a pretty tight race for the lead. Kurtosis in 2010 was 7.72 compared with 2009’s 4.56 and 2008’s 5.55. (In 2008, 11 players were above the 30-mark, and **Miguel Cabrera**‘s 37 home runs edged **Carlos Quentin** by just one.)

The numbers say that 2008 and 2009 were much more similar than either of them is to 2010. A quick look at the distributions bears that out – this was a weird year.

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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.

Using R, I fitted time-series models of the same functional form as the home runs per game model. I pulled the data from the Baseball-Reference.com AL Batting Encyclopedia and regressed the variable of interest on a time trend, its square, and a dummy for the designated hitter.

**First Assumption:** Intentional walks should decrease.

**Results:**

> ibb.lm <- lm(IBB ~ t + tsq + DH) > summary(ibb.lm) Call: lm(formula = IBB ~ t + tsq + DH) Residuals: Min 1Q Median 3Q Max -0.1350376 -0.0261969 0.0005516 0.0294412 0.1534536 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.656e-01 1.408e-02 18.870 < 2e-16 *** t 8.037e-03 1.199e-03 6.706 1.01e-09 *** tsq -1.393e-04 2.024e-05 -6.882 4.30e-10 *** DH -1.140e-01 1.055e-02 -10.805 < 2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.04689 on 106 degrees of freedom Multiple R-squared: 0.5961, Adjusted R-squared: 0.5847 F-statistic: 52.14 on 3 and 106 DF, p-value: < 2.2e-16 > ibb.2010.fitted <- (2.656e-01) + (8.037e-03)*56 + (-1.393e-04)*(56**2) + (-1.140e-01) > ibb.2010.obs <- .2 > residual.ibb <- ibb.2010.obs - ibb.2010.fitted > se.ibb <- .04689 > residual.ibb/se.ibb [1] 0.750113

Created by Pretty R at inside-R.org

Intentional walks per game increased, but the increase was by less than one standard error. Statistically, intentional walks did not change.

**Second Assumption:** Unintentional walks should not change.

**Results:**

> uBB <- (BB-IBB) > ubb.lm <- lm(uBB ~ t + tsq + DH) > summary(ubb.lm) Call: lm(formula = uBB ~ t + tsq + DH) Residuals: Min 1Q Median 3Q Max -0.69256 -0.12758 -0.01390 0.13178 0.77866 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 3.0879505 0.0732669 42.147 < 2e-16 *** t -0.0190285 0.0062392 -3.050 0.002892 ** tsq 0.0003623 0.0001054 3.439 0.000837 *** DH 0.1812598 0.0549094 3.301 0.001313 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.2441 on 106 degrees of freedom Multiple R-squared: 0.1876, Adjusted R-squared: 0.1647 F-statistic: 8.162 on 3 and 106 DF, p-value: 6.127e-05 > ubb.2010.fitted <- 3.0879505 + (-.0190285)*56 + (.0003623)*(56**2) + .1812598 > ubb.2010.obs <- 3.25 - .2 > residual.ubb <- ubb.2010.obs - ubb.2010.fitted > se.ubb <- .2441 > residual.ubb/se.ubb [1] -1.187166

Created by Pretty R at inside-R.org

Unintentional walks decreased by a bit over one standard error. Again, that isn’t evidence of a big enough fluctuation to say that it’s statistically different from our expectation.

**Third Assumption:** OBP drops, but by somewhat less than 3.4 standard errors.

**Results:**

> obp.lm <- lm(OBP ~ t + tsq + DH) > summary(obp.lm) Call: lm(formula = OBP ~ t + tsq + DH) Residuals: Min 1Q Median 3Q Max -0.0217348 -0.0044903 0.0002799 0.0046695 0.0182481 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 3.238e-01 2.230e-03 145.199 < 2e-16 *** t -5.703e-04 1.899e-04 -3.003 0.00334 ** tsq 1.472e-05 3.207e-06 4.591 1.22e-05 *** DH 8.245e-03 1.671e-03 4.933 3.02e-06 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.00743 on 106 degrees of freedom Multiple R-squared: 0.487, Adjusted R-squared: 0.4724 F-statistic: 33.54 on 3 and 106 DF, p-value: 2.532e-15 > obp.2010.fitted <- (3.238e-01) + (-5.703e-04)*56 + (1.472e-05)*(56**2) + 8.245e-03 > obp.2010.obs <- .327 > residual.obp <- obp.2010.obs - obp.2010.fitted > se.obp <- .00743 > residual.obp/se.obp [1] -2.593556

Created by Pretty R at inside-R.org

OBP dropped, but it dropped by quite a bit. Without more information it’s hard to judge whether a change of this magnitude is due to better pitching or power being taken away from hitters.

**Fourth Assumption:** Slugging average will drop.

**Results:**

> slg.lm <- lm(SLG ~ t + tsq + DH) > summary(slg.lm) Call: lm(formula = SLG ~ t + tsq + DH) Residuals: Min 1Q Median 3Q Max -0.0357646 -0.0087050 -0.0007988 0.0115133 0.0317497 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 3.937e-01 4.471e-03 88.050 < 2e-16 *** t -2.058e-03 3.807e-04 -5.404 4.04e-07 *** tsq 5.049e-05 6.429e-06 7.853 3.51e-12 *** DH 1.693e-02 3.351e-03 5.054 1.82e-06 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.01489 on 106 degrees of freedom Multiple R-squared: 0.6452, Adjusted R-squared: 0.6352 F-statistic: 64.27 on 3 and 106 DF, p-value: < 2.2e-16 > slg.2010.fitted <- (3.937e-01) + (-2.058e-03)*56 + (5.049e-05)*(56**2) + (1.693e-02) > slg.2010.obs <- .407 > residual.slg <- slg.2010.obs - slg.2010.fitted > se.slg <- .01489 > residual.slg/se.slg [1] -3.137585

Created by Pretty R at inside-R.org

A drop in slugging average of over three standard errors indicates that we may be working with something that’s ruined hitters’ power or that’s hurt their ability to hit in general. We have results that are consistent with either something harming power hitters specifically or hitters in general.

This isn’t evidence of steroid use. In fact, the same results would be consistent with a shift toward pitching talent. More work needs to be done on this year’s data before conclusions can be drawn. However, it does seem to indicate that, at least in the American League, the Year of the Pitcher narrative has some statistical foundation.

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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.

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