Author Archive

Mike Trout and the HBP Risk

If you’ve ever looked at Mike Trout’s Baseball Reference page, you’ve seen a lot of black ink, indicative of leading the league in some offensive category. Trout is currently leading the league in a lot of such categories — and he has done so in the past. He’s likely to lead the AL in homers for the first time this year, and as noted recently by Ben Lindbergh, that would be the 10th category out of 17 basic ones at Baseball Reference that he’s led the league in at least once in his career. Only about two dozen players have led the league in more of these 17 categories at some point in their careers.

Trout is also leading the league in another category that would also be a first for him: hit by pitch (HBP). He’s been plunked 15 times this season (editor’s note: now 16), one more than Shin-Soo Choo as of this writing. HBP is not what you would call a sexy stat, but it does have value. It’s as valuable as a walk — in fact, per FG’s linear weights, a little more so, apparently because it occurs slightly more in base-out states that have higher run expectancy (RE) than average.

HBP, like walks, are valuable because they put a runner on base, where he has a chance to score, while simultaneously avoiding an out, thus giving another batter a chance. They’re a good thing. But they also come with a risk. If a batter is hit by a pitch, he could suffer a significant injury and miss time. The resulting lost time is lost value. This raises an obvious question: is the increased value gained by getting hit by pitches greater than the potential risk of losing value to injury? If it is — and one would assume that in this stat-savvy age, it would have to be — by how much? Read the rest of this entry »

Mike Trout and The 1% Club

Like many other followers of FanGraphs, I never seem to get enough articles about Mike Trout — the general theme being: “another way Mike Trout is so great” — so I want to share one of my own. Contrary to popular belief, Trout did not invent WAR; even more shocking, the metric wasn’t developed for the primary purpose of showcasing how valuable he is. But that of course is what it does do. Many readers may know that beginning with his first full season, at age 20, and continuing up to his most recent, age 26, Kid Fish has had the most WAR through every season but one — his age-25 season, when he missed nearly fifty games with an injury — than any other player in history. So it shouldn’t be surprising that he is one of just 20 members of what I call The 1% Club: players who have equaled or exceeded 0.010 WAR per PA for their entire careers.

In fact, he’s currently second only to Babe Ruth:

Career War/PA Of 0.010 Or Greater
Player fWAR/PA (career) fWAR/PA (age 26)
Babe Ruth 0.0159 0.0172
Mike Trout 0.0138 0.0138
Rogers Hornsby 0.0138 0.0134
Ted Williams 0.0133 0.0139
Barry Bonds 0.0130 0.0107
Lou Gehrig 0.0120 0.0121
Willie Mays 0.0120 0.0120
Honus Wagner 0.0118 0.0080
Ty Cobb 0.0114 0.0131
Mickey Mantle 0.0113 0.0129
Tris Speaker 0.0109 0.0123
Joe DiMaggio 0.0108 0.0123
Joe Jackson 0.0106 0.0109
Mike Schmidt 0.0106 0.0109
Jackie Robinson 0.0106*
Jimmy Foxx 0.0105 0.0122
Dan Brouthers 0.0104 0.0118
Nap LaJoie 0.0103* 0.0095
Eddie Collins 0.0100 0.0125
Stan Musial 0.0100 0.0116

This list is based mostly on FanGraphs’s fWAR, and is for players with a minimum of 50 career WAR. However, two players, Nap LaJoie and Jackie Robinson, don’t quite qualify by fWAR, but they do if we use Baseball Reference’s rWAR (all the others on the list qualify using either metric). Trout is the only active player on the list, though if we lower the bar to 30 career fWAR, three more players appear, including Mookie Betts, who is at 0.0104. Even lowering the criterion to just 10 fWAR adds just one more active player, Aaron Judge (0.0103). Read the rest of this entry »

Can Ohtani Optimize His Hitting Value in the AL?

When Shohei Ohtani, AKA the Japanese Babe Ruth, was deciding which MLB team he wanted to join, the bet was that it would be an AL team, because of the possibility of batting as a DH when he wasn’t pitching. While he would get some guaranteed PA as a pitcher in the NL, plus probably some more as a pinch hitter, the total would likely have been no more than about 200 in a season. Hitting as a DH, he could theoretically bat every game except the ones he was pitching (because if he were removed from the mound, his replacement would have to hit or be taken out for a pinch hitter). While in practice it’s expected he won’t play every day between pitching starts, he has the possibility of getting, say, 300-400 PA as a DH.

Sure enough, Ohtani chose the AL Angels. No one knows exactly how much he will bat this year, but Steamer projections give him 65 games and 259 PA. Since he’s projected to start 24 games as a pitcher, his batting projections represent about half of the games he’s expected to have available when he isn’t starting (162 – 24 = 138). The hope, obviously, is that Ohtani can provide value with his bat as well as his arm.

But based on Steamer, the bat will not be nearly as productive. While he’s projected to produce 3.1 WAR as a pitcher, as a hitter the expectation is only .5 WAR. After all the talk about how good a hitter Ohtani may potentially be, this seems disappointing. Of course, 259 PA is less than a full season’s worth of hitting, but even if he were able to hit for about a full season — say, 650 PA — and maintained the same rate stats, he would be worth only about 1.3 WAR. That would actually make him a below average player.

Even allowing for the fact that he is a pitcher, his projected WAR value still doesn’t seem that impressive. To put it in perspective, Madison Bumgarner, widely recognized as one of the best hitting pitchers currently playing, had 0.5 WAR last year, despite missing about half the season with an injury. In fact, he produced that 0.5 WAR with just 36 PA, less than 15% of Ohtani’s projected total. And last year was not even Bumgarner’s best as a hitter. His wRC+ was 86, excellent for a pitcher, but in 2014 his wRC+ was 114, and he produced 1.3 WAR in just 78 PA. As we’ve just seen, that’s as much WAR as Ohtani would be projected to achieve in a full season of 650 PA.

Pitcher Hitting is Far More Valuable than DH Hitting

Why is Ohtani’s projected WAR as a hitter so low? It’s not because he’s expected to perform poorly with the bat. His projected wRC+ is 113, just about the same as Bumgarner’s best, and historically good. Since WWII, only 32 pitchers have exceeded that value for a season (minimum 70 PA). And those were career years, whereas Ohtani if anything would be expected to improve his hitting as he matures. In fact, since the live ball era began, only one pitcher has reached a career wRC+ of 100 (minimum 1000 PA): Wes Ferrell, who hit that number exactly. Since WWII, the highest career wRC+ by a pitcher is 81 by Bob Lemon, or 87 by Don Newcombe, who barely misses the 1000 PA minimum; only one other pitcher has even reached 60. Among active pitchers (minimum PA: 300), only Zack Greinke (54) and Bumgarner (51) are > 50, though Bumgarner has been a little over 90 for the past four years.

So Ohtani is projected to be an exceptionally good-hitting pitcher. His WAR problem is the result of playing the DH position. WAR, of course, measures a player’s production relative to other players at that position. The DH generally is one of the best hitters on the team, since any player who is a good hitter can fill that role; it doesn’t matter if he’s a disaster at any defensive position. Pitchers, in contrast, are almost always by far the worst hitters on the team.

Calculating WAR involves summing four values: batting runs + positional runs + replacement runs + league runs. The total is then divided by runs/win, which is currently very close to 10.0. Different amounts of positional runs are assigned to different positions, with pitchers getting by far the largest benefit, and DHs the worst. As of 2017, the positional run value for pitchers was about .119 R/PA*. This is about the same as the league average R/PA, reflecting the view that a replacement level pitcher will produce essentially no runs at all.

Thanks to the positional runs, Bumgarner got a big boost this past season, despite being a below league average hitter with just 36 PA:

36 PA x -.017 = – 0.7 batting runs

36 PA x .119 = 4.3 positional runs

36 PA x .0305 = 1.1 replacement runs

36 PA x. 0015 = 0.1 league runs

Total = 4.8 runs (.5 WAR)

The value of about – .017 R/PA for batting runs is based on a league average R/PA value of .122, and Bumgarner’s wRC+ of 86, or 14% less than average: .122 x – .14 = – .017. The other values can be determined by dividing total PA by total replacement runs or league runs for any hitter with a large number of PA (the larger the PA, the more accurate the calculation). Though Bumgarner was a below-average hitter, his hitting was far above average for a pitcher, and that produces value that is recognized in the very large positional run adjustment.

In contrast, the DH has a very large negative positional run value; as of 2017, it was about – .029 R/PA. Ohtani’s projected WAR for 2018 can thus be calculated as follows:

259 PA x .016 = 4.1 batting runs

259 PA x -.029 = – 7.6 positional runs

259 PA x .0305 = 7.9 replacement runs

259 PA x. 0035 = 0.9 league runs

Total = 5.3 runs (.5 WAR)

The value of .016 RAA/PA for batting runs is based on a 113 wRC+ and a league R/PA value of .122: .122 x .13 = .016.

How Much WAR Would Ohtani’s Hitting be Worth as a National League Pitcher?

So from a WAR point of view, Ohtani is at a considerable disadvantage hitting as a DH, rather than as a pitcher. In fact, the positional disadvantage is so great that it considerably outweighs the fact that he will get many more PA as a DH in the AL than he would as a pitcher in the NL. Assuming his wRC+ is 113, how much value would he produce as a hitting pitcher in the NL? Steamer projects him to throw 148 innings. Assuming he pitched the same total in the NL, and that he batted fairly high in the order (at least, say, fifth or sixth; based on his AL hitting projections of 259 PA/65 games, this should indeed be the case), he might come to the plate as often as 65 times.

65 PA x .016 = 1.04 batting runs

65 PA x .119 = 7.74 positional runs

65 PA x .0305 = 1.98 replacement runs

65 PA x. 0015 = 0.1 league runs (note league runs/PA are less in the NL)

Total = 10.86 runs (1.1 WAR)

So Ohtani, assuming he was the same hitter, would be worth more than twice as much WAR as a hitting pitcher in the NL than as a DH in the AL, though he would come to the plate only about 25% as often (and we haven’t even considered the possibility that he could add further value in the NL as a pinch hitter). This begs the question, actually two closely related questions: 1) how many more PA would Ohtani have to have as a DH to produce the same 1.1 WAR he would produce as a NL pitcher? 2) how high a wRC+ would he have to have as a DH with 259 projected PA to match that 1.1 WAR?

In both cases, Ohtani would need to produce about 5.6 more runs above replacement. To do that while maintaining his projected 113 wRC+, he would need about 266 more PA, or a total of about 525. To do that while maintaining his projected 259 PA, he would have to elevate his wRC+ to 131.

Of course, if were able to produce a 131 wRC+ in the AL, he could presumably do it in the NL, too, which would increase his value there. It would not increase it as much, though, because of his much fewer PA. So a better question to ask would be: how high does his wRC+ have to be to match his NL WAR, given the projected PA of 259 as a DH, vs. 65 as a NL pitcher? It turns out his wRC+ would need to be about 137. Above this value, he would produce more WAR as a DH, while below it he would produce more WAR as a pitcher. This value is close to what is usually considered the mark of an elite hitter, 140.

However, the projected PA values that we’re working with may be low if we want to consider Ohtani’s potential in years beyond his rookie MLB season. On the one hand, if he proves to be a good hitter, he may get more PA. We might project a maximum of 400 PA. To get this many, he would have to play as a DH in about 100 games. Of the remaining 62 games, he would pitch in 24 and rest in 38. In order to rest both on the day before and the day after he pitches, he would need a total of 48 rest days, but the remaining ten might come on the team’s day offs.

With regard to pitching, if Ohtani were in the NL, and becomes an ace, let’s assume he would start a little more often, and log a total of 90 PA as a pitcher. This is pretty close to a maximum value in the current environment; in the past decade, only seven pitchers have had more PA in a season. In addition, let’s assume he appears as a pinch-hitter 110 times, giving him a total of 200 PA. In the 90 PA as a pitcher, his positional run value would be .119 R/PA, as explained before. In his 110 PA as a PH, we assume his positional run value is – .029 R/PA, the same as for a DH in the AL.

Using these values, we can estimate the number of runs above replacement Ohtani would be worth in the NL, compared to the AL, for various values of wRC+:

wRC+ NL Pitcher1 AL DH2
120 19.0 11.8
130 21.4 16.6
140 23.9 21.52
150 25.7 26.4


1 – Assumes 90 PA as a pitcher + 110 PA as a pinch-hitter

2 – Assumes 400 PA as a DH

Because of the larger number of PA as a pitcher, plus the additional PA as a PH, Ohtani now produces more run value in the NL up to wRC+ values > 140. He would have to have a wRC+ of nearly 150 before he would produce more value as a DH.

Has Ohtani’s Decision Eliminated Some of His Potential Value?

Will Ohtani be as valuable a hitter in the AL that he could he have been in the NL? Probably not. If we start with his projected stats for 2018, he will produce only about .5 WAR as a DH. Assuming the same wRC+ of 113, and the 65 PA likely to accompany his projected 148 IP, he would produce more than twice that total, about 1.1 WAR, as a pitcher. This is because the positional advantage for a pitcher is huge, while there is a large positional disadvantage for the DH.

Some of this value gap may be reduced if Ohtani becomes a much better hitter than is projected for 2018, because the much greater number of PA available as a DH allows him to take greater advantage of better hitting. But he would have to hit considerably better. Still assuming 259 PA as a DH vs. 65 PA as a pitcher, his wRC+ would have to nearly 140, an elite level, for his WAR as a DH to match that of a pitcher in the NL. That wRC+ value could be lowered to as much as 120 if Ohtani were to log as many as 400 PA, which seems close to the maximum compatible with his pitching program. But we might also argue that were he in the NL, he would perhaps pitch a little more often, and thus receive more PA as a pitcher, plus appear as a PH in most games in which he didn’t pitch. Making what I think are some reasonable assumptions about total PA under these conditions, Ohtani would have to produce at nearly a 150 wRC+ clip to produce as much value as a DH. Only seven qualified hitters managed that this past season.

Considering the reputation as a hitter that accompanies Ohtani as he comes to the U.S., this seems a little deflating. Even if he managed to produce a 150 wRC+, which seems quite unlikely, his total hitting WAR would be about 2.6. That would just about equal Wes Ferrell’s mark in 1935, the highest single season WAR for a pitcher in the live ball era, which certainly would be a major accomplishment. But it would not be that much more than a good hitting pitcher like Bumgarner manages even without pinch-hitting, nor would it add so much to Ohtani’s total WAR as a two-way player that his combined value would likely reach historic levels. If he is to finish anywhere near the top of the WAR leaderboard, it will have to be mostly through his arm, not his bat.

But even if Ohtani produces relatively little WAR as a hitter, this should serve as a reminder that there are different ways to understand value. The prospect of a pitcher who can hit well enough to DH even just part of the time has another kind of value to a team. Ohtani’s presence as an option at DH may open up a roster spot for another player, much as Ben Zobrist has had value beyond his WAR because of his ability to play multiple defensive positions. Surely the Angels are aware of this, and won’t be put off by his actual WAR totals.

*Though pitchers are not usually included in discussions of positional runs, this value can be calculated from the values table for the batting data of any pitcher. It corresponds roughly to 80 total runs for a whole season, batting every game, though of course pitchers never even approach this.

WAR by Position: Why Do Catchers Lag?

(Author’s note: This analysis was originally published on the Baseball-Fever forum a year ago. I thought it might be of interest to the FG community.)

As I have perused the all-time list of career WAR, one feature has always struck me as odd and in need of some explanation: catchers are much lower than other position players. The highest career WAR (I’m using FG WAR or fWAR here, but BBRef’s rWAR makes the same point) of any catcher is Johnny Bench, who comes in at 42d among all position players, at about 75 WAR. That is not just lower than the highest career WAR at any other position. It’s less than two-thirds the next lowest WAR; moreover, every other position has multiple players with higher career WAR, the fewest being SS with four (and that doesn’t include Alex Rodriguez, who I count here as a third baseman).

The following table, which compares the top ten players in career WAR at each position, provides further perspective (If a player is listed at more than one position, I included him only in the position in which he played more. Since the corner outfielders comprise two positions, I took the average of the top two as highest, and the average of the top 20 as equivalent to the average of the top 10.):

Table 1. Top 10 Players in Career WAR by Position

Pos       Ave. PA     Highest WAR     Ave. top 10    Ave./700 PA

C               8677              74.8                     63.4               5.11

1B           10,137             116.3                     85.9              5.93

2B          10,458             130.3                    88.1              5.90

SS           10,440             138.1                    81.1               5.44

3B           10,534             114.0                    86.9               5.77

CF            10,210            149.9                    97.5               6.68

L/RF        11,267            166.4                    98.5               6.09


Except for catcher, the highest career WAR at every position is well over 100. Moreover, if we take the average WAR of the top 10 at each position, catcher again is well below the others. In fact, on that basis, there seem to be three general groups. The highest values are clearly associated with the OF. The highest WAR values of all time were achieved by outfielders, and the average WAR of the top ten center fielders as well as of the corner fielders is nearly 100.

A second group is comprised of all the infield positions. The highest WAR values of players in any position in this group are somewhat lower than the highest values of outfielders, but are roughly equal to the highest values at any other position in this group. Thus the highest WAR values range from about 115-140, and the average WAR of the top ten at each position ranges from 81-88, with an overall average of 85.5. This is 87.3% as high as the average value of the OF.

Finally, catchers are clearly in a class by themselves — and not in a good sense. As noted earlier, the highest career WAR attained by any catcher is only about 75, and the average of the top ten is about 63. This is less than two-thirds as high as the average value of the outfielders (64.8%), and about three-quarters as high as the average value of the infielders (74.2%).

At first glance, this ranking might not seem surprising. For most players, hitting is by far the most important component of WAR, and outfielders are on average better hitters than most infielders, who in turn are on average better hitters than catchers. But these differences are supposed to be compensated for by positional adjustments. For example, catchers are given more positional runs than players at other positions, and corner outfielders are given fewer positional runs than players at all other positions except first base. Specifically, the positional run benefit has the following general ranking: C > SS > 2B/3B/CF > LF/RF > 1B.

This raises the question, if these positional adjustments are approximately correct, why don’t the best catchers have about as much career WAR as the best outfielders? In fact, why are there significant differences also between outfielders and infielders? I will explore these discrepancies here.

This is not just an academic question. The relatively low WAR values for catchers have implications for their HOF chances. Assuming that WAR has some meaning for HOF voters — and even if some of them aren’t fans of this approach, they may still evaluate players using stats that are ultimately reflected in or correlated with WAR — they must either select fewer catchers than players at other positions, or set the bar somewhat lower for catchers. Based on the current HOF composition, one could argue that a little of both are occurring. Thirteen catchers are in the HOF, which is the lowest of any position except third base, which has 11. On the other hand, the mean WAR value for these catchers is about 50, well below the overall mean for the HOF of about 60. Moreover, 70% of the catchers in the HOF have a WAR of less than 60. No other position has more than 50% of its members below this value.

So it may be that, consciously or not, HOF voters think the best catchers are not quite as good as the best players at other positions, yet at the same time, go a little easier on them than they do on other players. I hope the following discussion will shed some light on how we are to understand the value of players at this position, which everyone recognizes as the most important one on the diamond for everyday players.

Positional Adjustments
I posed the issue earlier by pointing out that if one takes the positional adjustments seriously, one would think that the best players at every position would have about the same WAR. Though players at some positions don’t hit as well as players at other positions, they get extra value for playing what is considered a more difficult position. The positional adjustments are supposed to correct for the differences in hitting.

One might therefore first wonder if the positional adjustments are simply wrong, that catchers need to be given more runs. While this is a possibility — there has been some interesting work recently re-evaluating these adjustments — the amount of correction necessary appears far too large. For example, the difference between the average WAR of the top ten catchers and the average WAR of the top ten shortstops is about 18. The average length of the catchers’ careers is about 2200 games, or 13-14 full seasons, so to bring the catchers’ WAR up to that of the shortstops, one would have to give them an additional positional adjustment of about 1.3 WAR, or 13 runs, per year. That is two and a half times the current difference in positional runs between the two positions of 5 runs. An even larger adjustment in absolute though not relative terms would be necessary to bring the catchers’ WAR up to that of the outfielders.

Now the recent appreciation of pitch-framing — the ability of some catchers to receive the ball in such a way that a borderline call is more likely to be called a strike than it would if it were not for the catcher’s manipulations — could in fact add that much WAR, if not more, to the totals of some catchers. But that is not really relevant here, because when the positional adjustments were first developed, they did not (and still don’t) take into account pitch-framing. That is, it was assumed that even without pitch-framing, the positional runs actually given the catchers were adequate, and if pitch-framing does become adopted by the major sabermetric sites, it won’t be to compensate for some perceived shortage in positional runs.

That said, even before efforts to quantify pitch-framing were developed, it was recognized as a valuable skill by many observers familiar with the game. And it’s conceivable that when HOF voters decide on their choices, one reason that they’re fine with selecting catchers who, by WAR or by more traditional stats, may be inferior to some position players who are not chosen is that they feel that there is some hidden value in catching that WAR or traditional stats are not capturing. And pitch-framing could be a large part of that value. I won’t discuss pitch-framing further, but I think this is an important point to keep in mind.

Do Catchers Decline Faster than Other Players?
A second reason why the best catchers have lower WAR values might be that because of the demands of their position, they decline with age sooner and/or faster than other players, and thus don’t accumulate enough counting stats to finish their careers with really high WAR levels. Table 1 provides some support for this. The average number of PA by the top ten catchers, 8677, is significantly less (15-20%) than the average number of PA by the top ten at any other position, which ranges from about 10,000 to 11,000. If we normalize the WAR values per 700 PA, the differences between catchers and other position players are therefore reduced. However, catchers are still lowest, and they are quite a bit lower than all the other position players except for SS.

Of course, if catchers do decline sooner and/or faster than players at other positions, this might affect not only their counting stats, but their rate stats as well. How would we assess this possibility? If that were the case, one might expect that the WAR differences that do exist between them and other position players would be reduced if not eliminated earlier in their careers. It’s widely accepted that age-related decline in production begins in the late 20s. Traditionally, it has been thought that players improve steadily in their early 20s up until that age; more recent evidence suggests that players may actually peak at a younger age, then stay more or less at a plateau until their late 20s. But in any case, there is no evidence of a decline much before the late 20s, barring, of course, injuries or other health problems.

Accordingly, I next examined career WAR values at each position through age 27. As before, all OF comprise one group, and the highest WAR and average of top ten were modified for this group accordingly. I also remind the reader that the ten players in each group are not all the same players as the ten in the career cohorts shown in Table 1, though there is substantial overlap. That is, the leaders in WAR through age 27 are not necessarily the ultimate winners, as determined by career totals.

Table 2. Top 10 Players in WAR by Position Through Age 27

Pos   Average PA      Highest WAR     Ave. top 10     Ave./700 PA

C            4029                     50.4                   31.7                    5.51

1B           4115                      64.6                   39.8                   6.77

2B          3976                     64.6                    37.9                   6.67

SS          4937                     62.0                    38.0                   5.39

3B          4326                     53.5                    39.8                   6.44

CF          4921                     68.8                    51.3                    7.30

L/RF     4365                     68.3                    41.9                    6.72

Compared to the WAR values for full careers (Table 1), a number of differences are apparent in this table. First, the average PA for catchers is now about the same as that for several other positions, including 1B and 2B, and not much different (< 10%) from that for 3B or corner outfielders. This is consistent with the possibility that their lower average career PA results largely from earlier or faster decline, since if that were the case, we would expect to see less, if any, of this decline through age 27.

Interestingly however, the best SS and CF have a much larger number of average PA than players at all other positions. This might be because players at these two premier positions develop sooner, but I won’t pursue this further except to point out that this relationship is reversed later for CF. That is, if we compare Table 2 with Table 1, we see that while the top ten CF through age 27 had more PA than the corner outfielders, the latter had more at the end of their careers. When we normalize for PA, the CF are clearly higher than the corner outfielders, as well as any other position, but because their PA drops relative to corner outfielders as they age, their total career WAR values are comparable. One could speculate that CF decline a little faster because of the greater amount of outfield territory they’re expected to cover.

Second, the WAR differences observed over the full careers of these top position players are quite evident even at this earlier age. The average WAR of the top infielders through age 27, 38.8, is 86.2% the average WAR of OF, very similar to the 87.3% observed when comparing over a full career. Actually, the average WAR of IF is fairly close to the average WAR of the top corner outfielders, but as I noted above, the average WAR of the best CF at this age is much higher. Thus the ratio of the IF WAR to CF is only about 75%.

Similarly, the average WAR of catchers, 31.7, is 70.2% of the average WAR of OF, a little but not too much higher than the 64.8% observed over a full career, and much lower relative to CF, about 60%. The C WAR is also 81.7% of the average WAR of all the top IF taken together, compared to 74.2% for the career comparisons. While the highest WAR for a catcher through age 27 is much closer to the highest WAR at other positions at this age, indeed, is almost as high as the highest value for 3B, this value appears to be an outlier, as it is much higher than the next-highest value for a catcher at this age.

This finding of large WAR gaps between catchers and other players even at a young age is somewhat surprising, because it suggests, contrary to the evidence discussed earlier, that the lower WAR values for catchers are not in fact the result of an accelerated decline — not unless this decline begins much sooner than age 27. In fact, based on this evidence, it appears that most catchers produce lower WAR from the get-go.

A third conclusion we can draw from Table 2 is that the general order of OF > IF > C is for the most part preserved when WAR values are normalized for PA, though some of the differences are reduced. However, the normalized WAR value for SS at this age is much reduced, in fact, is a little lower than that for C. So the general order is now OF > 1B/2B/3B >> C/SS.

Offensive and Defensive Components of WAR Differences
To summarize the discussion so far, career WAR values generally trend as OF > IF > C. If the values are normalized for playing time, the differences are reduced somewhat in some cases, but the general order remains the same. If we consider WAR just through age 27, the order is still the same, OF > IF > C. If we normalize these values for playing time, the order is still generally preserved, except that now SS join catchers as the lowest group.

The fact that the order is generally preserved at age 27 suggests that while decline might be an issue for catchers — because of the lower average PA for their careers — some other factors must play a major role in accounting for the WAR gap. At this point, we need to look more closely at how WAR is determined. WAR at FG has four main components: offensive runs, defensive runs, league runs and replacement runs. Replacement runs are proportional to PA, and thus won’t account for any differences between players and groups when WAR is normalized for the same amount of PA, though they will add to differences when total PA are different. The same is true for league runs, which are a very minor component, anyway.

So let’s look at offensive and defensive runs. Offensive runs include batting runs and baserunning runs, and defensive runs include fielding runs and the positional adjustment. In the table below, I have listed the top 10 in career WAR at each position, the same groups that appeared in Table 1. For each group is shown offensive runs, defensive runs, fielding runs and positional runs. I have also listed the average wRC+ for each group of ten. This is a rate stat that measures hitting, so is useful to compare among the best players at each position.

Table 3. Offensive and Defensive Performance of Top 10 Position Players

Pos      wRC+    Off Runs     Fielding Runs     Pos Runs     Def Runs  Pos Runs/700PA

C           122          200.6               32.7                     79.2              111.9             6.39

1B          147          579.4               46.8                 -106.1               -59.3           -7.32

2B         132          427.6                40.5                   40.8                 81.3            2.73

SS          121          264.7                78.6                   112.1               190.7            7.52

3B         128          388.5               93.8                    22.8               116.6             1.52

CF         143           591.9                65.4                  -39.3                26.1            -2.69

L/RF     147           653.1                51.9                  -111.9             -60.0            -6.95

Consider wRC+ first. Notice that as expected, the best hitters are first basemen and corner outfielders, who have the highest positional adjustment. The center fielders are close behind, followed by the second and third basemen, while shortstops and catchers are the lowest, and also very close to each other. So the ranking is 1B/L-RF > CF > 2B > 3B > SS/C, which compares fairly well with the positional adjustments of 1B > L-RF > 2B/3B/CF > SS > C. The most significant discrepancies are that CF are somewhat better hitters than indicated by their positional adjustment, while SS are somewhat worse.

Now let’s turn to offensive runs. This includes baserunning as well as hitting, and since it’s a counting stat, it also reflects PA. The order is similar to that with wRC+, except corner fielders now are ahead of first basemen, who even trail center fielders slightly, and shortstops are ahead of catchers: L-R/F > CF/1B > 2B/3B > SS > C. This makes sense if we assume that outfielders, particularly center fielders, tend to be better baserunners than first basemen, and shortstops tend to be better baserunners than catchers; this can be confirmed by comparing the baserunning values of these groups (not shown). In addition, the top ten SS, as we have seen earlier, have a significantly larger average PA than catchers, so even if they are no better as hitters, they will accumulate more total value through hitting.

So some of the WAR difference between catchers and infielders, particularly SS, results from greater offensive runs, a reflection mainly of more playing time and, to a lesser extent, of better baserunning. In fact, the difference of about 60 runs corresponds to about 6 WAR. Recall that I showed earlier that the top ten catchers average about 18 WAR less than the top ten SS. So about one-third of this difference comes from offense, and mostly simply because of more playing time (because most offense is hitting, and by wRC+, the two groups are the same).

Now consider defense, where things get interesting. Defensive runs at FG are the sum of fielding runs, which evaluate a player’s actual defense, and positional runs, which vary according to the position. Catchers have a large total here (average about 112), which is to be expected, given that they have a large number of positional runs, about 80 on average. Note, though, that the top ten 3B have a slightly larger average number of defensive runs than catchers (about 116), and the SS have a much larger number (about 190). Why is this?

From the positional runs total, we can see that catchers have a much larger total than 3B, as would be expected, since their positional adjustment is much greater. The third basemen, though, have a much higher total of fielding runs, nearly 100 on average, vs. a little over 30 on average for the catchers. In other words, the top ten 3B were on average much better defensively at their position than the top ten catchers were at theirs, and this more than compensates for their lower positional adjustment. I will return to this point later.

SS, on the other hand, have a higher total of positional runs than catchers (about 112 on average), as well as of fielding runs (nearly 80). So on average they, like the third basemen, are also better defensively than the catchers. But how can shortstops have a higher total of positional runs than catchers, given that the latter have a higher positional adjustment? Clearly, because catchers don’t play every game at that position. They are sometimes rested by moving them to another defensive position, and that position is usually the one with the worst positional adjustment: first base. Thus it doesn’t take a lot of time at that position to have a significant impact on a catcher’s net positional adjustment.

How much impact? From the last column in the table, we can see that the top ten catchers averaged about 6.4 positional runs per full season over their career. This compares to the current positional adjustment of 12.5 runs that would be given them if they played exclusively at catcher. Since first base has a positional adjustment of -12.5 runs, we can estimate that the top ten catchers played an average of about 25% of their time at first base. The SS, in contrast, had a career positional adjustment of 7.5 runs, which is just about what they should have playing full time at that position.

The net result is that SS average about 80 defensive runs more than catchers (from the table, 190.7 – 111.9). This accounts for another 8 WAR or so in their differences, bringing the total up to 14 (6 for offense plus 8 for defense). We saw earlier that the top SS on average accumulate about 18 WAR more than the best catchers. Where do the other 4 WAR come from? Replacement. As was shown in Table 1, the top ten SS on average had about 1800 more PA than the top ten catchers. This corresponds to roughly 50 more replacement runs, or about 5 WAR, close enough for this rough estimate. Since all of the difference in replacement runs (50), and most of the difference in offensive runs (60, from Table 3) is due to the greater playing time of the SS, we can say that roughly 60% of the WAR difference is due to this greater longevity, and the other 40% (80 runs, from Table 3) to better defensive value. Of the latter, a little more than half results from better defense (45 more fielding runs, from Table 3), and the remainder from a net positional advantage (33 more runs, Table 3).

The other positional run averages shown in the table are fairly easy to account for. For second basemen, it’s about 2.7 runs, slightly higher than the 2.5 value for this position. This could reflect some time playing SS for some of these players, or higher positional adjustments in the past. I haven’t looked into the historical trends in positional runs, and am just going on what are generally considered the current values. For third base, it’s 1.5 runs, slightly lower than the 2.5-run adjustment, and may reflect a little action at 1B or in the OF. The negative value for CF, which have a positive positional adjustment of 2.5 runs, is not unexpected, because most CF play part of their careers, particularly as they get older, at the corners, where the adjustment is negative. The higher negative positional runs of the corner outfielders is of course expected. It’s actually slightly higher (less negative) than the positional adjustment of -7.5 runs, which probably reflects that most corner fielders have played a little at CF. Since the difference in adjustment between these two positions is 10 runs, the corner outfielders would only have to play CF about 5% of the time to bring their positional run average up to -7.0.

We’re now in a position to understand why the greatest catchers finished their careers with lower WAR than the best players at any other position, despite having the advantage of a greater positional adjustment. One factor, which I discussed earlier, is that on average they had fewer PA than other players, by about 15-20%. When we normalize WAR to PA, catchers are still the lowest, but the differences are reduced somewhat. We came to the same conclusion by showing that about 60% of the WAR difference between catchers and shortstops is due to offensive runs and replacement runs, which are mostly a reflection of more PA for the SS.

In addition, though, catchers rarely get full advantage of their positional benefit, because they play some of the time at another position, generally first base. Many catchers may move permanently to this position later in their career, but even when they are younger, they are likely to put in some time at 1B. This, I suggest, is a major reason why we find that even at age 27, when they should be at their peak and when they have played a comparable amount of time to players at several other positions, catchers still lag behind all other position players in WAR. Statistically speaking, they aren’t “pure” catchers; they’re in effect competing with other players who are supposed to be better hitters.

In fact, Johnny Bench, whose 50 WAR through age 27 I earlier described as an outlier among catchers, averaged 8.2 positional runs/700 PA at this point in his career. This relatively high net positional adjustment, together with a high amount of PA, account for his unusually high WAR.

There is a third factor evident from the analysis, though. As I noted above, the top ten catchers have a lower average total of fielding runs — meaning they are poorer defensively at their position — than players at other positions. This difference is especially great in comparing them to shortstops and third basemen, but in fact, catchers have the lowest average total of fielding runs of any group analyzed.

It’s not hard to understand why this might be the case. Since catchers as a group are relatively poor hitters, and since the largest component of WAR is usually hitting, a catcher who hits well but doesn’t play the position well is likely to rack up more WAR than a poor-hitting catcher who plays excellent defense. In fact, three of the top ten catchers — Joe Torre, Ted Simmons and Mike Piazza — finished their careers with negative fielding runs. Only one top-ten SS — Derek Jeter — and one top-ten 3B — Chipper Jones — finished their career with negative fielding runs.

That’s not to say that good-hitting, poor defensive players can’t make it at other positions, but there the difference in hitting between best and worst is not so great. The hitting standard is higher at these positions, which means that even an excellent hitter can’t exceed it as much as he might catching. That being the case, the bar for defense is in effect set a little higher.

What implications does this have for evaluating catchers? I think it justifies lowering the WAR bar a little for them. From Table 3, we can estimate that if catchers played full-time at that position throughout their career, they would add about 6 runs per season to their defensive total. Over an average career of 13-14 full seasons, that amounts to about 8 WAR. As we also saw, catchers lose 4-5 WAR in replacement value relative to other position players because of shorter careers. So if they played a career of normal length, and exclusively at catcher, they could add about a dozen WAR to their total, even assuming that they were little better than replacement at the end. That would raise the 50 WAR average for current members of the HOF to a little over 60, right in keeping with the average for other position players.

I think the nub of the problem is that when positional runs are adjusted, they assume that a player can and will play the entire season at a particular position, and that doing so will have no adverse effect on his career, above and beyond the normal aging process that all players undergo. In other words, positional runs do not look at the long-term picture. They consider the demands of the position in the present. It’s rather like comparing two cars, one that is expected to drive in snow, mud, extremes of heat and other challenging weather conditions on bad roads, while the other is used in mostly temperate weather on good roads. Just because the two cars have a certain relative performance at the outset does not mean that we should expect this relative performance to be maintained over their lifetime.

I’ll close by pointing out that other questions remain, in particular the WAR differences between OF and IF. Returning to Table 1, the top OF have an average WAR about 15% higher than the average IF. If WAR is normalized for PA, the difference between corner outfielders and infielders drops somewhat, but the difference between center fielders and infielders remains. Center fielders clearly have the highest WAR/PA of any of the positions.

The other factors that underlie the differences between C and the other players do not appear to contribute to the difference between OF and IF. The fielding-run average of OF, both CF and corner outfielders, is about in the middle, higher than that for C, 1B and 2B, but lower than for SS and 3B. While CF have a positive positional run adjustment, like catchers, their net adjustment is reduced by significant playing time at another position with a negative adjustment. Corner OF get a slight boost in their net positional runs when they play at CF, or in some cases perhaps at 3B, but this is a minor effect. So on the face of it, it seems that OF, and particularly CF, hit better than their positional adjustment would imply. This is also reflected in their average wRC+ values (Table 3), which are about on par with those of first basemen, which of course have a much larger positional adjustment.