Baseball

BaseballThe genesis of this project was in reading “The New Bill James Historical Baseball Abstract” in 2001. I was familiar with James’ work, but his “Win Shares” system, which distills all of a particular player’s contributions into a single number, opened my eyes to the potential of deep statistical analysis.

Beyond Win Shares itself, a couple of other things caught my attention in that book. The first was using “runs saved” to evaluate a pitcher (more on that later). The second was that, once he had Win Shares, James looked at the final numbers from several  angles to rate players. Not just total Win Shares, but Win Shares per 162 games, top 3 seasons, top 5 consecutive seasons … all these went into the evaluation.

The third nugget was, in doing detailed comparisons of players, he would sometimes run through their hitting stats and compare the offense they generated to the league average, i.e. what a typical team would do. So Rogers Hornsby generated as much offense in 1921 as an average 1921 team would produce in 33 games; while Eddie Collins, in 1916, generated 35 games’ worth despite having less impressive statistics. That was the thunderbolt for me – it occurred to me that expressing their statistics in that way would be almost as accurate as Win Shares, and could be applied to other sports, too. I could compare Walter Payton to what an average NFL team did in 1984, or Michael Jordan to  an average NBA team from 1991.

I started with baseball, using James’ work as a touchstone, checking every so often that the numbers I was generating moved in parallel to his. But I went off the reservation pretty early (I can’t let go of RBI, sorry), and after 100 or so players, I was ready to adapt Apples & Oranges, as I began to call it, to other sports. There were surprises along the way, but mostly I was heartened by how consistent it seemed to work as I moved to cricket, football, basketball, etc.

Baseball players are evaluated on two offensive and two defensive components. Offense 1 is total bases: singles, doubles times 2, home runs times 4, etc. We also count walks, steals, hit by pitch, sacrifice bunts, and steals. We subtract caught stealing and grounding into a double play. Then the whole mess is divided by the league average for a particular season.

Here are Babe Ruth’s numbers for 1920:

Games Hits 2B 3B HR BB HBP SH SB CS
142 172 36 9 54 150 3 5 14 14

We don’t have GDP for 1920. Anyway, that’s 546 total bases. The typical American League team in 1920 had 16.30 per game (not counting HBP and SH, which are bonus categories). Dividing 546 by 16.30 gives us 33.50 games’ worth.

Offense 2 is much simpler. We average the player’s runs scored and RBI, and divide by the league scoring average. For the Bambino in 1920, that’s 158 and 137, respectively, giving us an average of 147.50. Divide by 4.76 runs per game to get 30.99 games’ worth of runs. Now average with the first number to get a total offense of 32.24.

Defense 1 is outs. Putouts by catchers are adjusted for team strikeouts, and first basemen are adjusted (heavily) by infield assists. Infield putouts (including pitchers) and all assists count as half an out each. Outfield putouts and strikeouts are a full out, and catchers get a bonus for preventing stolen bases. Errors, wild pitches and passed balls each take away an out.

Defense 2 is for catchers and pitchers only. Pitchers are credited for each run they allow less than 1.5 times the league average for the number of innings they pitch. Catchers get a small share of the team’s ERA, or cERA if available, prorated to the number of games caught. All other players get a zero in this spot. Take the average of Defense 1 and 2, then average that number with the offensive total to get the grand total for that season. For Ruth, that’s 9.30 on Defense 1, 0.11 on Defense 2 (he pitched a little), yielding 4.70 on defense and 18.47 all around. Then add up every season to get the grand total.

So let’s start where I started, with the catchers:

Catchers Games Total Per 160 Sqr Root Sum Off Def
Johnny Bench 2203 196.96 14.30 14.03 28.34 21.76 6.85
Bill Dickey 1827 165.18 14.47 12.85 27.32 20.28 8.65
Gary Carter 2326 193.46 13.31 13.91 27.22 18.98 7.64
Carlton Fisk 2513 201.83 12.85 14.21 27.06 19.39 6.31
Yogi Berra 2195 182.97 13.34 13.53 26.86 20.34 6.34
Mickey Cochrane 1513 139.36 14.74 11.81 26.54 20.65 8.83
Ted Simmons 2362 188.37 12.76 13.72 26.48 20.43 5.09
Mike Piazza 1944 161.73 13.31 12.72 26.03 21.12 5.50
Gabby Hartnett 2006 163.93 13.08 12.80 25.88 18.37 7.78
Iván Rodríguez 2573 187.71 11.67 13.70 25.37 16.73 6.61
Roy Campanella 1247 111.47 14.30 10.56 24.86 21.04 7.57

The total is the average of the total offensive and defensive games’ worth that the player earned in his career. This number is then divided by the games played and multiplied by 160 to give us a 160-game average. That number is added to the square root of the total to give us the final rating (in bold). The last two columns are the offensive and defensive ratings per 160 games. In general, because they play so many games, baseball players have higher totals and lower 160-game averages than other athletes. For other sports, the average is quite a bit higher than the square root of the total. In baseball, they’re almost even. But that bold number tends to come out in the same ranges.

Johnny Bench rates a little low defensively because his pitching staff was mediocre, driving down his cERA, and he played a few hundred games at positions other than catcher. Defense is influenced most by playing a lot at a particular position, rather than how well you played it.

Campanella’s career is truncated at both ends: by the color line at the beginning and by a car crash at the end. In a fairer world, he’d rate higher. He’s dead even per game with Bench.

First Base Games Total Per 160 Sqr Root Sum Off Def
Lou Gehrig 2198 215.25 15.67 14.67 30.34 28.07 3.27
Jimmie Foxx 2335 205.22 14.06 14.33 28.39 25.01 3.12
Jeff Bagwell 2183 192.10 14.08 13.86 27.94 24.56 3.60
Harmon Killebrew 2448 201.90 13.20 14.21 27.41 23.35 3.04
Hank Greenberg 1417 136.47 15.41 11.68 27.09 26.86 3.96
Eddie Murray 3070 229.20 11.95 15.14 27.08 20.90 2.99
Willie McCovey 2596 199.46 12.29 14.12 26.42 21.63 2.96
Mark McGwire 1916 161.66 13.50 12.71 26.21 23.79 3.21
Johnny Mize 1902 159.92 13.45 12.65 26.10 23.74 3.16
Frank Thomas 2338 177.58 12.15 13.33 25.48 23.07 1.24

Because the Red Sox wasted Babe Ruth’s first five years as a pitcher, Gehrig ends up with the highest offensive average of the players I’ve rated. Once he stopped pitching, Ruth was at 30.81.

We see the effect of the designated hitter rule here. Eddie Murray was a good fielder who DH’d a lot. Frank Thomas was a lousy fielder who DH’d a lot. In both cases it cost them something like half a point on the final rating.

Hank Greenberg only played 1,417 games, due to World War II. Some guys are hurt by a short career, some guys are helped. It helped Greeberg; I don’t think he sustains those numbers over 2,200 games.

I can’t explain how McGwire does so well defensively other than to say he had a lot of balls hit his way.

Second Base Games Total Per 160 Sqr Root Sum Off Def
Eddie Collins 2860 270.34 15.12 16.44 31.57 23.16 7.09
Rogers Hornsby 2271 229.76 16.19 15.16 31.35 25.76 6.62
Nap Lajoie 2480 240.67 15.53 15.51 31.04 23.87 7.18
Joe Morgan 2699 249.00 14.76 15.78 30.54 22.58 6.94
Charlie Gehringer 2342 211.71 14.46 14.55 29.01 21.35 7.57
Craig Biggio 2890 236.97 13.12 15.39 28.51 19.87 6.37
Ryne Sandberg 2174 194.22 14.29 13.94 28.23 21.54 7.05
Roberto Alomar 2437 203.40 13.35 14.26 27.62 20.09 6.62
Rod Carew 2483 196.55 12.67 14.02 26.68 20.29 5.04
Jackie Robinson 1420 124.00 13.97 11.14 25.11 22.29 5.65

If you’ve studied “The New Historical Abstract,” then you know this is where I part ways with the guy who inspired me. Hornsby and Lajoie over Morgan …

There are four guys over 30.00 among second basemen, which has emerged as the dividing line between the immortals or the merely great. Or maybe it’s 29.50. Not sure yet. Anyway, four over 30, and all within a point-and-a-half of each other, is unusual.

Apples & Oranges rates second basemen, as a group, over shortstops in the field. Shortstop is the more difficult position, but second basemen are more productive because of all the double plays they turn. In fact, I give zero extra credit for double plays. Just getting an assist and a putout on the same play is enough to push them ahead.

Third Base Games Total Per 160 Sqr Root Sum Off Def
Mike Schmidt 2440 221.19 14.50 14.87 29.38 25.02 3.99
Eddie Mathews 2407 206.33 13.72 14.36 28.08 23.62 3.81
Chipper Jones 2592 208.27 12.86 14.43 27.29 22.65 3.06
George Brett 2750 214.60 12.49 14.65 27.14 21.70 3.27
Ron Santo 2243 182.08 12.99 13.49 26.48 21.91 4.07
Paul Molitor 2712 202.52 11.95 14.23 26.18 21.07 2.83
Home Run Baker 1600 141.46 14.15 11.89 26.04 23.91 4.39
Darrell Evans 2700 196.09 11.62 14.00 25.62 19.69 3.55
Brooks Robinson 2935 203.64 11.10 14.27 25.37 17.89 4.31
Stan Hack 1856 145.32 12.53 12.05 24.58 21.05 4.00
Wade Boggs 2478 174.13 11.24 13.20 24.44 19.14 3.34

Apples & Oranges doesn’t rate third basemen much higher than first basemen on defense. It makes a certain amount of sense; once you get past the fact that it’s more difficult to play third, you see that the number of plays the make is pretty similar. Brett and Molitor have their numbers depressed even further because they DH’d so much. In fact, Molitor is exhibit A for why I should have a DH category.

I was shocked at how low Boggs ended up. He deserves his own writeup, but for now I’ll just point out two things. One, his numbers fell off a cliff after 1991, his eighth year in the league. We remember early Boggs hitting doubles off the Green Monster, not the guy slapping singles for the Yankees. Second, a huge part of his value was in his walks, and I have a feeling that there’s diminishing returns on very high OBP players when it comes to scoring runs. I’d love to really go in-depth the issue one day.

Shortstop Games Total Per 160 Sqr Root Sum Off Def
Honus Wagner 2809 274.75 15.65 16.58 32.23 24.99 6.31
Alex Rodriguez 2860 252.37 14.12 15.89 30.00 24.00 4.24
Robin Yount 2873 237.70 13.24 15.42 28.66 19.60 6.88
Ernie Banks 2528 212.36 13.44 14.57 28.01 21.97 4.91
Derek Jeter 2901 230.87 12.73 15.19 27.93 20.06 5.40
Cal Ripken Jr. 3029 233.87 12.35 15.29 27.65 18.97 5.74
Arky Vaughan 1820 161.79 14.22 12.72 26.94 22.17 6.28
Joe Cronin 2129 174.78 13.14 13.22 26.36 20.04 6.23
Pee Wee Reese 2210 178.88 12.95 13.37 26.33 19.46 6.45
Barry Larkin 2197 176.31 12.84 13.28 26.12 19.86 5.82
Ozzie Smith 2615 193.70 11.85 13.92 25.77 16.79 6.91
Alan Trammell 2306 172.90 12.00 13.15 25.15 17.96 6.03

The great shortstops, unlike second base, tend not to be all-rounders … other than Wagner, of course. The next three players after him are great hitters who ended up moving to easier positions, and Jeter should have moved. Ripken was a natural third baseman.

Ozzie’s the only real glove-first guy on the list. Most other defensive specialists lose value at the end of their careers because they can’t stay in the lineup. But even for him, defense is less than half of his offensive value. Defensive production is shared too evenly for stars to dominate like they do on offense.

Wagner could play anywhere and that dilutes his defense. Just as a shortstop, he rates at a jaw-dropping 7.27. Robin Yount, on the other hand, helped himself by moving to center field, which, like second base, is more productive than shortstop.

Left Field Games Total Per 160 Sqr Root Sum Off Def
Barry Bonds 3034 306.61 16.17 17.51 33.68 26.75 5.59
Ted Williams 2299 239.37 16.66 15.47 32.13 27.87 5.44
Stan Musial 3049 281.54 14.77 16.78 31.55 24.97 4.58
Rickey Henderson 3141 273.87 13.95 16.55 30.50 21.74 6.16
Carl Yastrzemski 3325 275.84 13.27 16.61 29.88 22.05 4.49
Pete Rose 3629 283.52 12.50 16.84 29.34 20.34 4.66
Al Simmons 2234 207.28 14.85 14.40 29.24 23.03 6.66
Manny Ramírez 2413 204.20 13.54 14.29 27.83 22.94 4.14
Willie Stargell 2396 195.50 13.06 13.98 27.04 22.78 3.33
Tim Raines 2536 202.34 12.77 14.22 26.99 20.44 5.09
Joe Jackson 1346 130.74 15.54 11.43 26.98 25.78 5.30
Minnie Minoso 1835 155.58 13.57 12.47 26.04 21.66 5.47

Bonds … yeah, I know. Whatever he did to his body, the results are there on the field. The home runs counted, the games he helped win counted, and the ERAs he inflated counted. Same goes for McGwire and Sosa.

Pete Rose is hard to place, since he played all over the field. He had the most games at first base, but all but two those all came in the second half of his long career, after he left the Reds. He essentially played a whole normal career before that. Of the other positions, left field is the one he played the most.

Williams lost 4¾ seasons to military service. With those games, he’d probably be neck-and-neck with Bonds, maybe even ahead.

Al Simmons leads in defense because he played a good deal of center field. Henderson’s the top “true” left fielder.

Center Field Games Total Per 160 Sqr Root Sum Off Def
Ty Cobb 3052 318.01 16.67 17.83 34.50 27.19 6.15
Willie Mays 3017 305.97 16.23 17.49 33.72 25.40 7.05
Tris Speaker 2809 279.42 15.92 16.72 32.63 24.60 7.23
Mickey Mantle 2466 242.59 15.74 15.58 31.32 25.74 5.74
Joe DiMaggio 1787 191.11 17.11 13.82 30.94 26.53 7.69
Ken Griffey Jr. 2689 240.27 14.30 15.50 29.80 22.39 6.21
Billy Hamilton 1591 151.58 15.24 12.31 27.56 24.44 6.05
Duke Snider 2179 188.26 13.82 13.72 27.54 21.95 5.70
Jim Wynn 1929 170.93 14.18 13.07 27.25 22.30 6.05
Kirby Puckett 1807 159.39 14.11 12.62 26.74 20.90 7.33

I was mildly surprised that Cobb came in ahead of Mays. Maybe if we had caught-stealing data for Cobb’s career that would be different, but I think his numbers would hold steady relative to the league average. Could it be that we underrate Cobb as a ballplayer because he was such a terrible person?

It’s harder to make the wartime case for Joe DiMaggio than it is for Ted Williams. With an extra 450 games in his prime, DiMaggio probably passes Mantle, but no more.

I mentioned that Apples & Oranges rates center field ahead of shortstop, defensively — mostly because an outfield putout counts twice as much as an infield putout. Why? Two reasons. First, infield outs generally take two people, one to field and make the throw, the other to get the out, so they split credit. Second, the stakes in the outfield are higher. If an infielder screws up, there’s a man on first and the players on base advance once. If an outfielder misses one, it’s at least a double, and all the runners score.

Right Field Games Total Per 160 Sqr Root Sum Off Def
Babe Ruth 2544 302.38 17.95 17.39 35.34 27.94 7.97
Hank Aaron 3315 321.63 15.52 17.93 33.46 25.78 5.27
Frank Robinson 2843 268.77 15.13 16.39 31.52 25.69 4.56
Mel Ott 2745 256.29 14.94 16.01 30.95 24.59 5.28
Sammy Sosa 2369 217.91 14.72 14.76 29.48 23.82 5.62
Sam Crawford 2534 225.60 14.24 15.02 29.26 24.06 4.43
Reggie Jackson 2897 239.02 13.20 15.46 28.66 22.27 4.13
Roberto Clemente 2459 208.60 13.57 14.44 28.02 21.42 5.73
Paul Waner 2553 213.62 13.39 14.62 28.00 21.05 5.73
Tony Gwynn 2467 194.15 12.59 13.93 26.53 19.70 5.49

If Ruth’s numbers look off, it’s because he started as a pitcher early in his career and, as I explain below, pitcher starts count double in determining averages. That’s also why his defensive average is so high.

Roberto Clemente and Paul Waner, both right fielders for the Pirates, are almost exactly even. Makes me wonder about Ralph Kiner …

Starting Pitcher Games Total Per 160 Sqr Root Sum Off Def
Walter Johnson 808 177.51 19.20 13.32 32.53 6.72 31.69
Cy Young 913 174.48 16.09 13.21 29.30 5.64 26.54
Bob Gibson 537 117.75 18.33 10.85 29.18 5.48 31.17
Roger Clemens 744 151.74 16.35 12.32 28.67 0.38 32.32
Tom Seaver 664 137.24 16.65 11.71 28.36 3.34 29.96
Christy Mathewson 647 128.49 16.99 11.34 28.33 5.70 28.29
Randy Johnson 627 131.25 16.85 11.46 28.31 0.98 32.73
Pete Alexander 703 134.93 16.51 11.62 28.12 4.90 28.11
Greg Maddux 782 149.87 15.45 12.24 27.69 2.82 28.08
Warren Spahn 758 140.83 15.77 11.87 27.64 4.52 27.02
Lefty Grove 624 114.67 16.89 10.71 27.60 3.79 30.00
Steve Carlton 757 141.35 15.28 11.89 27.17 4.13 26.44
Kid Nichols 621 118.35 15.98 10.88 26.86 6.43 25.59
Pedro Martínez 492 97.06 16.97 9.85 26.82 1.05 32.89
Bob Feller 572 104.25 15.77 10.21 25.98 3.69 27.84
Carl Hubbell 541 96.46 15.75 9.82 25.57 3.71 27.78
Sandy Koufax 405 73.07 16.10 8.55 24.65 1.85 30.35

Starting pitchers forced me into my first judgment call. On the one hand, they’re massively valuable on a per-game basis; more so than any other group of players in any sport. On the other, they can’t go every game, needing three or four games off for every one they pitch. If I rated them like everyone else, they’d end up with final values in the 40s. But cutting their scores by three-quarters seemed an extreme way to balance the scales, especially given that I’m comparing them, among others, to NFL players who play 16 games a year and get a week off.

The compromise I came up with was to count every pitching start as two games when determining the 160-game averages. It’s not a number grounded in any scientific formulation, just one that I found gives us the best balance between their game-to-game production and their general unavailability. Games started are on the individual player pages.

Relief Pitchers Games Total Per 160 Sqr Root Sum Off Def
Hoyt Wilhelm 1072 66.03 9.40 8.13 17.53 0.81 17.99
Dennis Eckersley 1099 77.03 8.44 8.78 17.21 0.31 16.56
Rollie Fingers 974 46.34 7.33 6.81 14.14 0.49 14.17
Mariano Rivera 1211 52.27 6.85 7.23 14.08 0.02 13.70
Goose Gossage 1021 47.06 7.12 6.86 13.98 0.09 14.14
Bruce Sutter 667 28.47 6.83 5.34 12.17 0.52 13.14
Dan Quisinberry 692 26.70 6.17 5.17 11.34 0.03 12.32

Baseball statisticians twist themselves into knots trying to find extra value for relievers in “high-leverage” situations. I don’t … but even if you do, it doesn’t make up for the plain fact that relievers don’t do very much when compared to starters or regular position players. Pitching the ninth inning with a lead isn’t that valuable, beyond serving as a security blanket for the manager.

As I write this, the Tampa Bay Rays are engaged in a high-profile experiment to have relievers begin the game, then bring in the “starter” to take care of innings 2 through 6 or whatever. I don’t think it’ll mean much … it will just expose the lie of the high-leverage situation. Pitch Sergio Romo in the first, sixth or ninth and it won’t matter … he’ll give you the same mediocre innings.

Eckersley rates as high as he does because he started 361 games in the first half of his career. (But Wilhelm started only 52 games and still comes out ahead …)

Quisinberry gets dinged for an extremely low strikeout total. He had great control and did a lot of things well to keep the score down, but ultimately relied on his defense to get almost all his outs.

To come: I still have a batch of 19th-Century players, who’ll go in their own section, and very rough estimates on some Negro League stars. They’ll go up once I’m caught up on the other sports.

To do list:
Suzuki Ichiro
David Ortiz
Edgar Martinez
Trevor Hoffman
Lee Smith