Count von Count Riddler

I periodically attempt the FiveThirtyEight Riddler, edited by Oliver Roeder. This week he’s actually presenting two, a shorter “Riddler Express”, and a more time consuming “Riddler Classic”.

The Sesame Street character Count von Count likes to, well, count, and he now has his own twitter feed! For those who don’t recall the character from the show, he’s a purple muppet dressed in black, as a sort of kindly Dracula, who would count up in an eastern European accent.

Well, the twitter feed is simply the Count counting, albeit in words written out describing the number. As I type this, his latest tweet is “Eight Hundred Seventy Nine!”

So the Riddler Express is to find out how high can Count von Count count on twitter in this way before hitting its 140 character limit. Because he is enthusiastic, all his tweets must end with an exclamation mark.

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Pirate Riddler

This week’s FiveThirtyEight Riddler is a logic puzzle. Assume 10 “Perfectly Rational Pirate Logicians”. The pirates have found 10 gold pieces, and the puzzle is to figure out how they will allocate the loot among themselves. There are several constraints.

First, the pirates themselves are ranked in a strict hierarchy, with the Captain at the top, and then the others ordered beneath them, so if for any reason the Captain is no longer able to fulfill his duties, the second in command becomes new Captain, and everyone else moves up one step on the hierarchy.

Second, the Pirates practice a form of democracy. While the Captain, due to rank, gets to propose an allocation, the whole crew, with one vote per pirate, votes on the proposal. If that proposal gets half or more of the vote, it carries, but if more than half of the pirates vote against it, they will mutiny, killing the old Captain, and leaving it to the new captain to propose an allocation.

So our perfectly rational pirate logicians have three constraints in determining how they will vote on a proposed allocation:

  1. They value life above all, so they will not vote in a way to put their own lives at risk of mutiny if they can at all avoid doing so.
  2. They are greedy, so as long as their life is not at stake, they will vote for something which maximizes their own personal share of the loot.
  3. They are bloodthirsty, so if they have two choices in which they’d remain alive but get the same booty, they will prefer to mutiny and kill the captain.

Given the above constraints, how will the 10 pirates allocate their 10 newly found gold pieces?

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FiveThirtyEight Baseball Division Champs Puzzle

Update: I’ve added a link to the Perl progam I used to do these simulations.

Oliver Roeder presents a weekly puzzler on FiveThirtyEight, and this week it was a baseball-themed puzzle. Assume a sport (say, “baseball”) in which each team plays 162 games in a season. Also assume a “division” (e.g. the “AL East”) containing 5 teams, each of exactly equal skill. In other words, each team has exactly a 50% chance of winning any given game. The puzzle is to compute the expected value of wins for the division-winner.

Interestingly, the problem is open to interpretation, and the result I get depends on what assumptions I make. My initial assumption was to treat each game for each team as a simple coin-flip. I ran 100,000 simulated “seasons”, getting an average of 88.4 wins for the division leader. But games have two teams, and who the opponent is could matter to this problem. In an extreme situation, the “coin flip” model could result in winning the division with 0 wins, in the highly improbable event that each team lost every game.

Since I happened to have the 2016 MLB schedule available, I used it for each game. This adds the constraint that in games involving two teams in the same division, one team winning implies its opponent must lose. Doing this, I got an average of 88.8 wins for the division winner.

The third variant I tested produced the toughest constraint: I assumed the five teams only played games among themselves (at least 40 against each opponent). Thus every win for one team always means a loss for its opponent. This gave me an average of 89.3 wins for the division winner.

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Comparing 2014 Projections – ERA and WHIP

Yesterday I ran comparisons of several projections systems for an all-inclusive batting statistic, wOBA. Today I’m running the same tests, computing root mean square error (RMSE) and mean absolute error (MAE), for two commonly used fantasy statistics, ERA and WHIP. These tests are bias-adjusted, so what matters is a player’s ERA or WHIP relative to the overall average of that system, compared with the player’s actual statistic relative to the actual overall average. The lower the RMSE or MAE, the better a projection system predicted the actual data.

I have data for these projection models:

  • AggPro – A projection aggregation method from Ross J. Gore, Cameron T. Snapp, and Timothy Highley.
  • Bayesball – Projections from Jonathan Adams.
  • CAIRO – from S B of the Replacement Level Yankees Weblog.
  • CBS Projections from CBS Sportsline.
  • Davenport Clay Davenport’s projections.
  • ESPN Projections from ESPN.
  • Fans Fans’ projections from
  • Larson Will Larson’s projections.
  • Marcel – the basic projection model from Tom Tango, coauthor of The Book. This year I’m using Marcel numbers generated by Jeff Zimmerman, using Jeff Sackmann’s Python code.
  • MORPS – A projection model by Tim Oberschlake.
  • Rosenheck Projections by Dan Rosenheck.
  • Oliver – Brian Cartwright’s projection model.
  • Steamer – Projections by Jared Cross, Dash Davidson, and Peter Rosenbloom.
  • Steamer/Razzball – Steamer rate projections, but playing time projections from Rudy Gamble of
  • RotoValue – my current model, based largely on Marcel, but with adjustments forpitching decision stats and assuming no pitcher skill in BABIP.
  • RV Pre-Australia – The RotoValue projections taken just before the first Australia games last year. Before the rest of the regular season I continued to tweak projections slightly.
  • ZiPS – projections from Dan Szymborski of Baseball Think Factory and ESPN.

First up is ERA, comparing the 75 pitchers projected by all systems: Continue reading

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Comparing 2014 Projections – wOBA

In the past three years I’ve done reviews of baseball projections systems with actual data for those systems for which I could get data. Will Larson maintains a valuable site of projections from many different sources, and most of the sources I’m comparing are from that.

As in the past, I’m computing root mean square error (RMSE) and mean absolute error (MAE) for each source compared to actual data. For these tests, I am doing a bias adjustment, so the errors are relative to the average of a source. I care more about how a system projects players relative to its own projected averages than about how well it projlects the overall league average.

I have data from these systems:

  • AggPro – A projection aggregation method from Ross J. Gore, Cameron T. Snapp, and Timothy Highley.
  • Bayesball – Projections from Jonathan Adams.
  • CAIRO – from S B of the Replacement Level Yankees Weblog.
  • CBS Projections from CBS Sportsline.
  • Davenport Clay Davenport’s projections.
  • ESPN Projections from ESPN.
  • Fans Fans’ projections from
  • Larson Will Larson’s projections.
  • Marcel – the basic projection model from Tom Tango, coauthor of The Book. This year I’m using Marcel numbers generated by Jeff Zimmerman, using Jeff Sackmann’s Python code.
  • MORPS – A projection model by Tim Oberschlake.
  • Rosenheck Projections by Dan Rosenheck.
  • Oliver – Brian Cartwright’s projection model.
  • Steamer – Projections by Jared Cross, Dash Davidson, and Peter Rosenbloom.
  • Steamer/Razzball – Steamer rate projections, but playing time projections from Rudy Gamble of
  • RotoValue – my current model, based largely on Marcel, but with adjustments for pitching decision stats and assuming no pitcher skill in BABIP.
  • RV Pre-Australia – The RotoValue projections taken just before the first Australia games last year. Before the rest of the regular season I continued to tweak projections slightly.
  • ZiPS – projections from Dan Szymborski of Baseball Think Factory and ESPN.

In addition, I’ve computed a source “All Consensus”, which is  a simple average of each of the above (ignoring a source if it doesn’t project some particular category).

Not all the models had enough data to compute wOBA, so the tables (below the jump) only include those sources which do. The other sources do affect the All Consensus values for those stats where they do have data.

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RV Current for NBA

Similar to what I’ve done with baseball, I’m now running new projections daily for NBA players under the name RV Current. These projections add current year data into the model, increasing the weight given to the current season as more games are played.

This early in the season, the numbers aren’t much different from my preseason projections. But RV Current will continue to adjust to changing factors and on-court play, whereas the preseason projections just stay the same.

I should add that one other feature of player search pages: when showing projections for some mid-season future date range, they now automatically prorate projections based on known injuries. The site will try to determine a target return date from injury reports, and if a player isn’t expected back soon, his number of games will be reduced by the number he’s expected to miss. The injury reports page now also shows a Target Return? date, which, when present, will result in that players’s stats being scaled down when shown in a Search page. For a PlayerDetail page, the projections will simply show an expected full year projection for a player (which will be for much fewer than 82 games if a player has been especially injury prone in the past).

Projections are always fuzzy, but by incorporating newer data into daily projections, and taking known injuries into account when searching for player data, I’m trying to make them a little bit clearer.



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Points-based scoring in MLB?

Tom Tango proposed a points system for MLB, allowing for ties and not using extra innings. He proposed giving each team 5 points to start. Extra inning games stayed at 5 points, treating them as a tie. If you win by 1, you get 1 more point; winning by 2 gets 3 more points, and winning by 3 or more is 5 more points, while losing by 1, 2, or 3+ would result in earning 1, 3, or 5 fewer points.

He added in a 1 point bonus  if a home team won by 2 or less without batting in the bottom of the 9th, or if they won with either 0 out, 1 out with 1 on, or 2 out with 2 on (presumably giving value to their chances of scoring if they played the 9th to completion), with a corresponding penalty for a visiting team losing in such circumstances.

So each game would result in a total of 10 points allocated to the two teams. An equivalent framing would be:

  • 10 – win by 3+
  • 8 – win by 2
  • 6 – win by 1
  • 5 – tie/extra innings
  • 4 – lose by 1
  • 2 – lose by 2
  • 0 – lose by 3+

Add/subtract 1 point for handling the bottom of the 9th.

He asked someone to run the numbers for 2014, and I took a crack at it. My database keeps line scores, but not the base-out state when a walk-off game ends, so I couldn’t do the bonus for winning in the bottom of the 9th with extra outs left or runners on, but I handled the rest.

I started thinking about this model in more detail. If MLB actually played under this sort of points system, that would change incentives for teams and managers. Now winning by 3, or even 2, becomes a lot better than winning by just 1. Lots of saber-inclined people complain bitterly about how the current save rule distorts bullpen management, with managers often bringing in a closer to pick up an easy save rather than using him in a tie game which has a higher leverage index. But in this modified scoring system, it actually would make more sense to use the closer with a 3-run lead than to preserve a 1-run lead, or in a tie game. You gain just 2 points relative to your opponent if you go from a tie to a 1-run lead, but if your 3-run lead drops to 2, you drop 4 points. So a leverage index under that scoring system would actually be higher when you have a 2-3 run lead than in a tie game!

That doesn’t fit well with me intuitively, so I thought about tinkering with his model. My first thought was rather than 10-8-6-5-4-2-0, trying 10-9-7-5-3-1-0. That gives the first marginal run more than your opponents more weight than any other, but it also makes that first insurance run worth exactly the same. To keep symmetry, but to have diminishing returns as your margin of victory increases, I switched to a 12-point, rather than 10-point, scale: 12-11-8-5-2-1-0. This preserves higher importance for getting a win than for winning by more, which is good. The main downside I see is that under a 10-point scale per game, points per game provides a nice, easy comparison with winning percentage under the old model, whereas with a 12-point scale, the average, rather than being 5.00, is now 6.00.

Still, I suppose one could just look at points per potential points as a proxy for winning percentage if one were so inclined. Hockey or soccer standings don’t typically bother with that, so maybe there wouldn’t be much interest.

I’ve created a page that can show both the original proposal from Tango or whatever other ranking you’d like. The original Tango proposal is here, and this page shows standings using my 12-point scale proposal. The page has data going back to 2010, and you can enter your own point values for the various win conditions if you’d like to try something else!

Update: Tango agreed that the original weights were off, but he views a 10-point system as a constraint. He came up with the same alternate 10-point scale I did, so I’ll change the page to default to using that. This link implements the modified proposal.

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Tracking Injuries…

I’ve just rolled out some enhancements to RotoValue’s handling of injury reports.

Now in addition to displaying reports, and highlighting the injury on player searches, I’ve added a new field, called Target Return:

NBA Injury Report Continue reading

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2015 NBA Projections Take 1

I’ve run the first version of my 2015 NBA Stat projections. There are two versions, RotoValue and AdjRotoValue.

My model starts with a weighted average of recent performance, adds regression to a per-position mean, and applies an aging adjustment (very young players will, other things being equal, tend to improve, while older ones will tend to decline). The RotoValue projections are the output of this basic model. Here’s the top 20 Fantasy Players by my projections for 2015 in a 9-category league:

Top 20 NBA Fantasy Players 2015 Continue reading

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2014 Fantasy All Stars

It’s easy to find lists of the best players in fantasy baseball. Lots of people have opinions on the matter, and plenty use formulas and models to rank players. Clayton Kershaw is baseball’s best starter, and was likely the most valuable pitcher in almost any format. Mike Trout was also outstanding, and while not clearly the best position player for 2014 (in some formatsJose Altuve or Victor Martinez might be worth a little more), he’s a top 3 pick in any draft format.

Today I want to highlight players who exceeded expectations the most. Sure, Trout and Kershaw are great players, but to own them you needed to have a top draft pick, or spend an awful lot of your salary cap at auction, or make an overwhelming trade offer to their owners. Owning a player expected to earn $10 but who winds up earning $20 or more has a much bigger impact on winning your league.

So the most valuable fantasy players are those who produce much more than expected, providing first round value with a mid or late round pick. To highlight such players in 2014, I’m comparing RotoValue prices computed using 2014 actual statistics with those computed using preseason projections, and for this article, I’m using Steamer’s highly regarded projections as input. For dollar values, I’m using a 12-team 5×5 mixed league with an active roster of 8 pitchers and 10 batters. The full description of that league is here, and I describe the basic model to convert statistics to prices given the configuration of a league here.

Player Team Position Actual 2014 Diff
Michael Brantley Indians CF/LF $40.50 $-1.80 $40.50
Victor Martinez Tigers 1B/DH $40.19 $2.84 $37.35
Johnny Cueto Reds SP $46.35 $11.28 $35.07
Corey Kluber Indians SP $38.29 $3.66 $34.62
Nelson Cruz Orioles DH/LF/RF $36.11 $3.43 $32.68
Anthony Rendon Nationals 2B/3B $32.11 $-7.54 $32.11
Todd Frazier Reds 1B/3B $29.96 $-7.50 $29.96
Charlie Blackmon Rockies CF/LF/RF $26.48 $-33.84 $26.48
Jose Altuve Astros 2B $38.84 $13.87 $24.97
Brian Dozier Twins 2B $24.41 $-3.99 $24.41
Dee Gordon Dodgers 2B/SS $24.17 $-23.09 $24.17
Corey Dickerson Rockies CF/LF $22.41 $-14.29 $22.41
Jon Lester Athletics SP $29.76 $7.99 $21.77

Diff is the lesser of the player’s actual RotoValue based on his 2014 stats and his RotoValue based on 2014 minus his RotoValue based on the preseason Steamer forecasts: after all, if you forecast a player to have negative value, you wouldn’t start him. So his actual value is that above 0, not whatever negative price a forecast might imply. My table shows all players who earned at least $20 more than their Steamer projected stats were worth.

Michael Brantley is the fantasy MVP by this calculation, as he earned $40.50 this year despite being projected to be below replacement by Steamer (-$1.80). Steamer projected a mediocre line of .272, 8 HR, 61 R, 55 RBI, and 13 SB, which ranked 68th among players who eventually qualified at outfield. For a league with 36 starting outfielders, an 24 starters at “any” position, that’s below replacement level. But Brantley, who turned 27 in May, posted career bests across the board, batting .327 with 20 HR, 94 R, 97 RBI, and 23 SB (with just 1 CS). Brantley was the second-best position player outright, behind Mike Trout.

Not far behind is Tigers’ DH Victor Martinez (.332, 32, 87, 103, 3 actual, .289, 13, 66, 69, 2 projected). Steamer projected a continuing decline for the 35-year old former catcher, but he instead posted career bests in average and HR. Martinez was the third most valuable batter, period. Steamer was less optimistic on Martinez than my RotoValue projections, which had him worth $16.26 (.295, 16, 69, 88, 1), but Martinez still had a much better year than any projections.

Johnny Cueto was the best pitcher by this metric, and second-best behind Clayton Kershaw overall, as he earned $46.35. Cueto led the NL in innings pitched and strikeouts (242), and ranked second to Kershaw in ERA (2.25), WHIP (0.960), and wins (20). His Steamer projections (1.251, 3.74, 146 K, 11 W) were worth just $11.28. Cueto not only stayed healthy all year after missing most of 2013, he also struck out nearly a batter an inning, by far his highest rate in the big leagues.

Indians’ starter Corey Kluber was almost as big a surprise to Steamer as Cueto. Projected for 1.299, 4.07, 7 W, 146 K, Kluber had a breakout year, boosting his strikeout rate over 10 per 9 IP while posting career best percentages of 1.095 and 2.44. His 18 wins tied the more heralded Max Scherzer and Jered Weaver for the AL lead, while his 269 strikeouts trailed only David Price in all of MLB. While his WHIP far behind Cueto’s, resulting in a lover overall RotoValue, the two pitchers beat their Steamer projected prices by about $35 each, by far the biggest pitching surprises.

Before this season Nelson Cruz only had one season where he played more than 130 games, or had more than 500 AB. While he had always shown great power, he had not put together the monster season he seemed capable of. He was on pace last season before a drug suspension ended his year 50 games early. Steamer projected .253, 24 HR, 63 R, 71 RBI in 466 AB, while my RotoValue projections were quite similar: .258, 21, 56, 71 in 433 AB. And while the per AB rates were good, Cruz was projected to miss at least a quarter of the season, depressing his value because of lower cumulative category totals.

This year, however, he put it all together, leading the majors with 40 HR in 613 AB, and ranking 4th with 108 RBI, while batting .271 with 87 runs and 4 SB. His fantasy year basically matched Miguel Cabrera, as he hit 15 more HR to compensate for fewer runs scored and a lower batting average.

As with Cruz, projections for Anthony Rendon did not anticipate a full season: Steamer projected 448 AB, 11 HR, 55 R, 52 RBI, and 3 SB, numbers which resulted in a negative RotoValue in this format. Rendon matched Cruz’s 613 AB while hitting .287 with an NL-leading 111 runs scored, 21 HR, 83 RBI, and 17 SB. His $32.11 RotoValue was highest among regular third basemen (Miguel Cabrera played 10 games at 3B this year, and might have qualified there in some leagues), while he also likely qualified at 2B. He had little minor league track record, playing just 101 games for 6 teams in parts of 2 seasons, but in that small sample size of 337 AB he showed excellent offensive potential, with a .407 cumulative wOBA. 2014 was probably the last chance to get Rendon cheaply for quite some time.

Todd Frazier had shown power but struggled with getting on base before this season. Steamer projected those trends to continue: .241, 18 HR, 55 R, 61 RBI, 6 SB, numbers which, like Rendon, did not project to be worth owning in this format. Instead, Frazier had a stellar year, posting career bests in all five fantasy categories: .273, 29 HR, 88 R, 80 RBI, and 20 SB. Perhaps much of Frazier’s breakout was bad luck reversing itself, as his BABIP rose from .269 last year to .309 in 2014. But he also added value in steals. While he hadn’t run much in the majors before, Frazier did go 17-21 in steal attempts in just 90 games at Louisville in 2011. His fantasy owners surely appreciated the attempts.

Charlie Blackmon was not even expected to start in the crowded Rockies outfield last spring. Steamer projected him to hit .270 in just 162 AB, with 3 HR, 20 R, 18 RBI and 4 SB. Instead, a torrid April turned him into an every day player, with an expected rise in his cumulative totals. Blackmon hit .389 in April, with 5 HR, 23 RBI, and 7 SB, good for a $54.03 RotoValue for the month, the best in baseball. He cooled off considerably after that, but his year-end totals of .288, 19 HR, 82 R, 72 RBI, and 28 SB were still worth $26.48. Quite nice for someone who wasn’t expected to start! But in practice, I doubt too many owners actually had him in their lineup for all of his hot start. From May 1st onward, he hit .271, 14 HR, 59 R, 54 RBI, 21 SB in 494 AB, good for a $17.63 RotoValue. That’s still a nice return for a player probably unowned after most drafts last year.

Steamer expected Jose Altuve to be a good player: .281, 8 HR, 74 R, 59 RBI, 29 SB, numbers worth $13.87. That’s a solid, productive middle infielder. Instead, Altuve had a huge fatasy year. He led the majors in average at .341, and added 7 HR, 85 R, 59 RBI, and an AL-leading 56 SB, making his year worth $38.84. In some formats, Altuve was worth more than Mike Trout. While he doesn’t have much home run power, Altuve did hit 47 doubles this year. One mild caution sign on an otherwise stellar year: he probably got a little lucky on balls in play. His 2014 BABIP was .360, about 40 points higher than his 2012/2013 averages. If he reverts to those values, his batting average would drop back, which would also reduce his opportunities to steal.

Brian Dozier’s line is perhaps the most surprising of all in this list. Steamer projected .245 with 11 HR, 58 R, 50 RBI, and 12 SB in 481 AB, numbers which would give a slightly negative RotoValue. That forecast actually was spot on in batting average, as Dozier hit .242. But instead of 481 AB, he nearly reached 600, and he posted much better cumulative stats: 23 HR, 71 RBI, 21 SB, and an amazing 112 runs scored, second only to Mike Trout in all of MLB. So he showed more power than projected, and ran more, but the bigger change was in his walks. Steamer projected just 38 BB, and a .303 OBP, numbers in line with his first two big-league campaigns. But Dozier actually walked 89 times, giving him a good .344 OBP despite the low batting average. He still scored more runs than I’d expect just from his OBP, but those extra walks made the run total less shocking. Dozier hadn’t shown much power in the minors (just 19 HR in over 1500 AB over four seasons), but he’s now got 41 HRs over his last two big league seasons. He’s become a much better fantasy player than his minor league numbers would have suggested.

Dee Gordon has long tantalized fantasy owners with the promise of lots of steals from the middle infield. In 2011 he seemed a budding star, batting .304 with 24 SB in just 56 games, but he struggled the next two years, spending more time in AAA Albuquerque than in the majors. So his 2014 projections were weighted down by those two poor years of MLB performance. Steamer projected Gordon for 250 AB, a .247 average, and 21 SB, well below a replacement level fantasy player. But in 2014, Gordon won the starting SS job in the spring and fulfilled his long-expected promise, batting .289 with 2 HR, 94 R, 34 RBI, and an MLB-best 64 SB. His BABIP, which was under .300 in the past two seasons, was .346 this year, so while his fantasy owners greatly enjoyed 2014, if the BABIP regresses, he might not be so fun to own next year. Also, despite an average more than 50 points higher than Brian Dozier’s, Gordon’s OBP of .325 was lower, as he walked just 31 times.

While Charlie Blackmon got the early-season attention for flirting with a .400 average last April, Corey Dickerson rather quietly had a fine season himself in the Rockies outfield. Steamer projected Dickerson for more playing time, but still not a full regular job: .278, 10 HR, 40 RBI, 37 R, 7 SB in 281 AB, not enough playing time to have positive RotoValue in this league. Dickerson didn’t play as much as Blackmon, but he was almost as valuable, batting .312 with 24 HR, 74 R, 76 RBI, and 8 SB in 436 AB. Given that Dickerson is three years younger, hit better in the minors, and on a per-AB basis had a better year in 2014, I’d rather own him next season than Blackmon. Depending, of course, on the price!

The final player on the list is Jon Lester. Prior to this season, it seemed like the now-30 year old Lester’s best years were behind him. He had bounced back from a career-worst year in 2012 to a little worse than his early career averages – a good, but not great, starter. Steamer projected him for a 4.01 ERA, 1.323 WHIP, 13 wins, and 156 Ks in 192 IP, numbers a little worse than 2013, but much better than 2012. That seemed reasonable (my own projections were eerily similar: 4.04, 1.335, 12, 170 Ks in 205 IP). Instead, seemingly out of nowhere, Lester pitched like an ace this year: 2.46, 1.102, 220 Ks, 16 W, earning $29.76. His was the 7th best season among MLB pitchers in this fantasy format – for all practical purposes tied for 6th with David Price ($29.82; 3.26, 1.079, 271 K, 15 W). The big change, it seems, was improved control: in past years Lester walked 3-3.5 batters per 9 innings; in 2014, he cut that to 2, the lowest rate by far of his career. His strikeout rate got back above 9 for the first time since 2010. The trade to Oakland has him in a better pitchers’ park, although if anything he was a little more effective before the trade than after it this year. In any event, Lester projected to be an $8 pitcher, but wound up as a $30 pitcher.

In compiling this list I was at first surprised that there were no relievers at the top. Every year someone projected as a middle reliever or set-up guy winds up as a closer and racks up plenty of saves, and I initially thought such a player would make the list. But I’m used to playing a 4×4 format, where saves is one of just 4 pitching categories. These rankings are based on a 5×5 format with strikeouts, and relievers simply don’t pitch often enough to rack up high strikeout totals. So relievers are worth less in this format than in 4×4. Francisco Rodriguez was projected to be not worth owning by Steamer in this league (3.57, 1.242, 4 W, 5 SV, -$9.07), but wound up with the Brewers’ closing job, earning $14.87 (3.04, 0.985, 5 W, 44 SV). His season ranked 3rd among relievers behind only Greg Holland and Craig Kimbrel.

The other positions not represented in the table above were first base and catcher. Mets 1B Lucas Duda just missed the list, as his year earned $19.91 despite being projected to be unowned, while Devin Mesoraco earned $19.21 while projecting to be a bench player.

If you had several of these players on your fantasy team, you probably had a very good year overall.

By contrast, if you had Prince Fielder, Cliff Lee, or Carlos Gonzalez you probably had a tough year.

Thanks to Jared Cross for making Steamer data available on RotoValue. I still believe that projections, and Steamer is among the best at it, are the best way to value talent for an upcoming fantasy season. It’s inevitable that some players will outperform projections by quite a bit. If you knew in advance who would do that, you’d be win win your league!

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