How League Size Affects Prices

Last week I did two posts¬†showing the top 10 in each league for both 4×4 and 5×5 scoring formats using the RotoValue pricing model. In each case I was assuming a 10 team league with 13 batters (14 in the AL, adding a DH) and 10 pitchers, a $260 salary cap, and a 4 player reserve purchased at auction but whose stats don’t count. Today I’ll compare how prices of the top 10 vary based on league size, keeping the roster sizes and salary cap the same, but looking also at 8 and 12 team fantasy leagues.
For the NL, the top 10 5×5 players in 2011 were:

Player Pos Price
8 Team 10 Team 12 Team
Matt Kemp OF $47.04 $48.18 $49.73
Ryan Braun OF $41.16 $42.54 $43.99
Clayton Kershaw P $36.18 $37.44 $37.16
Albert Pujols 1B $31.37 $33.27 $34.30
Prince Fielder 1B $30.90 $32.82 $33.87
Roy Halladay P $31.11 $32.58 $32.53
Cliff Lee P $30.79 $32.28 $32.25
Joey Votto 1B $29.65 $31.62 $32.73
Justin Upton OF $29.15 $31.02 $33.02
Troy Tulowitzki SS $27.91 $28.70 $30.09

Top batters gain value when the league gets larger, which is understandable. There’s more money to be spent, and while there are more players to own, the players being owned get much worse on offense, if only because of playing time. An 8 team NL needs a total of 40 starting outfielders, but in the 16-team NL, there are 48 starters. There is similar surplus at infield positions, and most major league teams give significant playing time to 2 catchers, but the fantasy league starts just 16. So in the 8-team format, some players getting regular playing time will remain unowned. In the 10 team format, that excess goes away (50 starting fantasy OFs, but only 48 in the NL, for example), and in the 12 team format there’s a squeeze for playing time. So the marginal batter gets much worse.
By contrast, pitching is much less affected. 16 NL teams have 80 pitchers in their rotations, and at least another 80 bullpen arms to choose from. The 8 team NL would use not even half of those pitchers, and even the 12 team league would use only 3/4. There’s better replacement-level talent among pitchers than batters, so increasing league size has less impact on pitchers’ prices. Indeed the very best pitchers prices actually dropped going from the 10 to the 12 team league (although pitchers further down the list still showed higher prices in the larger league).
Now let’s see the American league table, again for the same 3 roster sizes:

Player Pos Price
8 Team 10 Team 12 Team
Jacoby Ellsbury OF $37.15 $37.75 $39.37
Curtis Granderson OF $33.79 $34.66 $36.43
Justin Verlander P $34.80 $33.93 $33.76
Jose Bautista 3B/OF $30.05 $30.33 $31.66
Dustin Pedroia 2B $26.44 $29.94 $31.06
Ian Kinsler 2B $26.15 $29.67 $30.80
Robinson Cano 2B $26.11 $29.63 $30.77
Miguel Cabrera 1B $29.00 $29.37 $30.26
Adrian Gonzalez 1B $28.85 $29.23 $30.13
Jered Weaver P $26.13 $25.96 $26.09*

* Weaver ranked 12th in RotoValue among 12-team leagues, behind both Alex Gordon ($26.98) and Melky Cabrera ($26.91).
The AL follows a similar pattern to the NL: top batters gain value as league size increases, but elite pitchers stay about the same. As with the NL, good, but not great, pitchers, do see their prices rise: for example, Ricky Romero was worth $18.58 in an 8 team league, $19.02 in a 10 team league, and $19.48 in a 12 team league. Yet while his price rose, his relative ranking was falling, from 30th to 36th to 45th overall. Batters hold value better than pitchers, because as competition for talent becomes fiercer (more dollars chasing the same number of good players), the advantages of top batters relative to replacement level grows bigger than that for pitchers.
With similar roster sizes, American League fantasy leagues already face a greater squeeze on talent than NL leagues: the AL has just 14 teams, not 16, so even an 8 team AL league would use almost all the starting OFs (40 fantasy starters, 42 AL starters). In a 12 team league, some very weak position players indeed must be in someone’s starting lineup.
While no catchers made the top 10 in either league, they came closer in the smaller fantasy leagues. In the AL, Mike Napoli ranked 12th ($24.28) and Victor Martinez 13th ($23.86) in the 8 team format, but they fell to 17th ($23.30) and 20th ($22.92) in 10 team, and 20th ($24.00) and 22nd ($23.63) in a 12 team format. This happens because the weakest starting fantasy catcher in an 8 team AL league that starts two catchers is already a rather bad player, whereas at OF or an infield spot that player might still put up decent numbers. Yet when you move to a 12 team league, someone is starting quite weak players at every position, and so the strong players at those positions where the worst starter is now weak gain the most relative value.
Another thing I find interesting in the AL table is the huge jump the second basemen get in going from an 8 team to a 10 team league. Pedroia, Kinsler, and Cano all see their prices rise more than $3 each, while first basemen Miguel Cabrera and Adrian Gonzalez see less than a $0.40 rise. The reason for this is the position depth. In just an 8 team league, you need only 24 middle infielders, and in the 14 team AL, the 24th best middle infielder is still pretty good. But when you switch to a 10 team league, and you now need 30, teams now must start much weaker middle infielders. There’s a dropoff at corner infield, too, but not nearly so steep (in part also because it’s quite common for DHs to gain 1B eligibility during the year). So because there’s more depth at corner infield, as talent becomes scarcer, the middle infielders’ values rise much more.
The key point is that value is relative to context. When there are fairly decent alternatives at a position, it is less important to try to get a very good player. But when the position is quite weak, that makes the premium on its stars much higher.

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