FanNation - The Republic of Sport

Yet another ranking system, using a diminishing returns run differential metric, is introduced this week that combines the features of the previous ratings via a) runs scored/run allowed (RS/RA) and b) wins/losses (W/R). In the past few weeks I have written about two different ranking systems: the RS/RA ratings that take into account runs scored and runs allowed and use the Pythagenpat formula to determine a hypothetical win/loss percentage, and the W/L ratings that use only win/loss data to determine a win probability for any two teams. The RS/RA system awards teams that score more runs than their opponents, even if many of them are scored in blowouts and are therefore essentially meaningless; the W/L system never uses the run margin, so that, for example, a three-run win is always valued the same as a one-run win. This week I introduce another ranking system (actually, a family of ranking systems) that tries to incorporate aspects of both the RS/RA and W/L systems. It uses run differentials in individual games, but each additional run is valued less than the previous one by a factor r that ranges between 0 and 1. For example, if the factor is r = 1/2, a one-run win counts as a differential of 1, a two-run win counts as 1 + 1/2 = 1 1/2, a three-run win counts as 1 + 1/2 + 1/4 = 1 3/4, etc. Math geeks will recognize that this is a geometric series and that the maximum differential for a given r is 1/(1-r), i.e., for the r = 1/2 case, the maximum differential for a game is 2. I call the number ???r??? the diminishing returns factor, since each additional run counts less than the previous one. The ratings are then determined by doing a least squares fit to the actual games results (similar to the original RS/RA ratings). A home field advantage factor is also calculated for each value of r. The result is the diminishing returns run differential (DRRD) rankings. Using r = 0 means that a win counts as a difference of 1 between the teams, regardless of what the actual run differential is. It turns out that this gives almost the same rank ordering as the W/L ranking system introduced last week. This similarity is not too surprising considering both systems use the same data, i.e., only wins and losses. Slight differences in the rank ordering sometimes occur when the ratings for two teams are very close. Using r = 1 means that the full run differential in each game is used. Not surprisingly, this gives rankings that are very similar to the RS/RA ranking system. There are some differences due to the fact that the RS/RA system uses the Pythagenpat formula, which mathematically uses run ratios rather than run differences. It???s obvious now that we can choose a value of r in between 0 and 1 to have a ranking system that combines features of both the RS/RA and W/L systems. A value near 0 will emphasize winning, but makes some allowance for winning margin; a number near 1 will emphasize run differentials, but will discount blowouts to some extent. In the table below, this family of rankings is shown for r = 0 to 1.0 in steps of 0.1. The order is chosen according to the r = 0 rankings, which are nearly identical to the W/L rankings. The 1.0 rankings on the far right are nearly identical to the RS/RA rankings. The rankings are for games through Sunday, August 10, and the actual wins and losses, runs scored and runs allowed are also shown. Team W L 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 RS RA Ana 72 43 1 1 1 1 1 1 1 2 2 2 5 538 484 Tam 69 46 2 2 2 2 2 3 3 3 3 4 3 520 464 Bos 66 50 3 3 3 3 3 2 2 1 1 1 1 579 474 ChW 64 50 4 4 4 4 4 4 4 4 4 3 2 573 505 Min 64 51 5 5 5 6 6 6 6 6 6 7 8 571 537 NYY 63 53 6 7 7 7 7 7 7 7 7 6 6 562 513 ChC 70 46 7 6 6 5 5 5 5 5 5 5 4 618 474 Tor 59 57 8 8 8 8 8 8 8 8 8 8 7 498 460 Mil 65 51 9 9 9 10 12 12 13 14 14 15 16 540 512 Tex 60 57 10 10 10 11 11 11 12 12 13 14 14 652 690 Bal 55 59 11 11 11 9 9 9 9 9 11 11 12 555 568 Det 56 59 12 12 12 12 10 10 10 10 9 10 10 579 564 StL 64 54 13 13 13 13 13 14 14 15 15 16 17 560 530 Phi 62 53 14 14 14 14 15 15 15 13 12 12 13 563 493 Oak 54 61 15 15 15 15 14 13 11 11 10 9 9 467 450 KCR 53 63 16 17 17 17 17 17 18 18 20 21 21 488 565 NYM 61 54 17 16 16 16 16 16 16 16 17 17 15 555 514 Fla 61 55 18 18 18 18 18 19 20 22 22 22 23 546 568 Hou 56 59 19 19 19 19 20 21 23 23 23 24 24 511 560 Cle 50 64 20 20 20 20 19 18 17 17 16 13 11 532 531 LAD 58 57 21 21 21 21 21 20 19 19 18 18 18 484 456 Ari 59 57 22 22 22 22 22 22 21 21 21 20 20 524 504 Pit 53 62 23 23 24 24 24 24 25 25 25 26 26 554 631 Atl 54 62 24 24 23 23 23 23 22 20 19 19 19 532 509 Cin 52 65 25 27 27 27 27 27 27 27 27 27 27 505 594 Col 53 65 26 26 26 26 26 26 26 26 26 25 25 547 604 Sea 45 71 27 25 25 25 25 25 24 24 24 23 22 476 550 SFG 48 66 28 28 28 28 28 28 28 28 28 28 28 438 532 Was 44 72 29 29 29 29 29 29 29 29 29 29 29 440 557 SDP 44 72 30 30 30 30 30 30 30 30 30 30 30 435 549 We see that the Angels are ranked first for low values of r, where wins are valued more than run differentials. As the value of runs increases, the Angels ranking decreases, reaching 5th for r = 1.0. The Red Sox are ranked first for r = 1.0, and are still ranked 3rd for r = 0. The Rays are 2nd or 3rd across the board, except for a 4th place ranking for r = 0.9. It???s easy to see in the table how teams with good run differentials and not as good records do better for larger r, and teams with a better record than run differential do better for smaller r. As with the RS/RA and W/L systems, AL teams get a more favorable ranking than NL teams with similar RS/RA ratios or win percentage due to the AL???s 149-103 inter-league record, which leads to much higher schedule strengths for AL teams. It???s interesting to see how some teams??? rankings vary with r. The Indians have the largest variation, going from 20th for r = 0 (due to their poor record) to 11th for r = 1.0 (since they have scored more runs than they allowed). Similarly, the A???s range from 15th to 9th. The Brewers have the largest variation in the other direction, from 9th to 16th, since their run differentials is not as good as their record. On the other hand, five teams (Jays, Reds, Giants, Nats and Padres) have the same ranking across the board. The rankings with r near 0.5, which splits the difference between RS/RA and W/L, look fairly reasonable to me (at least near the top), but your mileage may vary. The advantage of the hybrid DRRD system is that you can choose how much you want to emphasize runs versus wins. One can certainly quibble with some of the relative rankings in the table above. For example, the Jays are always ranked ahead of the Brewers, despite having a significantly poorer record, which on its face does look right. However, the Jays are in the toughest division (with the Rays, Red Sox, Yankees, and even the Orioles are 37-32 against non-AL East teams), so this may not be as far-fetched as it first appears. In the next week or two I may look at some apparent ranking anomalies to see how they stand up under closer inspection.