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Text File | 1995-07-24 | 14.1 KB | 324 lines

BASEBALL.INF August 1, 1995 JUST HOW DOES THIS THING WORK? A few people have asked how SBS goes about simulating a game, so I decided to write down a few notes for those interested. HITTING vs PITCHING - the first step: A hitter can do one of six things in SBS. He can: 1) Make an out. 2) Get a walk. 3) Get a single. 4) Get a double. 5) Get a triple. 6) Get a Home Run. (He could also get on base on an error but that is really a subset of making an out as far as the stats are concerned). SBS calculates from the hitter's record the probability of each occurrence. Then the pitcher's record is considered which modifies the probabilities. This will be demonstrated by working through an example. Consider the batter named Joe Hitter: AB Hits 2B 3B HR BB K AVG Joe Hitter 482 147 20 4 12 41 71 .305 Compute PA (Plate Appearances) = AB + BB = 523 (ignore sacrifice hits and Hit-By-Pitched-Balls which would make PA a little larger) Compute HBB (probability of Walk) = BB / PA = .078 Compute H1 (probability of single) = (Hits - (2B + 3B + HR)) / PA = .212 Compute H2 (probability of double) = 2B / PA = .038 Compute H3 (probability of triple) = 3B / PA = .007 Compute H4 (probability of HR) = HR / PA = .023 ------- .358 What's left is the probability of making an out (or possibly getting on on an error): 1.000 - .358 = .642 We have determined Joe's probabilities as a whole against all the pitchers he faced that particular season. But now we have to calculate probabilities given a particular pitcher. Consider a player named Jack Pitcher: IP Hits HR BB K Jack Pitcher 200 210 15 50 80 If a pitcher threw 200 innings we know he got approximately 600 batters out. The ones he did not get out got hits or walks or reached on errors. Compute BF (batters faced) = (IP x 3) + Hits + BB Sometimes a pitcher gets a few extra outs such as double plays and runners getting thrown out on the bases. On the other hand sometimes he faces extra hitters because his defense makes errors. These two factors just about cancel each other out so we can leave the BF equation alone for purposes of explanation. We now need to compute the probabilities for the pitcher for the same events that we calculated for the batter. Compute BF (batters faced) = (IP x 3) + Hits + BB = 860 Compute PBB (probability of Walk) = BB / BF = .0581 Compute P1 (probability of single) = Hits x .717 / BF = .1751 Compute P2 (probability of double) = Hits x .174 / BF = .0425 Compute P3 (probability of triple) = Hits x .024 / BF = .0059 Compute P4 (probability of HR) = HR / BF = .0174 The statistics do not usually tell us how many singles, doubles and triples a pitcher allowed. Usually just the totals hits and home runs are given. However, we can use the multipliers .717, .174 and .024 to estimate singles, doubles and triples from the total number of hits. [If all "HR's allowed" are zero in the .DAT file, SBS uses a "league average" for P4 found from data in the .CFG file. This essentially removes any influence a pitcher has over this statistic, however]. Comparing the percentages we obtained from the hitter with the pitcher we have come up with the following: Event Hitter Pitcher ------ ------ ------- walk 7.72% 5.81% single 20.90% 17.51% double 3.77% 4.25% triple 0.75% 0.59% home run 2.26% 1.74% out 64.60% 70.10% At first glance it might seem that all we need to do now is average the hitters and pitchers events like this: single = (20.9% + 17.51%) / 2 = 19.21% etc. for the rest of the events This method is unacceptable, however, because it penalizes the outstanding players and rewards the poor players. That is, it tends to lump everyone together too much. In our example above we have a good hitter, (.305 vs the league) against a quite average pitcher. Certainly we could not expect his single% to DROP to 19.21% from 20.90%! After all if this is an average pitcher we would expect our batter to do at least as well against him as he did against the rest of the league! The solution is to use "league averages" for the events and to compare our pitcher's performance against the league averages. For example, we can pick up a baseball statistics magazine containing the statistics from the preceding year, and calculate the total "batter's faced" for all the pitchers for the entire season. We can also total the number of walks, hits, and home runs -- and estimate using our multipliers above -- the total number of singles, doubles, and triples. Then we can calculate our "league averages". For example, we find that for an entire season there was 17,500 innings pitched, 16,500 hits, 1450 Home Runs, 6,300 walks. Calculate League Averages: League Avg. BF = 17,500 x 3 + 16,500 + 6,300 = 75,300 " " " " LABB = 6,300 / 75,300 = .0837 " " " " LA1 = .717 x 16,500 / 75,300 = .1571 " " " " LA2 = .174 x 16,500 / 75,300 = .0381 " " " " LA3 = .024 x 16,500 / 75,300 = .0053 " " " " LA4 = 1,450 / 75,300 = .0193 Finally we can combine our hitter percentages with our pitcher percentages to get meaningful probabilities: Combined percentages: walk% = HBB * (PBB / LABB) = .0536 single% = H1 * (P1 / LA1) = .2329 double% = H2 * (P2 / LA2) = .0421 triple% = H3 * (P3 / LA3) = .0083 home run% = H4 * (P4 / LA4) = .0204 Note that if the pitcher's percentages are nearly equal to the League Averages, the second factor becomes essentially 1 and the hitter performs as expected. But if the pitcher's percentages are substantially better (lower) than the League Averages, the second factor will be less than 1 and the hitter will suffer. The reverse is true if the pitcher's percentages are worse (larger) than the League Averages. RIGHTYS VS LEFTYS - the second step: The example above is the basis of how a given hitter is expected to perform against a given pitcher. But we also can fine-tune our model to correct for the baseball maxim that right-handed batters do better against left-handed pitchers and vice-versa. [A batter facing a like-handed pitcher suffers somewhat]. This is, of course, a very individual thing -- not affecting some players while severely affecting others. SBS does not know which players are exceptional in this area -- the data files do not show a breakdown versus right or left handed opponents. But we can make some broad assumptions which are useful in large simulations. Approximately two-thirds of all innings pitched are by right-handers. Because a typical batter will see so much more right-handed pitching than left-handed pitching, his average vs. left-handed pitching will show a greater fluctuation. Consider the following typical scenario for a RIGHT-handed hitter: AB Hits Avg. _________________ Total | 600 180 .300 | vs. Right-Handed Pitching | 400 116 .290 | vs. Left-Handed Pitching | 200 64 .320 Notice that his boost vs left-handed pitching (20 points) is twice that of his penalty vs. right-handed pitching (10 points). This is because he sees approximately twice as much right-handed pitching over the course of a season. For the typical LEFT-handed hitter: AB Hits Avg. _________________ Total | 600 180 .300 | vs. Right-Handed Pitching | 400 124 .310 | vs. Left-Handed Pitching | 200 56 .280 Notice that his penalty vs left-handed pitching (20 points) is twice that of his boost vs. right-handed pitching (10 points). Again, this is because a full-time player sees twice as much right-handed pitching as left-handed pitching. Actually SBS does not reward and/or penalize by an absolute number of batting "points" but instead increases or decreases each of the hitter's probabilities by a percentage. SBS uses 3% and 6% for the percentages to reward or penalize. This adjustment is spread out among all the types of hits, not just singles. PITCHER FATIGUE FACTOR - the third step: We have looked at two of the three major factors used in determining the percentages of events. The last major factor is the Pitcher Fatigue factor. That is, how does the effectivity of a pitcher vary over the course of a game -- or when does he tire out. SBS uses a linear function for pitcher fatigue which makes a pitcher more effective than normal if the pitcher has worked less than about 4 innings and less effective than normal if the pitcher has worked more than about 4 innings. However SBS treats starting pitchers differently from relievers. SBS assumes relievers tire more quickly so the break-off point is about 2 innings instead of 4. PUTTING IT ALL TOGETHER: Lets say we now have arrived at our five percentages and have adjusted them the way we want for the righty/lefty effect and the pitcher fatigue effect. We now need to "stack" them on top of each other and calculate the "break" points. Now the percentages are some fraction between 0 and 1. bk1 = walk% bk2 = bk1 + single% bk3 = bk2 + double% bk4 = bk3 + triple% bk5 = bk4 + home run% We now call our random number function which returns a (pseudo) random number between 0 and 1 -- and compare it with our break points. If "x" is our random number: If x is greater than 0 but less than bk1 --> walk If x is greater than bk1 but less than bk2 --> single If x is greater than bk2 but less than bk3 --> double If x is greater than bk3 but less than bk4 --> triple If x is greater than bk4 but less than bk5 --> home run If x is greater than bk5 but less than 1 --> out OR on by error Handling the "outs" is a matter of deciding to which defensive player the ball was hit, whether or not it was a ground ball or a fly ball, and whether or not the defensive man handled it cleanly. Whether or not a player "pulls" the ball is influenced by the velocity of the pitcher. That is, his ability to "get around" on the pitcher. SBS uses a function based on a pitcher's strike out percentage to simulate his velocity and thus a hitter's ability to pull the ball. So a pitcher with big strike out totals is more difficult to pull than the pitcher who doesn't strike out many. OK, this is crude but its the best we've got! SPEED/STOLEN BASES: The .dat files contain a column for stolen bases which SBS translates (via a formula) into a general purpose speed rating (1-9). You can view this speed rating by popping up your lineup or the opponent's lineup. The numbers 1 through 9 are roughly proportional to a player's chances of stealing 2nd or 3rd base. That is, a player with a speed rating of 9 would have approximately a 90% chance of stealing 2nd or 3rd. A rating of 5 would be a 50% chance, etc. If the opponent calls a pitch-out the chance of success is reduced by 25% (but the chance of walking the batter increases by 25%). The chance of success is also reduced if a runner on 1st is trying to steal against a left-handed pitcher or a runner or 2nd is trying to steal against a right-handed pitcher. The formula to calculate the speed rating from the .dat file information estimates the number of times the player made it to first base (ABs, singles & BBs) and then multiplies that by a fraction to estimate the number of steal opportunities the player might have had. Then it compares that estimate to the number of stolen bases and assigns a speed rating. The method is somewhat crude in that is penalizes fast players that happen to play on teams that just do not attempt to steal. On the other hand it helps players who are efficient at stealing bases even if they are not actually all that fast. The speed rating has other uses beside the stolen base. It helps determine the likelihood of the player hitting into a double play or successfully executing a drag bunt. It also helps determine if a runner goes from 1st to 3rd on a single or scores from 2nd on a single. Or if a runner on 1st can score on a double. (The number of outs and where the ball is hit is a big factor here also. For example, runners tend to play it safe with no outs but usually will try to take the extra base with two out). INFIELD "IN": This defensive strategy will cut off almost all runners who would otherwise score on a ground ball to an infielder [especially to the shortstop or second baseman]. The penalty is that the batter's base-hit percentages are adjusted upward dramatically because more ground balls will go through the infield. A .250 hitter becomes a .350 hitter. [When the player or the automatic manager chooses to play the infield in, it is only in effect for the current batter]. AUTOMATIC MANAGER: SBS has not yet been programmed for brilliant management, but it does make basic offensive and defensive maneuvers. On defense SBS can: 1) pull the infield in 2) call for a pitch-out 3) call for an intentional walk 4) evaluate pitcher and go to the bullpen if necessary On offense SBS can: 1) pinch hit if a suitable pinch hitter is available 2) sacrifice bunt or squeeze bunt 3) steal The automatic manager does no pinch running or double-switch stuff. No "chess games" vs the other side. You will find that on offense the automatic manager is fairly aggressive. He is not shy about trying to steal bases or squeeze home a run. HAVE FUN: I hope this gives you a general idea of how the program operates. If you have questions, feel free to write.