Tuesday, October 29, 2013

Cardinals vs Red Sox - World Series Game 6 Simulation Results



                                 Top 100 Most Likely Final Scores
RankCardinalsRed SoxOccurrencesRankCardinalsRed SoxOccurrences
1234699951065999
2124294652755618
3343860453575295
4323163254825002
5212938655834855
6132604456704782
7452558857764773
8432550958814687
9312455359284549
10012450560384438
11242428461844241
12422346462184058
13411955363074032
14021897164483684
15141884465853471
16201712466783422
17521699267923249
18251695368583121
19531689869803114
20541683470932932
21351669871292878
22101652572912862
23031538073392745
24301510674862736
25511480675082612
26561466876682582
27151327777192539
28401310678942513
29621192879492273
30041160880872170
31631160081952157
32361157482901906
332610701831021880
346110696841031799
356410389852101736
364610098861011706
3750996087591703
3865950888091692
3916921289961669
40058388903101632
41728029911101556
4273763992891538
43677575931041538
4460729994691491
45717074954101390
46276994961051237
4737678597971228
4874661998791145
49476430991001117
501762441005101078

World Series Remaining Game Odds


With a maximum of two games remaining in the 2013 World Series this is the last installment of the reverse engineered game odds.  The only unknown left is the odds for Game #7.  The Game #6 odds and the final series winner odds are both out and from those two knowns we can reverse engineer what the Game #7 odds are (or should be).

     Individual Game Odds
Game # Red SoxCardinals
Game 1100%0%
Game 20%100%
Game 30%100%
Game 4100%0%
Game 5100%0%
Game 653.16%46.84%
Game 755.75%44.25%
Series79.27%20.73%

And using the nifty spreadsheet calculator that one of my readers made for me, we can also see the chances that each team wins the series in X number of games.  There are only three possible outcomes left obviously and they are the Red Sox winning in six or seven games or the Cardinals winning in seven games.  Here is another table showing those odds.

ResultChance %Odds
79.27%
Red Sox in 40.0%NA
Red Sox in 50.0%NA
Red Sox in 653.16%0.88
Red Sox in 726.11%2.83
20.73%
Cardinals in 40.0%NA
Cardinals in 50.0%NA
Cardinals in 60.0%NA
Cardinals in 720.73%3.82

Monday, October 28, 2013

Red Sox vs Cardinals - World Series Game 5 Simulation Results




                                       Top 100 Most Likely Final Scores
RankRed SoxCardinalsOccurrencesRankRed SoxCardinalsOccurrences
11246055173565
22345165271558
33434435360552
42132145418502
53231805557495
60128735675485
71328205738453
84324225876424
93123625908418
102423596029396
111422556170377
120222396283375
134522336382374
141021426419367
154221176548351
160319866681348
172017936739343
184117716858316
192517486984308
200416727009304
211516597185277
223515587278276
235415337349256
243015127492254
255214817580249
2653147176110231
275112537786228
2826124978210225
295612167968225
300511888093216
314011678191211
3216115082010204
3336113283310198
346310038487198
35629588594193
36469188659165
37179128795164
386485788410162
39068548990159
406584490103149
41508289169144
422781492211143
436179293101141
443770494111137
45476369596135
46076069689128
477459797102127
48675959897123
497257899011118
5028571100311113

Sunday, October 27, 2013

Red Sox vs Cardinals - World Series Game 4 Simulation Results




                                       Top 100 Most Likely Final Scores
RankRed SoxCardinalsOccurrencesRankRed SoxCardinalsOccurrences
12341345171665
21236035276629
33433915357598
43228665460569
52126745507561
64325355628542
71323735783530
84523285882528
92422805938514
103121636018493
114221536184465
121419646285447
130119036348444
145417746481441
154117016570433
162516856619420
170216726708376
183516526878376
195316436958370
205216197039366
211015937129360
222015627286351
230315447393340
241515347480315
255614967592308
265113727694301
273013427768300
280412507891292
296312097949290
302611758087272
3136115081210251
3262111882110240
336411088309233
341610858495221
3565108385410214
3640105986310207
3705104487102206
384610238859205
396190989103200
40678179089196
41508079196196
42178039269182
432779393104179
443777994101172
457476195211158
460675996311157
47737599790157
48477139897149
497269899010148
5075667100105141

Friday, October 25, 2013

Red Sox vs Cardinals - World Series Game Three Simulation Results




                                       Top 100 Most Likely Final Scores
RankRed SoxCardinalsOccurrencesRankRed SoxCardinalsOccurrences
1234294851755988
2123938652475746
3343457953825340
4323443754835065
5213166955704965
6432755856764930
7312597257574921
8132525558814567
9422495459844314
10452328560284309
11242319961074220
12012184862383973
13412050463183933
14141989464853770
15101895365923396
16201840766483313
17521829567933118
18531803068803091
19021786969783048
20541779170862962
21251675071912951
22351621372582838
23301613173942740
24031591174082668
25511474075292637
26151416876392536
27561320777192466
28401271778872355
29041251679682297
30631247580952069
31621218981902041
32641105882492002
332610874831021900
343610684841031839
356110537851011815
36651010886961761
37509662872101657
38469613881041615
3916958989091598
4005930390591591
41728209913101532
42737940921101475
4374745893691314
44717135941051314
45607028951001238
4667686296971230
4727678897891202
48376475984101178
49176343991121149
500663121001131092

World Series Individual Game Odds Reverse Engineered


Here are the odds of each remaining World Series game based on the knowledge of the Vegas odds that each team wins the World Series and the Vegas odds for games 1,2 and 3.  The odds for games 1,2 and 3 give us a good approximation for the odds in games 5,6 and 7 and we can move the game four odds around in such a way that the chances for each team winning the series match the Vegas odds.

Here is a look at the table with the individual game odds.

Game #Red SoxCardinals
Game 1100.0%0.0%
Game 20.0%100.0%
Game 350.6%49.4%
Game 449.3%50.7%
Game 545.9%54.1%
Game 652.0%48.0%
Game 758.6%41.4%
Series52.4%47.6%

And here is a table with the chances of the series ending with one team winning in X number of games.

ResultChance %Odds
52.4%
Red Sox in 40.0%NA
Red Sox in 511.5%7.73
Red Sox in 619.0%4.28
Red Sox in 722.0%3.55
47.6%
Cardinals in 40.0%NA
Cardinals in 513.5%6.38
Cardinals in 618.5%4.40
Cardinals in 715.5%5.43

Notes
- HFA of 4% is assumed
- Data was computed with spreadsheet provided by one of my readers.

Thursday, October 24, 2013

World Series Individual Game Odds


Vegas has come out and given the Red Sox a 68.75% chance of winning the World Series.  So I am going to try to reverse engineer the odds of the remaining games as if we didn't know who the pitchers were, just where the games were being played (no advanced handicapping).  What we know is that the Red Sox were a 53.9% favorite in Game #1 and are a 53.4% favorite in Game #2.  Knowing the odds in Game #1 gives me a hint at the odds in Game #5 (assuming 4 man rotations and HFA of 4%), so I am going to subtract 8% from the Game #1 odds and give the Red Sox a 45.9% chance of winning Game #5.  I can do a similar thing with the Game #6 odds, as I can copy the Game #2 odds as that game will be played in the same park.  Now I just need to massage the numbers in games 3,4,5 and 7 in an attempt to make the Red Sox chances of winning come as close to 68.75% as possible.  The game 7 odds will be an 8% difference of the game 3 odds.

Using the nifty spreadsheet that my reader gave me in one of the previous similar exercises I did in the NLCS we come up with the following table of individual game odds needed to have the Red Sox be 68.75% favorites to win the World Series following the Game #1 results.  To take this to the next level you would break down the odds of games three and four by looking at the probably starting pitchers.  Where one of the two games would move up in odds, the other would need to move down.

Game #Red SoxCardinals
Game 1100.0%0.0%
Game 253.4%46.6%
Game 349.7%51.2%
Game 449.7%51.2%
Game 545.9%51.2%
Game 653.4%46.6%
Game 757.7%43.2%
Series68.7%31.3%

And below is the table that shows the percent chances and odds of each possible result in the World Series.

ResultChance %Odds
68.7%
Red Sox in 413.2%6.58
Red Sox in 517.5%4.70
Red Sox in 620.1%3.98
Red Sox in 717.9%4.59
31.3%
Cardinals in 40.0%NA
Cardinals in 56.4%14.58
Cardinals in 611.8%7.47
Cardinals in 713.1%6.62


Wednesday, October 23, 2013

Cardinals vs Red Sox - World Series Game #2 Simulation




                                     Top 100 Most Likely Final Scores
RankCardinalsRed SoxOccurrencesRankCardinalsRed SoxOccurrences
12345545106629
21241575275570
33438035357565
43230295483558
52128105576522
61326295681490
74525965782483
84324915870470
93123925938466
102423806018463
110123266184442
124222786228431
131418646307403
140218556448379
154118056578351
162517366685351
175417146793334
185316906858331
193516846980322
205216577092322
212015417139299
220315237291298
231015167386297
245614977429286
255114477568274
263014177608263
271513617719259
280411867895256
294011537949252
306211528087248
313611498194248
3263113682102213
3326112283103203
3464102984210202
3561102385101198
364610198690193
376598287310179
38169268809177
395092589104175
40728589059171
410585491110170
42738059269169
43677829389155
447175094410150
45277089596150
467468596105146
473768397100135
48476719897126
491765199211123
5060639100510120

Thursday, October 17, 2013

Dodgers vs Cardinals - NLCS Game 6 Simulation Results




                                        Top 100 Most Likely Final Scores
RankDodgersCardinalsOccurrencesRankDodgersCardinalsOccurrences
1125564451273958
2234739952173864
3214648753833677
4014089954673640
5323939255373525
6103700856753487
7313555857473011
8203424258912871
9343140159072784
10302974860842772
11412659761762716
12422619462922708
13432489363902676
14132472564282414
15022446765572296
16402278266182281
17241865467932213
18511843868852054
19521779769381993
204517141701011771
21031686071081766
22141656072481679
235016291731001617
24531530574941580
25541325875191513
26611239476781504
272511494771021499
28041137778291447
29621135279861425
30601102880581321
31351082981391283
321510001821031239
3363968983871181
3456820184951105
3571781785091085
3664761686681013
37057334871111009
387071348849925
3972711789110916
4026674590104906
4165639491112875
4236635092210870
4316619993110847
447359849496808
4546548695113770
468150639659711
4774468297310698
4806451198010648
4982450799105603
50804448100410568

The Odds Couple of Games


Vegas now lists the Dodgers chances of winning the NLCS as 23.2% and gives them a 55.7% chance of winning Game #6 in which Clayton Kershaw pitches. From those two pieces of information we can reverse engineer the Dodgers odds in Game #7. Below is a table showing this information. The math is getting a lot easier with only two possible games remaining.

GameLAD PitcherSTL PitcherLAD Win%
         6C.KershawM.Wacha55.70%
         7H.RyuA.Wainwright41.70%
NLCS Winner23.20%

Wednesday, October 16, 2013

Oddly Enough for The Dodgers


Not hope remains for the Dodgers in the NLCS. Vegas odds give the Dodgers a 13.6% chance of winning the NLCS, a feat that would involve winning the last three games of the series, with the last two games being played in St.Louis. The Dodgers are a generous 61.8% Vegas favorite in Game #5 and knowing that and the 13.6% number we can reverse engineer the probable odds of Game #6 and Game #7. Also we can easily calculate the odds that the series ends in a 5, 6 or 7 game victory for the Cardinals or a seven game victory for the Dodgers.

Reverse Engineered Game Odds
GameLAD StarterLAD Win%
5Z.Greinke61.8
6C.Kershaw56.0
7H.Ryu39.2

Series Result Odds
Result% Chance
Cardinals in 538.2%
Cardinals in 627.2%
Cardinals in 721.0%
Dodgers in 713.6%

Cardinals vs Dodgers - NLCS Game 5 Simulation Results



                                      Top 100 Most Likely Final Scores
RankCardinalsDodgersOccurrencesRankCardinalsDodgersOccurrences
1234771751605803
2124649152745517
3343673453285216
4213163454185031
5323155655754969
6012897456574517
7132848157384446
8242443358764316
9312407359824254
10432407360704063
11452330061833917
12022309462813825
13142265863083790
14422129264483514
15032081865843485
16101950166293222
17201787867193154
18251787168782988
19411734769852869
20151634870922760
21041634471392751
22351617972582712
23541520073802675
24531511974932551
25301488375912425
26521462576092381
27561296477862377
28511242478492100
29051204179942087
30261153380682072
314011337812101981
32161129982871977
333610786831101916
3462987184951814
3563976085901720
36469252863101691
37649013871021659
38618731881031611
3906864289591537
40658585901011487
4150804391961419
42277781920101393
4317755393691278
44376874941041272
45736445954101264
4672631996891244
47676308972111167
48475914981111150
4971587699971067
500758111003111039

Tuesday, October 15, 2013

A Case For Ricky Nolasco Game Four NLCS


In case you've been on the moon or busy watching soccer there has been some discussion in Dodgers-Land about whether or not to skip Ricky Nolasco in Game #4 of the NLCS or bring back Zack Greinke to pitch on short rest. I decided to take a back of the envelope look at which decision is the correct way to go. My exercise won't go into the nitty-gritty details which would add a little more precision to the numbers but it will provide a good framework and maybe some guidance into what the best decision is.

In general there is a 0.5 RA/9ip penalty for pitching on three days rest and there is probably a little penalty for pitching on too many days rest but let's leave that number unknown for now. What I did is made a table with the RA/9 expectancies for each of the Dodgers four starting pitchers. Then output tables showing which starting pitching arrangement looks best. The RA/9ip estimates can be changed if you don't agree with them, this is just the framework and with the framework you can tell how bad of a pitcher Nolasco must be to make skipping him and starting Greinke (and even perhaps Kershaw and Ryu) on short rest.

Input Table
PitcherRA/9IP
Kershaw2.25
Greinke3
Ryu3.5
Nolasco4

Now let's come up with some rotation arrangements. Let's first start off with the one where Nolasco pitches Game #4 and Greinke, Kershaw and Ryu all pitch on regular rest.

GameRestLAD StarterRA/9
4NormalNolasco4
5NormalGreinke3
6NormalKershaw2.25
7NormalRyu3.5
Total12.75

Now let's see what happens if Nolasco is skipped and Greinke (G4, G7), Kershaw (G5) and Ryu (G6) all pitch on short rest. Notice the 0.5 RA/9ip penalty applied.

GameRestLAD StarterRA/9
4ShortGreinke3.5
5ShortKershaw2.75
6ShortRyu4
7ShortGreinke3.5
Total13.75

This particular arrangement does not fair too well as you are applying four 0.5 RA/9ip penalties, adding up to 2.0 RA/9ip over four games. Nolasco's projection MUST be very very bad for this option to win out. How bad? I will visit that later.

Now onto the arrangement where Zack Greinke pitches Game #4 on short rest then Nolasco pitches Game #5 and Kershaw and Ryu pitch the last two games on full rest. I call this the "Rearranging The Deck Chairs" option.

GameRestLAD StarterRA/9
4ShortGreinke3.5
5NormalNolasco4
6NormalKershaw2.25
7NormalRyu3.5
Total13.25

This option always loses out to the first option as you are just swapping Game #4 and Game #5 starters and adding a penalty to Greinke's start. This option is stupid.

So it comes down to the first two options and the first option will win out unless you think that Nolasco is a terrible pitcher. Just how terrible in terms of RA/9ip? And you can feel free to combine Nolasco's RA/9ip with that of Volquez if you think they will tag team their start. Only good thing about that is that you can get an early pinch hitter at-bat in the game. But let's get back to the question of how bad would Nolasco's RA/9ip projection have to be to make the second option a better one than the third. The break even point for Nolasco's RA/9ip projection is 5.0. If you think his RA/9ip projection is worse than 5.0 then the second option would be better and you would go with a three man rotation. Of course there are some other minor things to take into consideration, so you could add or subtract those in to the RA/9ip projections but this exercise gives you an idea for which rotation arrangement is best.

I think the Dodgers should start Nolasco and if he isn't terribly sharp or being hit hard to pinch hit for him in either his first or second at-bat and then to use Volquez until he bats and then to let the bullpen finish out the game. Hopefully, you won't go extra innings as you will be using a lot of your bullets early on in the game.

Monday, October 14, 2013

Cardinals vs Dodgers - Simulation Results NLCS Game #4




                                           Top 100 Most Likely Final Scores
RankCardinalsDodgersOccurrencesRankCardinalsDodgersOccurrences
1234759351475743
2124584352705119
3343754653755073
4323288954824861
5213217555574685
6012699356814659
7132624257834645
8312577758284494
9432489759764422
10452371560074222
11242327061184010
12422314862843910
13022016663383894
14142003864483309
15101962865803294
16411942166853151
17201899567923124
18031656468783084
19301654669913048
20521620870932906
21251618571582835
22351618072082710
23531617073292671
24541605574862535
25511454375192514
26151402076392456
27561341377942441
28401338878682209
29041268179902171
30621132880872043
316310590811022034
32261057082492001
33361053783951925
346110135841011837
35509768851031737
36649653862101716
3716942887091704
38059345883101559
39469132891101506
4065888290591484
41727527911041482
4260723592961427
4371713393891369
44737039941001353
4527674995691222
46676682964101202
4706651297971172
48376264981121167
49176150991111128
507461371001051119

Updates NLCS Individual Game Odds


Here is an updated list of the individual game odds for the remaining games of the NLCS. As a reminder, the way the game odds are calculated is take the Vegas odds of the Cardinals winning the NLCS, which the last time I looked was (-350, +290) 76.19% chance of winning. We can give the Dodgers a 0% chance of winning for the games they already lost and we can input a win probability of 47.4% for Game #3 as those odds have already been published. Now to figure out the odds of the remaining games (Games 4-7) we need to adjust them until the string of games gives us a 23.81% chance of the Dodgers winning the series. To do this, I used the nifty excel spreadsheet that one of my readers gave me in the comments of the previous post on this topic. While these won't be the likely odds for Games four thru seven they are good "ballpark" estimates. And if you don't agree with any of these game odds, that is fine... but you will need to adjust the odds of some of the other games to even out any changes you made one way or the other.

GameAway StarterHome StarterDodgers Odds
1Zack GreinkeJoe Kelly0.0%
2Clayton KershawMichael Wacha0.0%
3Adam WainwrightHyun-Jin Ryu47.4%
4Shelby MillerRicky Nolasco59.0%
5Joe KellyZack Greinke65.0%
6Clayton KershawMichael Wacha57.0%
7Hyun-Jin RyuAdam Wainwright42.0%
Total23.8%

Saturday, October 12, 2013

Cardinals vs Dodgers - NLCS Game #3 Simulation Results




                                     Top 100 Most Likely Final Scores
RankCardinalsDodgersOccurrencesRankCardinalsDodgersOccurrences
11255885117409
22348375227402
32143495383386
40141085437375
53236165567366
63132975675365
71032645747356
83432235892321
92030415990320
101326546091319
114225916184304
123025216257286
130225116307285
144324646476261
154123796528253
164020256693251
172420156785248
180318306818227
194518236938220
2051179070101217
2114174671100192
2252168472102184
235315717394174
245014237408169
255414197548162
262512737686160
276112137778158
280412097829156
293511807919151
3015114980103137
3162114281111132
32609988287131
33639788358126
34569578495119
35648138539117
360579486104117
377178887112115
387276988110110
393673189113107
40167259049102
41266729168101
4270670920994
43656339310591
4473606949690
45466059531080
46815579621078
47065369712073
4874497989768
49824629910668
508045110012268

Friday, October 11, 2013

Dodgers vs Cardinals - NLCS Game #1 Simulation Results



Note: Vegas has the Dodgers as 55.6% favorites in Game #1 (ML -130, +120)

                                       Top 100 Most Likely Final Scores
RankDodgersCardinalsOccurrencesRankDodgersCardinalsOccurrences
12344025117569
21240595237566
33435315381555
43233765483551
52131925576536
64327495647510
73126955706476
84224855857459
94523845984432
101323526080395
110122636128386
122421096292379
134121076385378
141019416418363
155218376507358
163018216691351
172018196738342
185318166878324
195418016948323
201417457058310
215116807193293
220216297286292
230315277329291
244015167495276
253514577594268
262514457687246
275613227790231
286212347819229
291512297968221
306311978008220
3161118881102219
325011258249215
336410878339211
3404107684101203
3565104085103187
362693286210184
373692487104171
387386988310167
39728658959162
406083090112153
41468039109152
427179592110150
43167889396149
44057649489141
45677329597136
467472096100136
47276359798129
487558698105129
498258399211120
5070573100410116

Thursday, October 10, 2013

NLCS Individual Game Odds


Vegas has some out and made the Dodgers a 55.6% favorite to win the NLCS over the St.Louis Cardinals. So what I've done is gone ahead and assigned individual game win probabilities to each game not necessarily based off of what my sim outputted, but more along the lines of fudging the odds of all seven games in attempt to make the 55.6% come out as the true chances of winning the series for the Dodgers. Below is what I came up with.

GameAway StarterHome StarterDodgers Win%
1Z.GreinkeJ.Kelly50%
2C.KershawM.Wacha59%
3A.WainwrightH.Ryu47%
4L.LynnR.Nolasco55%
5J.KellyZ.Greinke59%
6C.KershawM.Wacha59%
7H.RyuA.Wainwright38%

I took this set of game win probabilities and put it in a C program that played a 7 game series one million times, using a random number generator to determine game winners and losers and the odds of the Dodgers winning the series came out to approximately 55.6% of the time. You can argue that the odds for an individual game are a little off, but where you lean one game matchup for one team, you need to lean another matchup for the other team. It doesn't matter if I swap Greinke and Kershaw (Games 1/2, 5/6) in the games they pitch in, the odds still come out the same. Where it might matter is having Kershaw available to pitch out of the pen in Game #7. Either way, the Dodgers surely do not want this series to go to a seventh game.

Wednesday, October 09, 2013

Tigers vs Athletics - Simulation Results ALDS Game #5




Note: Vegas favors the Tigers, with a 50.4% win probability

                              Top 100 Most Likely Final Scores
RankTigersAthleticsOccurrencesRankTigersAthleticsOccurrences
1234785051075421
2124699552755267
3343571753475221
4213506754184650
5323473355284638
6132791156764490
7012776857574434
8432576958824302
9312511659834064
10242285760704026
11452256761814000
12422243962383956
13022185563083590
14102135664843547
15142081165293182
16031951866483170
17201892967853149
18411829368193113
19541633669783068
20531601970922835
21301573371802751
22251553172932720
23521534273912611
24351519974392607
25041435775582586
26151424976862549
27561252477092363
28511221178942206
29401110979682184
30051071380872130
31631027281491965
322610170822101951
33169911831101864
3436966984951860
35629664851021843
3664963086901809
37659223873101759
38468681881011746
39618467891031745
40507984900101552
4106759491591530
4217701792961507
43277004931041421
4467653994891350
45726524954101260
4673622096971240
47376075971001193
4874590098691191
49715778991111175
506057701001051149

Tuesday, October 08, 2013

Pirates vs Cardinals - Simulation Results NLDS Game #5



Note: Vegas gives the Cardinals a 59.92% chance of winning this game.

                                        Top 100 Most Likely Final Scores
RankPiratesCardinalsOccurrences RankPiratesCardinalsOccurrences
1125273 5119476
2234980 5272472
3013661 5338468
4343519 5429463
5133323 5573436
6213175 5671432
7022921 5774409
8322827 5809406
9242639 5960393
10032554 6075377
11142499 6157372
12312140 62110339
13452120 6348338
14102104 6476329
15432073 6539309
16041963 6658299
17251832 67010298
18421832 6882292
19151790 69210291
20201725 7083288
21351578 7170276
22411558 7284275
23051493 7349255
24301326 7481247
25161303 7578242
26521245 76310238
27531213 77211209
28361197 7885201
29261196 7980196
30561195 80011190
31541165 81111189
32061116 8292178
33511015 8359171
3440965 8491170
3517954 8586165
3646857 8693164
3707840 8794160
3827836 88311157
3963813 8968154
4062799 9087154
4137708 91410150
4218695 92212137
4364681 93112125
4465644 9469122
4508630 95012120
4650620 9695116
4761613 9796116
4847609 9889110
4928605 99411103
5067536 100312100

Red Sox vs Rays - ALDS Game #4 Simulation Results




                            Top 100 Most Likely Final Scores
RankRed SoxRaysOccurrencesRankRed SoxRaysOccurrences
12337225147686
23435405276677
31230635384671
43228775457655
54526415505648
64325955681616
74223465717603
82122895885566
92422655993514
103122156070500
111320396192495
125320076206481
135219566338481
145418566494464
154117996528441
163517406686439
171416206748437
185616176878425
192516086991409
206315487058399
215114887195362
226214487207353
230114037380342
246412867468337
252012817587337
260212337618336
2765121877102329
283012097839301
291512087929292
304611678096290
3136116581103284
326111548219272
3310113483104270
347210728449269
3503105385101236
367310498690230
3740103287310222
382610198859222
397497289105221
40679009097202
41718769169196
42048359208191
43508229389189
441680294112185
457579595210183
463776496113180
47277499779163
488373298106163
498270299110158
5060694100410156