Love him, hate him, or just don’t care about him, Barry Bonds is on the cusp of eclipsing baseball’s most cherished record, the title for most career home runs. Want to know when he’ll do it?
Using essentially the same system as the playoff odds report, we can model Bonds’ home run hitting on a game-by-game basis in order to get an estimate for just when #756 will carry over an outfield fence. All of this will assume that the chances remain relatively stable–if he deliberately avoids hitting home runs on the road (by, say, bunting against the shift), or if pitchers start walking him even more often to make sure they’re not the next Al Downing, then all bets are off.
In its simplest form, we need to know
- How likely is he to play in any given game?
- How many plate appearances will he get in the games he plays?
- How likely is he to hit a home run in each plate appearance?
Last year, Bonds played in 130 of his team’s 161 games; so far this year, he’s played in 31 of 34. The model is going to assume that he generally has a 90% chance of playing in any particular game, assuming he’s not hurt–we’ll get to that in a minute. However, given the stated preference for setting the record at home rather than on the road, as well as the ovation, reaction, and opprobrium he receives from the same split, we’re going to bias the stats a little bit towards home games; rather than a flat 90%, let set it at 95% at home and 85% on the road. We’ll also decree that he won’t play both ends of their scheduled doubleheader in Pittsburgh on August 13, if he’s still under the record.
Injuries, though, represent a real issue, one that has to be taken into consideration. Without them, there is a pretty much 100% chance that Bonds will break the record this year. I don’t think it’s nearly so clear that he’ll stay healthy–we’re talking about someone who missed virtually all of 2005, after all, who could do further damage to his knees at almost any time. To account for that, I built a 1% chance of injury into every game he plays, a percentage that is probably a little bit on the low side, given his history and status. You might expect that he’ll probably play more cautiously than usual to try and avoid injuries. Any such injury in my system forces him out until he recovers; the recovery chance starts out at modest 20% chance of returning, but each day he misses reduces the chance of returning the day after that; think of it as saying that every game missed indicates the injury was a little more serious than first thought. The way it is set up, an average injury will cost Bonds10 games–but it could also last the rest of the season.
Once we establish that he plays in a particular game, the rest is more straightforward. Between last year and so far this season, Bonds has averaged 3.79 PA/game, so I simply adapted his real distribution of PAs per game for use here. It is heavily weighted towards 3 or 4 per game, but can be anything between 1 and 6.
For his home run rate, we’ll lean on last year’s results pretty heavily, with a nod towards this year, and we’ll let that change as the year progresses. That means I’m going to combine his 2006 and 2007 performances and use the total to set his home run rate per PA. We’ll adjust that depending on what park he’s playing in, but won’t worry about the opposing pitchers–the variability even within one pitching staff is just too large.
If we didn’t allow any injuries in the model, then Bonds always reaches 756 this season. The distribution after a million runs looks like this (starting with games of May 11):
Earliest reach May 17 @ Houston
10% chance by June 3 @ Philadelphia
20% June 6 @ Arizona
30% June 9 Oakland
40% June 11 Toronto
50% June 15 @ Boston
60% June 17 @ Boston
70% June 20 @ Milwaukee
80% June 24 Yankees
90% June 30 Arizona
Latest August 29 Colorado
The basic numbers put the most likely time period for 756 in the first three weeks of June, when the Giants are playing 13 of 19 on the road; I’m expecting some sort of nagging injury to dog him through then, with an eye towards the nine-game homestand against the Yankees, Padres, and Diamondbacks that closes out June into July.
Making an explicit injury allowance makes for some dramatic changes at the back end; the longer it runs, the more likely an injury is going to affect the outcome.
Earliest reach still May 17 in Houston 10% chance by June 4, back one day 20% chance by June 7, back one day 30% chance by June 10, back one day 40% chance by June 13, back two days 50% chance by June 16, back one day 60% chance by June 20, back three days 70% chance by June 25, back five days 80% chance by July 3, back nine days 90% chance by August 9, back forty days
With an explicit injury provision, Bonds did not reach 756 home runs in 6.4% of the million seasons I ran, about one chance in 16, which gives those who hate him a meaningful rooting interest. Again, though, the peak likelihood corresponds to the six-game road trip to Boston and Milwaukee from June 15-20.
Actually, that’s only the peak cumulative likelihood, which is distorted because the tail is so much longer than the front. The single most likely day, with a 3.75% chance, falls on June 11 (at “only” a 36% cumulative chance), with a 3% chance or better every day from June 6th through the 19th. The two most likely series to see him reach the milestone are both at home, led by the Toronto series from June 11-13 and the Oakland series of June 8-10, with an 11.2 and 10.8% chance, respectively. The next four most likely series are all on the road–10.5% in Boston June 15-17, 9.1% in Arizona June 5-7, 9.0% in Milwaukee June 18-20, and 8.0% in Philadelphia from June 1-4. The next three most likely come after the Giants return home from Milwaukee–7.2% against the Yankees from June 22-24, then 5.55% against the Padres on the 25-27, then 4.1% against the Diamondbacks from June 29 through the first of July. The overall odds are slightly tilted towards it happening on the road.
The complete list from this morning’s run:
This day Cumulative
137 May 17 4 4 @HOU
138 May 18 18 22 @OAK
139 May 19 50 72
140 May 20 143 215
141 May 21 358 573 HOU
142 May 22 663 1236
143 May 23 1254 2490
145 May 25 2094 4584 COL
146 May 26 3244 7828
147 May 27 4920 12748
149 May 29 6962 19710 @NYM
150 May 30 9280 28990
151 May 31 12146 41136
152 Jun 1 15020 56156 @PHI
153 Jun 2 18669 74825
154 Jun 3 21378 96203
155 Jun 4 25015 121218
156 Jun 5 27813 149031 @ARI
157 Jun 6 30418 179449
158 Jun 7 32717 212166
159 Jun 8 34754 246920 OAK
160 Jun 9 35981 282901
161 Jun 10 36985 319886
162 Jun 11 37536 357422 TOR
163 Jun 12 37246 394668
164 Jun 13 36964 431632
166 Jun 15 35932 467564 @BOS
167 Jun 16 35107 502671
168 Jun 17 33547 536218
169 Jun 18 32030 568248 @MIL
170 Jun 19 30015 598263
171 Jun 20 28274 626537
173 Jun 22 26092 652629 NYY
174 Jun 23 24148 676777
175 Jun 24 22137 698914
176 Jun 25 20254 719168 SDP
177 Jun 26 18526 737694
178 Jun 27 16674 754368
180 Jun 29 15202 769570 ARI
181 Jun 30 13258 782828
182 Jul 1 12193 795021
184 Jul 3 10862 805883 @CIN
185 Jul 4 9707 815590
186 Jul 5 8583 824173
187 Jul 6 7749 831922 @STL
188 Jul 7 6846 838768
189 Jul 8 5961 844729
194 Jul 13 5441 850170 LAD
195 Jul 14 4751 854921
196 Jul 15 4325 859246
197 Jul 16 3784 863030 @CHC
198 Jul 17 3320 866350
199 Jul 18 2976 869326
200 Jul 19 2733 872059
201 Jul 20 2576 874635 @MIL
202 Jul 21 2325 876960
203 Jul 22 2033 878993
204 Jul 23 1900 880893 ATL
205 Jul 24 1825 882718
206 Jul 25 1757 884475
207 Jul 26 1518 885993
208 Jul 27 1444 887437 FLA
209 Jul 28 1348 888785
210 Jul 29 1286 890071
212 Jul 31 1219 891290 @LAD
213 Aug 1 1205 892495
214 Aug 2 1169 893664
215 Aug 3 1135 894799 @SD
216 Aug 4 1055 895854
217 Aug 5 1066 896920
218 Aug 6 996 897916 WAS
219 Aug 7 979 898895
220 Aug 8 962 899857
221 Aug 9 951 900808
222 Aug 10 946 901754 PIT
223 Aug 11 932 902686
224 Aug 12 920 903606
225 Aug 13 906 904512 @PIT (2)
226 Aug 14 926 905438 @ATL
227 Aug 15 882 906320
228 Aug 16 818 907138
229 Aug 17 913 908051 @FLA
230 Aug 18 827 908878
231 Aug 19 845 909723
232 Aug 20 849 910572
233 Aug 21 806 911378 CHC
234 Aug 22 800 912178
235 Aug 23 804 912982
236 Aug 24 829 913811 MIL
237 Aug 25 760 914571
238 Aug 26 816 915387
239 Aug 27 764 916151 COL
240 Aug 28 773 916924
241 Aug 29 753 917677
243 Aug 31 734 918411 @WAS
244 Sep 1 754 919165
245 Sep 2 760 919925
246 Sep 3 752 920677 @COL
247 Sep 4 762 921439
248 Sep 5 710 922149
250 Sep 7 728 922877 LAD
251 Sep 8 667 923544
252 Sep 9 693 924237
253 Sep 10 704 924941 ARI
254 Sep 11 722 925663
255 Sep 12 650 926313
257 Sep 14 674 926987 @SD
258 Sep 15 655 927642
259 Sep 16 698 928340
260 Sep 17 646 928986 @ARI
261 Sep 18 630 929616
262 Sep 19 633 930249
263 Sep 20 688 930937 CIN
264 Sep 21 642 931579
265 Sep 22 639 932218
266 Sep 23 617 932835
267 Sep 24 608 933443 SD
268 Sep 25 572 934015
269 Sep 26 574 934589
271 Sep 28 616 935205 @LAD
272 Sep 29 618 935823
273 Sep 30 566 936389
Not this year 63611 1000000
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