Engine Replacement Research

[RulerofRails]

When I looked up replacement age, I came up with this: viewtopic.php?p=35933#p35933

Maybe there are more details somewhere else, but I will comment about this to start. The increase I am seeing is far less, just a bit over half of the 10% increase per year mentioned.

Now I am assuming that the engine used in that example was from Lirio's loco pack which has a 16k initial maintenance, but it mentions a base price of 170k when from what I can see Lirio's number is 150k.

I tested for 23 years (last engine age: 22). The average increase in maintenance cost per year is 5.80% (corrected basic math error) over this time period. The nice thing is that the real test numbers agreed with a couple of samples I pulled up beforehand with some time-travel thanks to the 1.06 cheat code "wolverine@msu".

The suggested value of measuring initial maintenance cost relative to purchase price gives a value of (16/150) 10.7% on the raw numbers. If the real value of 18k for the first year is used we get (18/150) 12%. Because breakdown chance increases at the end of the year, I would have to assume that maintenance cost increases are applied once a year too, but I haven't proved this. I think the difference here is explained by the Expert level which definitely mentions maintenance cost as a way difficulty is increased. I haven't tested how the Expert level is applied over the values in succeding years yet.

Here's a table with some results:

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So my reading in practical terms, (ignoring reliability which is Good here) the optimum time for replacement of this engine is an age of 15*. This is always true as long as you play a further 5 years. I barely checked reliability, but an engine age of 20 gave a 10.6% breakdown chance, FWIW.

*EDIT: In simple terms this is the displayed age. When correcting the graph I changed the values in the graph to display 1st, 2nd, 3rd etc. years because I thought this is less confusing since maintenance is a cost OVER a particular year.

A basic side-test seems to indicate that the yearly maintenance increase comes at the turn of the year no matter if the engine was originally pruchased in January or December. So, there is an advantage to buying early in the year. You get a reliability advantage also.

[Gumboots]

I cant remember if I was using Lirio's pack back then or not. It may be default stats. However, the annual increase in maintenance cost on Expert level is definitely way more than 5.45%. I know because I've checked it umpteen times. It's close to 10%, but not exactly. Part of the "not exactly" will be due to each year being rounded off to the nearest $1k.

I have no idea what the annual increase is on lower difficulty levels as it's been ages since I looked at them. They may have an effect on breakdown chance over time as well. Would have to check it to find out.

Nevertheless, since Expert level is generally what we are interested in, and since we already know things will be easier on lower levels, I think we should test all this new stuff on Expert level. If it's easier and more reliable and cheaper on lower levels, that's how it's meant to be anyway. We don't want stuff breaking everywhere on Expert level though. That would mean we were wasting our time.

[Gumboots]

Come to think of it, annual percentage increase in maintenance cost may be related to reliability rating. That's something else to test. IIRC the increases I was seeing were for Average or Above Average. Can't remember for sure.

[RulerofRails]

I will run some more tests. I did discover a mistake in my percentage calculations. I took the percentage of the current year instead of the previous year. This increases the average over this period to 5.80%. Plan to test other engines as well, and will also check for reliability setting effects. Then I will edit the OP to fix this mistake in case I find some more info to add.

[Gumboots]

I just saw the additional info you edited into the OP. This part caught my eye:

I barely checked reliability, but an engine age of 20 gave a 10.6% breakdown chance, FWIW.

Assuming we're talking about a loco with no consist behind it (please confirm this), that tallies with what I've worked out for the same reliability rating on Expert level over the same period of time. So if your test loco was sans consist then I'd say it's confirmed that changes in game difficulty level do not affect reliability.

[RulerofRails]

So if your test loco was sans consist then I'd say it's confirmed that changes in game difficulty level do not affect reliability.

This figure was without consist at 100% oil, but it was made on the Expert level. I will state if I use a caboose in a test, I haven't used one yet.

I put on a test on the Medium difficulty level checking maintenance and reliability simultaneously on a parked Big Boy which had Lirio's stats except for a downgrade to Average reliability. The results: reliability was within 0.1% all through the 23 year test. The complete results for maintenance cost are below.

Medium Difficulty Setting:

Expert Difficulty:

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Using averages is a little deceptive because in the first couple of years there tends to be at least one 10%+ figure. The figure does drop off with time.

Another interesting thing I discovered is that there is a 20% increase in breakdown chance if the train has no water. Running without sand has no effect.

I also played with Lirio's Mikado with reliability down-graded to Atrocious over 10 years and saw no difference in the maintenance costs over that period. I didn't bother to run this long enough to make a full graph.

In these tests I saw no difference in maintenance cost or reliability (at the same weight) for a train that was working hard or sitting idle for many years in a station. To double check, I got a 20+ year old museum train out on some hauls. When compared to the second one that had been working hard all this time, reliability was exactly the same depending on load, oil gauge level and presence of oil and water. A train that has been run without oil even only once for a short time will suffer higher rates of cost and breakdown chance increase.

[Gumboots]

Ok, so come to think of it that approx. 10% annual maintenance cost increase may have been with Connies or something, which have a lower reliability rating. We should check a few more locos with different ratings. It'd be good to get the entire scale covered from Near Perfect down to Very Poor (the lowest that is actually used).

By the way, the figures we've been getting for reliability variation with age and weight tie in with what you got back when you tried the double furniture cars on a Red Devil. You reported 45% breakdown chance after 3 years. That would be about right for a 3 year old Red Devil with a double-weight freight consist and about 70% oil level, assuming no caboose. The drop back to 15% breakdown chance when you reverted to standard cars also fits.

Using averages is a little deceptive because in the first couple of years there tends to be at least one 10%+ figure. The figure does drop off with time.

Another interesting thing I discovered is that there is a 20% increase in breakdown chance if the train has no water. Running without sand has no effect.

Yep, I knew about those factors. I had noticed reliability was loosely tied to water level in some way but had never got around to quantifying it. Same with oil, except it happens faster with oil. I had quantified the oil effect, and that's 20% increase in breakdown chance for 50% oil level.

I also played with Lirio's Mikado with reliability down-graded to Atrocious over 10 years and saw no difference in the maintenance costs over that period. I didn't bother to run this long enough to make a full graph.

Cool. That's handy to know. I may have been wrong about the 10% annual increase then. I'll double check some saved games and see what I can turn up.

By the way, IMO there's no point testing locos that have an Average reliability rating for 23 years. They're screwed way before that anyway. Anyone who keeps them longer than 10 years is nuts. Even an Above Average is only good for 15 years at the most.

In these tests I saw no difference in maintenance cost or reliability (at the same weight) for a train that was working hard or sitting idle for many years in a station. To double check, I got a 20+ year old museum train out on some hauls. When compared to the second one that had been working hard all this time, reliability was exactly the same depending on load, oil gauge level and presence of oil and water. A train that has been run without oil even only once for a short time will suffer higher rates of cost and breakdown chance increase.

Good to know about the lack of variation due to workload. And yep, I can confirm that one about permanent damage to any train that runs out of oil even once it its life. I've seen that happen before.

[RulerofRails]

We should check a few more locos with different ratings. It'd be good to get the entire scale covered from Near Perfect down to Very Poor (the lowest that is actually used).

Working on it. Although I already tested for effect of the reliability scale, locos with a lower IMAC (such as 5k) may be more affected by rounding.

I had quantified the oil effect, and that's 20% increase in breakdown chance for 50% oil level.

I think you might have not remebered the right figure here. I am seeing 50% increase in breakdown chance at 50% oil level. I watched carefully while a train was filling from 13%. The figures are almost exaclty (within 0.5%) of taking the full (100%) oil level figure and then using the total decrease in oil level as a percentage multiplier on that figure.
For example: given 70.4% with full oil:
At 13% which means that 87% of oil has been used can be calculated as 70.4%*1.87=131.65%. Actual figure is 131.4%.
At 28% oil level, or 72% of oil used: 70.4%*1.72=121.08%. Actual figure is 121.1%
At 65% oil level, or 35% of oil used: 70.4%*1.35=95.04%. Actual figure is 94.4%

By the way, IMO there's no point testing locos that have an Average reliability rating for 23 years.

Agree, but because I was doing the test for engine maintenance mainly at that point, collecting more data wasn't difficult.

[Gumboots]

About the increase in breakdown chance with drop in oil level, what I was finding with the ubiquitous freighty Kriegsloks was they'd leave Rome with full oil and get down to Salerno, top up with water at Salerno, then get back to Rome with about 70% oil. I may have been able to skip the water stop at Salerno but whatever.

Anyway, they were leaving Rome with a full consist and a breakdown chance of around 24% with the 7 D freight and caboose. They'd get back to Rome with the same consist and roughly 70% oil and a breakdown chance around 30%. So on that basis, I figured that for those locos hauling that consist at that age, breakdown chance went up by 1% for every 5% reduction in oil level. Without a caboose it'd be 2% increase per 5% drop.

I think your formula for the multiplier is more accurate though, so will be cross checking with that.

I have a question about how you quantified the reduction in reliability with water level too. Was this done by carefully checking reliability with reduced water but 100% oil? That would be the only way to know.

Same question applies to oil level. Were the oil level results taken with 100% water?

[Gumboots]

Oh, while I think of it, here's a caveat for all my results to date. I have been running WP&P's custom cars (all of them) for ages. I started doing this simply because they looked much cooler than the default ones. I suspect this is the reason why anyone would start using them.

However, some of them do have different weights to default cars for the same era. Usually they will be heavier, to some extent. I should cross check all my consist weights carefully to account for this (haven't been doing that so far). There's a full list of weights and dates here.

Since we started getting into this detailed analysis I have thought of one obvious fault with the WP&P cars as they stand. In the early 20th century (roughly 1910 to 1950 IIRC) his express cars are the same weight as most freight cars. This is why I have been having trouble getting the Schools to be a good express hauler, without being able to haul freight like Superman on methedrine. With the way WP&P set car weights, if it's going to be a good express hauler in the 1930's it just has to also be a good freight hauler. This is obviously going to be a problem for game balance, so his cars need complete revision of their stats.

[RulerofRails]

I have a new idea that may explain the differences we have seen. I believe the caboose breakdown chance reduction is fudging your results. As far as I know, the effect of the Oil level is applied before the 50% reduction in OVERALL breakdown chance you get from the caboose. Whereas, the effects we are talking about are applied to the INITIAL not OVERALL values.

My test route runs out of water for the last 10% or so of the journey. I put the game on super slow and watched what happened to the breakdown bar at the moment water ran out. I then checked this against what I saw the moment a drop of water appeared in the bar when the train got to the service tower. Once there is a drop of water in the bar, the reliability stays the same as the bar fills up. It's only the effect of having NO water, level is not important, 5% is no different to 73%. The results were consitent. I checked on multiple runs, consist, no consist, different Oil levels, etc.. As always, check it out and see if you can see the same thing, otherwise I will examine it some more.

[Gumboots]

Fair point on the caboose factor. I will check things more thoroughly, with and without caboose. Personally I just don't run without a caboose unless the locomotive is bulletproof, simply because I hate breakdowns and prefer to avoid them as much as possible. I figure doubling the number of breakdowns is likely to cost as much, or more, in lost turnover as losing the last car off a consist (it's usually a low value car anyway).

Good to know that having any amount of water will be fine for reliability, and that there is no permanent penalty for running out. Also worth knowing about the temporary penalty for running out (which is quite a high penalty if you have to travel any distance like that).

[Gumboots]

Hey idea: if we assume that most people (poor deluded souls) are running inline sheds and towers everywhere, and if we further assume they will minimise the number of these because they are clever and saving money (see previous comment in brackets) then we can be pretty sure that their trains will spend a fair amount of time with oil levels as low as 40%.

Due to the random spacing of cities and inline facilities, I would not be at all surprised if their trains were frequently running as low as 20% oil. If you're just relying on the loco randomly being below 50% oil when it gets to a certain shed, it's easy to miss it if the oil just happens to be 51% and most people won't check this. They'll just plonk down a shed and forget about it.

So really we should decide what an acceptable level is for the breakdown bar (edit: my 2c is that anything over 30% is getting dodgey). From those two factors it would be easy to whip up a chart to show when locos of any particular reliability rating and oil level should be replaced. This would tie in with the optimum replacement years due to maintenance costs. Chart the lot, for a range of consists, reliability ratings, and oil levels. Once we have the basic stats and algorithms nailed down, this would be quite a simple proposition.

I'm not suggesting we cater to negligence. I'm just suggesting we could provide guidelines for people who haven't noticed this stuff.

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By the way, I will sometimes use inline sheds and towers myself, but if I do they are often scheduled just as maintenance spurs would be. If they are not scheduled (depends on specific scenario requirements) then I go overboard on the number and placing of them to ensure my locos always have some chance at a decent oil level. That's another reason I prefer spurs: it saves me money on facilities.

And even when I'm running stacks of trains, I don't get stacks of breakdowns. Taking those 10 to 15 year old Kriegsloks with 7 freight + caboose, my entire roster for that game (31 locos) was averaging less than one breakdown per year. Now that's not stacks of trains (it was just a convenient example) but it is a pretty low percentage of breakdowns for that consist and that locomotive at those ages.

Basically I would only expect to see a breakdown every couple of months even when running a very large roster. I like that.

[RulerofRails]

So I finished a new run with late 1800s locos including the Connie. All locos are Lirio's stats in this test. I wont post all the results up, but the average of year-on-year cost increase is sitting in the 5.75% to 6% range so far. I reckon you should try to run at least one test to check/confirm these results.

An odd one out from these tests is the Shay which has a "raw" initial annual maintenance cost of 10k (11k on Expert), against a purchase cost of 40k. Basically a real initial maintenance cost of 27.5% of purchase price. After 10 full years service, the total cost of the increases is 45k (year 9 is 36k). That's close enough that I would currently aim for a 10 year life on these engines. After 10 years the cost starts escalating quickly, and if these engines are used for 20 years you will pay 5x purchase price in extra maintenance costs, with two replacements (one at year 10 and another at year 20 if you are playing on) you save 3x the purchase price. The Fairlie is similar.

The earliest engine I tested was the Norris at 13 years lifespan (20% IAMC to PP ratio). I expect the other engines available in the earliest era to have similarly shorter lifespans. I don't think this matters because most players will likely replace these engines as soon as a better one comes along

The other locos tested with more reasonable maintenance costs seem to be pretty close to an optimum 15 year lifespan from my calculations (they fall fairly close to the ratio of IAMC being 10% of purchase price. Keep in mind that Lirio's changes have made improvements to lifetime for some engines. Ironically, doubling the price of the American 4-4-0 (now called the Standard) has made the cost effective life of this engine longer. It was 10 years and now it becomes 14. Here's a graph of the earlier Consolidation. I am assuming this is the one you meant.

It's all to do with the percentage you figured of Initial Annual Maintenance Cost in Engine Purchase Price. My conclusion to this is that the 10% value is pretty safe for 15 year lifespan engines. If we want longer lasting engines, we need to think about lowering this value. I have no problem with having a couple of specialized engines outside this range, especially the earliest and mountain ones.

There seems to be less effect from reducing the value. 27% for the Shay and Fairlie giving an optimum lifespan of 10 years, 20% for the Norris giving 13. The lowest one I tested was 7.2% which gave an optimum lifespan of 17 years. To get 20 year lifespans would probably need around 5% value. One way to conceptualize the possibilities is to think of each value in "Costs due to increases" column as the price a loco would need to have to be to have that lifespan.

Personally, 15 years is a fine lifespan. Counting that the cost of a year 15 replacement isn't earned back until year 20, which is perfect for most games, I don't see a lot to improve on this front. Maybe some testing on how maintenance increasing events are applied is in order at some point.

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Yeah, we should try to nail down a theoretical maximum. Maybe we should put most of that in the reliability thread or even start a new one. I want to look a little closer at your research about the effect of consist weight. 30% with caboose and 60% without, if that's what you mean, seems a reasonable high side to me.

[Gumboots]

Aha. I think I know what's going on. I tend to replace Connies, or any loco with a similar rating, pretty early. I work them hard, and commonly replace them at 7 or 8 years. Taking the first first 7 years of your chart and averaging those gives about 8% increase per annum. Now that I think about it, I had noticed it wasn't exactly 10%, and could have actually been 9%, but put that down to rounding errors so just called it 10% for a handy ballpark reference.

So I'm happy to take your figures on this, but I'm thinking that it may still make more sense to average the increases over a shorter period that closely matches the expected service life from a reliability perspective. So for Connies I'd personally be using an 8% figure for annual maintenance cost increase. I don't think a 23 year average is relevant until the reliability rating is at least Good, at a minimum, and preferably Very Good.

The ultimate example in the other direction is the Firefly. Given its Very Poor rating, I commonly chuck them out and replace them after only three years service. If I do that they're pretty good. If I try to keep them longer they inevitably drive me bonkers with breakdowns. So for a Firefly you might as well just average over the first three years. This means replacement due to maintenance cost isn't the issue anyway, as reliability always gets there first. It makes Fireflies horrendously expensive to run, so I only ever use them on a few premium express routes.

Anyway, my old calculations with an assumed 10% annual increase gave roughly 10 years economic life for a 10% IAMC. IIRC 15 years would have required about 6% IAMC, so you getting 15 years life with an IAMC of 10% and an actual annual increase of 6% makes sense. IIRC I also figured out that getting a 20 year economic life with a 10% annual increase would require IAMC of around 4%, which ties in pretty well with your updated calculation of 6% IAMC and 6% annual increase. So your figures seem right to me, even without me testing them.

I'm happy to aim for 15 year replacements, if doing it purely on the basis of maintenance cost.

And yes, I meant breakdown bar at 30% with caboose or 60% without.

[Gumboots]

Hey just as an idea, if revamping loco stats we could set IAMC to a level based on the reliability of the loco, such that really crappy ones rapidly become very expensive to run anyway. This sort of makes sense to me.

The breakdown chance curve is a basic parabola with an offset origin. If we take 10% IAMC as giving us around the desired average economic life of 15 years-ish, then we'd want IAMC for an Above Average reliability rating to be somewhere around (7/3)(initial breakdown chance) + 3. Ok, so let's just use (7/3)(initial breakdown chance) + 3 as a guideline for a reasonable IAMC for an average locomotive.

That would give these guidelines:

Very Poor : 23.1%
Poor: 19.1%
Below Average: 15.6%
Average: 12.8%
Above Average: 10.0%
Good: 7.4%
Very Good: 6.0%
Outstanding: 4.9% (based on y=x^2 curve)
Near Perfect: 3.7%

This would make sense with Fireflies. Their best replacement year on a maintenance cost basis would be somewhere around Year 5 or 6, by which time they are totally cactus anyway. For an American 4-4-0 (PopTop version) the IAMC would be about where it always was, which works for a lifespan of around 9 years. This fits with how long they are useful from a reliability perspective. OTOH, if only considering maintenance cost you could keep a Kreigslok for how long they will last before crashing and burning, which is about 15 years-ish. For a loco with a Good rating, which will usually last 20 years anyway, the IMAC is still about right. For the really high ratings the IAMC is lower, but still high enough so they're not effectively free maintenance.

So it's all looking pretty good as far as I can tell. Then we could just adjust purchase price so it plays well for game balance.

[Gumboots]

Hey I just ran a test with a Connie. PopTop stats, not Lirio's, and Expert difficulty level. It turns out that I only have Lirio stats on 1.06, and my 1.05 is still on PopTop stats.

Maintenance costs:

10k (listed as 9k but was actually 10k)
11k
12k
12k
13k
14k
15k
16k
17k
18k
19k
21k
22k
23k
24k
25k
27k
28k
29k
31k (20th year)

So that's an average of just over 6% increase per year. That tallies with your results. OTOH I worked out the best replacement year for this one, which has IAMC of 8.33%, and it came out at the tenth year. At the tenth year, buying another Connie and running it for another ten years costs the same as keeping the original Connie for 20 years, but obviously buying a second one at ten years means better reliability over the entire 20 years.

Edit: To break the figures down, Connie #1 costs me $120k to buy. Maintenance on Connie #1 for the first ten years adds up to $138k. So that's $258k for Connie #1 and maintenance together, for the first ten years.

Maintenance for Connie #1 for the entire twenty years adds up to $387k, plus the obvious $120k I spent to buy it, so that's a total of $507k if I keep it twenty years.

OTOH, if I retire Connie #1 at ten years it will have cost me that $258k I mentioned earlier, so if I replace Connie #1 with Connie #2 then Connie #2 will only cost me another $258k (total of purchase price + ten years maintenance). That gives a total of $516k for two Connies over twenty years, which is so close to $507k that IMO you'd be bonkers to not go for it and get much better reliability.

Anyway, what this means is that if we want to optimise economic life at around the 15 year mark, then IAMC will have to be a fair bit lower than 8.33% of purchase price. It'd have to be somewhere around 6% at a guess.

[Gumboots]

Another costing, on the Kriegslok this time. Post-1960 era, Expert difficulty, PopTop stats. IAMC is listed as $14k, but was actually $15k. That's exactly 15% of purchase price. Years went like this:

15k
17k
18k
19k
21k
22k
24k
25k
27k
28k
30k
32k
34k
36k
37k
39k
41k
43k
46k
48k (20th year)

Optimum replacement year at is Year 8. IOW, at the start of the year that says they are 8 years old, and at the end of the year that says they are 7 years old (which is really 8 because RT3 thinks the first year is 0).

Anyway, lay down $100k for one war surplus German choofer. Maintenance costs for the first 8 years add up to $161k. Total cost for choofer and 8 years' maintenance = $261k. Maintenance for the next 8 years, if you keep said choofer, adds up to $263k. This is on top of the $161k for the first 8 years. IOW, total for Choofer #1 over a 16 year span would be $424k.

That's enough to buy another choofer and pay its maintenance costs for the first eight years of its life. Obvious thing to do is retire the first choofer as soon as it has its eighth birthday and get yourself a new one. No brainer. Which has me wondering why I didn't think of this before, instead of keeping them until they were 15 years old and all rattly.

Ok, so Connie at 7.5% IAMC has optimum replacement time of year 10. Kriegslok at 15% IAMC has optimum replacement time of Year 8. Not a lot of difference in years for a doubling of IMAC. Pretty obvious from this that a 15 year replacement time is going to require a really low IAMC. We could do that, and compensate with fuel consumption if we want to.

[Gumboots]

Ok, so I did the Schools as well. That has a listed IAMC of $8k in the early beta version, but when run in the game on Expert level it gets charged as $10k for the first year. Purchase price is $160k, so the in-game IAMC is 6.25% of that. This sounds low, but even this level only extends optimum economic life to 12 years. Figures follow.

10k (Year 1)
10k (yup, same as Year 1)
11k
12k
13k
14k
14k
15k
16k
17k
18k
19k (Year 12)
20k
21k
22k
23k
24k
25k
26k
27k
29k
30k
31k
32k
34k (Year 24)
35k
37k
38k
40k
41k
43k

Didn't test past the 30th year. Anyway, purchase price = $160k. Maintenance for first 12 years = $169k. Total = $329k.
If kept for another 12 years, maintenance for the whole 24 years is $491K, plus the $160k purchase price = $651k.

If you retire the first loco at 12 years instead, you pay another $329k for the second 12 year period. Total = $658k.
Again, same cost and better reliability if you take the second option. Another no-brainer.

There aren't many data points yet, but I whipped up a rough graph with what looked like reasonable curve fitting.

Edit: Oh I just noticed I borked this graph. I used 7.5% IAMC for the Connie. That's what is listed in the stats, but the extra $1k charged during the game makes it into 8.33% IAMC. That'll change the curve somewhat. I'll get some more data points and make another graph.

Borked graph removed. See next post.

[RulerofRails]

My optimum times were discounting reliability completely. I can see that your calculation for reliability is to replace engines as soon as economics allows it. I guess I took a different angle. I fixed another bug in my graph that was due to me using auto-fill on my spreadsheet incorrectly. The results are now a little higher. Because this topic fascinates me I decided to try to show it from a slightly different angle. You did well to pick the 8 year time out for the Kreigslok. According to my figures that the first year that it's within 5% of mimimum as hopefully can be seen from the graph I made thanks to your data.

I decided to upload the spreadsheet I made. Hopefully I got all the bugs out. It includes all the data on maintenance I have gathered as well as what you posted in a couple of posts here. To use it just copy in a set of data and then update the engine price and everything else should be automated.

I also worked out the increase in maintenance between an 8 and an 11 year old loco to be 8.09% at Above Average without caboose as D-era carriages. It's hard to put a price on reliability. Your strategy is good for avoiding as many breakdowns as possible while not being exorbitant. If reliability is a concern it's definitely the way to go. With the better engines there is no point IMO.